Nope
Sea
ioe Prams dye - pendent ied fir PAAR AT Ro A tp eis Ae i
sy “Ne , ’ ry
ie cent ton? vata
Sates | rare
‘ m a Parone ae!
tonsy ae Paver enya ; fai 2
6 HR AN et Lie : LM Panne pe or oes
nes Rye en nary! ae i 7 aba Md
BROAN alr
vf imi ‘ D7, te CN Pee ee a Oost i: yo te : eeoemee
i a NBT sa pom tasain vio Ab sient Ain 4%: ; ah Paes Aan - Ae OPE Beate
fh Ae Sea fie He
. Pek Oe Repel
Eee 4 elf hate | quinter>
¥ 5 atietly
istit ee
<PrHahee Hoagie ay iW hy
PPP citaP rl oD
OH Gtk AR nai eet ee e
Shida mdasad papa pee ea
a Petrsiok
*.
* Nesettintete Aha Riv tye ft
At
at = Pha
THE ~O5
LONDON, EDINBURGH, anp DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
CONDUCTED BY
SIR ROBERT KANE, LL.D. F.R.S. M.R.I.A. F.C.S.
SIR WILLIAM THOMSON, Kynr. LL.D. F.R.S. &e.
AND
WILLIAM FRANCIS, Pu.D. F.L.S. F.R.A.S. F.C:S.
<
‘Nec aranearum sane textus ideo melior quia ex se fila gignunt, nec noster
vilior quia ex alienis libamus ut apes.” Just. Lips. Polit. lib. i. cap. 1. Not.
LONDON: . ee
TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET.
SOLD BY LONGMANS, GREEN, READER, AND DYER; KENT AND CO.; SIMPKIN, MARSHALL
AND CO.; AND WHITTAKER AND CO.;—-AND BY ADAM AND CHARLES BLACK,
AND THOMAS CLARK, EDINBURGH ; SMITH AND SON, GLASGOW ——
HODGES, FOSTER, AND CO., DUBLIN ;—-PUTNAM, NEW
YORK ;—AND ASHER AND CO., BERLIN,
“Meditationis est persecrutari occulta; contemplationis est admirari
perspicua..... Admiratio generat queestionem, questio investigationem,
investigatio inventionem.”—Hugo de S. Victore.
—‘“Cur spirent venti, cur terra dehiscat,
Cur mare turgescat, pelago cur tantus amaror,
Cur caput obscura Phoebus ferrugine condat,
Quid toties diros cogat flagrare cometas ;
Quid pariat nubes, veniant cur fulmina ccelo,
Quo micet igne Iris, superos quis conciat orbes
Tam vario motu.”
J. B. Pinelli ad Mazonium.
e
ALERE FLAMMAM,
CONTENTS OF VOL. VI.
(FIFTH SERIES).
NUMBER XXXIV.—JULY 1878.
Wes. Croll on the Origin of Nebule ..:. 2)... ee
Mr. T. Bayley on the Analysis of “Alloys containing Copper,
Miner elt rae cerns shes Wei ue cee:
Dr. W. Ramsay on Picoline and its Derivatives ...........
Frederick Guthrie on Salt Solutions and Attached Water
Prof. Hughes on the Physical Action of the Microphone ....
Mr. R. Meldola on a Cause for the Appearance of Bright
Peco neo eolar Spectrmm 0)... wae ee eee see
Dr. E. J. Mills’s Researches in Thermometry..............
Mr. R. H. M. Bosanquet on the Relation between the Notes
SeeeOpenaud stopped Pipes:.. 22... eg eee
Notices respecting New Books :—
The Rey. R. M. Ferrers’s Elementary Tueatise on Sphe-
rical Harmonics and Subjects connected with them
Mr. H. F. Blanford’s First and Second Parts of the Indian
Meteorologist’s Vade Mecum ; and Tables for the Re-
duction of Meteorological Observations in India
Proceedings of the Geological Society :—
. Mr. W. A. E. Ussher on the Chronological Value of the
Triassic Strata of the South-western Counties ......
Mr. G. Maw on an Unconformable Break at the ESE of
the Cambrian Rocks near Llanberis............0...
Mr. J. A. Phillips on the so-called Greenstones of Contra
anrembiasver Cornwall tt ete Mies oe ye Se ee a
Mr. N. H. Winchell on the Recession of the Falls of St.
MAROC tA thio te ae cpa gee c tk ee aT Te
Capt. H. W. Feilden and Mr. C. BK. De Rance on the
Geological results of the Polar Expedition under
Adumiral Sir George: Nares?.. 2.0 Vee nee ode
66
67
iv CONTENTS OF VOL. VI.—FIFTH SERIES.
Ammonio-argentic lodide, by M. Carey Lea ........--++-- i 3
On the Production of Plateau’s Film- systems, by A. Terquem. a)
On the Magnetic Rotation of the Plane of Polarization of Light
under the Influence of the Earth, by Henri Becquerel ...- 76
On the Crystallization of Silica in the Dry Way, by P. Haute- —
Pomalle fe SN 78
Outlines of the Actinic Theory of Heat, by Prof. C. Puschl.. 79
NUMBER XXXV.—AUGUST.
Colonel A. R. Clarke on the Figure of the Harth .......... 81
Mr. W: Siemens.on Telephony: “is 3... . 2)... 3 eee 93
Frederick Guthrie on Salt Solutions and Attached Water.... 105
Mr. W. J. Millar on the Transmission of Vocal and other
Sounds by Wires ole. a Cilcek ode 115
Mr. D. J. Blaikley on Brass Wind Instruments as Resonators.
A Plage Te) re snk vara dee geet at eda 119
Prof. P. E. Chase on the Nebular Hypothesis.—IX. Radiation
amd HOtatiOn vo. is 6s sek © bitkeh te seseilesea eee 128
Prof. W. E. Ayrton on the Electrical Properties of Bees’-wax
and Lead Chloride. (Plate IV.).: 7... 4.6.23. eee 132
Mr. J. Brown on the Theory of Voltaic Action ............ 142
Notices respecting New Books :—
Prof. P. Smyth’s Astronomical Observations made at the
Royal Observatory, Edinburgh, Vol. XIV., for 1870-77. 145
Proceedings of the Geological Society :—
Dr. J. Geikie on the Glacial Phenomena of the Long
Island, or Outer Hebrides> a... 440040 see 146
Dr. J. Croll on Cataclysmic Theories of Geological Climate 148
Mr. T. F. Jamieson on the Distribution of Ice during the
Glacial. Period 5 oo. fhe ee so 149
Prof. T. G. Bonney on the Serpentine and associated
Igneous Rocks of the Ayrshire Coast.............. (149
Dr. H. Hicks on the Metamorphic and overlymg Rocks
in the neighbourhood of Loch Maree, Ross-shire .... 150
Mr. W.A. E. Ussher on the Triassic Rocks of Normandy _
and ther Environments; ..../. 0.) 9. .:20)4eye ee 152
Dr. C. P. Sheibner on Foyaite, an Eleolitic Syenite occur-
ring in Portugal °. 2... - 2.2%. ilies ah) ae - 153
Photography at the Least-refrangible End of the Solar se
trum, by Capt. Abney, ht. H.,-FRsS:. 127) see iest a0 eee 154
On the Friction of Vapours, by Drs.J..Paluy:.23 295: 225 jee 157
On the Depolarization of the Electrodes by the Solutions, by
Mo dappmann....5.. 5 35:5 28 Fn eer eae 159
CONTENTS OF VOL. VI.—FIFTH SERIES.
NUMBER XXXVI.—SEPTEMBER.
Mr. J. N. Lockyer on Recent Researches in Solar Chemistry
Mr. O. Heaviside on the Resistance of Telegraphic Electro-
“LI ETL ETS 0 cc CARS ies Pelee eer eee mE OME gn eae ee See CD MO
Mr. J. E. H. Gordon on the Effect of Variation of Pressure on
the Length of Disruptive Discharge in Air. (Plate III.) ..
M. K. Zoppritz on Hydrodynamic Problems in reference to
semineonyot Ocean Currents... . 2... 6.4.3 es nye
Mr. R. Sabine on Motions produced by Dilute Acids on some
PReeER TPE OUT EACES 0. co. Sep bk BE Sooo eta okgh B85
Mr. J. Ennis on the Origin of the Power which causes the
PeEMepePeMAbLONS.. 2.20. 5. 8s bees ace OAS gpg keh eens
M. V. Dvorak on Acoustic Repulsion. With a Note by Prof.
ReeM NT el ata) «py nian Lh leh Mas euay sy Ste ee ae.
Proceedings of the Geological Society :—
Mr. C. Callaway on the Quartzites of Shropshire ......
Peon Erestwich on Artesian Wells «......50.50-4-
On some Problems of the Mechanical Theory of Heat, by Prof.
MMMM ATINATATE i500 215 5) fe. Sey co Veil shel v's on, he ee al ose
On the Relation of the Work performed by Diffusion to the
Second Proposition of the Mechanical Theory of Heat, by
(Po: ie LCST Ai Ba i ema uae are eer ery ba? ee
On Mosandrum, a New Element, by J. Lawrence Smith ....
NUMBER XXXVII.—OCTOBER.
The Rev. J. F. Blake on the Measurement of the Curves
formed by Cephalopods and other Mollusks. (Plate LV.) ..
Prof. H. Hennessy on the Limits of Hypotheses regarding the
Properties of the Matter composing the Interior of the Earth
Mr. A. M. Worthington on the Blue Colour of the Sky
Lord Rayleigh on Acoustic Repulsion....................
Prof. S. P. Thompson on certain Phenomena accompanying
2 LOTS eo UDG ao ea
Dr. R. 8. Ball on the principal Screws of Inertia of a Free or
Pomtapoaicentucid Body.) ti.) ..' 81 Cees te ere oe
Prof. W. C. Unwin on the Discharge of Water from Orifices
mere ettG “Peniperabules:. 2002 ak ehe a i~ Woes 2 wig ble dG tenes
‘Messrs. J. A. Wanklyn and W.J. Cooper on the Action of
Alkaline Solution of Permanganate of Potash on certain
Rees a alse dal sell eel Le Sp. aie A fee i.
Prof. E. Edlund’s Researches on Unipolar Induction, Atmo-
spheric Electricity, and the Aurora Borealis. (Plate VIII.)
Vv
Page
161
Wag
185
192
rally
216
225
233
234
236
237
238
241
263
207
270
272
274
281
288
289
vl CONTENTS OF VOL. VI.—FIFITH SERIES.
Page
Notices respecting New Books :—
Prof. W. K. Clifford’s Elements of Dynamic; an Introduc-
tion to the Study of Motion and Rest in Solid and
Piutd Bodies . . 3. bo. 5 Sie Si ghey ie a 306
Mr. k, A. Proctor on the Moon, her Motions, Aspect,
Scenery, and Physical Condition...... yee ee 309
Proceedings of the Geological Society :—
Mr. C. Moore on the Paleontology and some of the Phy-
sical Conditions of the Meux’s-Well Deposits ........ 310
Dr. A. Wichmann’s Microscopical Study of some Huro-
nian Clay-slates 0. ce a)... ee 311
Mr. T. M. Reade on a Section through Glazebrook
Moss, Lancashire: oi oot. 2 eee 312
Mr. C. B. Brown on the Tertiary Deposits on the Solimées
and Javary Rivers;im Brazil: . > $7.2 6. eee 312
Mr. J. C. Ward on the Physical History of the English
Lake-district, with Notes on the possible Subdivision
ot the Skiddaw Slates «2... 4°). ee 313
Mr. F. Ruddy on the Upper Part of the Bala Beds and
Base of Siluman-im North Wales > 9.5)... eee 313
A Spectrometric Study of some Sources of Light, by A. Crova. 314
On the Excitation of Electricity by Pressure and Friction, by
HeWritsch’ so eae Oe 316
On the Solar Eclipse of July 29th, 1878, by Professor Henry
Draper, MDs. She hee oe eae 318
On Watson’s Intra-Mercurial Planet, by Pliny Harle Chase.. 320
NUMBER XXX VIII.—NOVEMBER.
Mr. T. Gray on the Experimental Determination of Mag-
netic Moments in Absolute Measure. (Plate V.) ........ 321
Mr. J. W. L. Glaisher on Multiplication by a Table of Single
Bintry nO er ne ea GEG SEER, BR Ee eee - 331
Prof. 8. P. Thompson on Magnetic Figures illustrating Elec-
trodynamic Relations. (Plates VI. & VIL.).............% 348
Prof. J. Purser on the Applicability of Lagrange’s Equations
in certam Cases of Fluid-Motion. i. 07% 3. 2.0 ee 354
Prof. E. Edlund’s Researches on Unipolar Induction, Atmo-
spheric Electricity, and the Aurora Borealis ............ 360
Mr. J. Hood on the Laws of Chemical Change.—Part I. .... 371
Prof. 8S. P. Thompson on the Phenomena of Binaural Audi-
tion. —seart Us ee as en's este 383
Notices respecting New Books :—
Messrs. P.G. Tait and the late W. J. Steele’s Treatise
on Dynamics of a Particle, with numerous Examples... 391
A Consideration regarding the Proper Motion of the Sun in
Space, by 8. Tolver ‘Prestom avn. Oo. Gn ene ee, oe
CONTENTS OF VOL. VI. FIFTH SERIES. Vil
Page
On the Dissociation of the Oxides of the Platinum Group, by
_H. Sainte-Claire Deville and H. Debray................ 394
On a Universal Law respecting the Dilatation of Bodies, by
MM fe) 5 srt ne ta a eps op siage yeh say nes ae + ae 397
On Diffusion as a Means of converting Normal-T’emperature
Mest imto Work, by S. Tolver Preston ...+...2. 2. 4..-- 400
NUMBER XXXIX.—DECEMBER.
Mr. G. J. Stoney on the Mechanical Theory of Crookes’s (or
eeERte aioe) SLPS In GaseS .. 2. 5... cee ee ne ap te tae 401
Prof. E. Edlund’s Researches on Unipolar Induction, Atmo-
spheric Electricity, and the Aurora Borealis
Mr. 0. Heaviside on a Test for Telegraph Lines ......... 436
Prof. W. C. Rontgen on Electrical Discharges in Insulators.. 438
Prof. P. E. Chase on the Nebular Hypothesis.—X. Predictions 448
Sir J. Conroy on the Light reflected by Potassium Permanga-
ee Eo ec Pa Oh ae weary ge de ward tie gle dees 454
Mr. A. 8. Davis on a possible Cause of the Formation of
| PLL EHS” "LUA TIIS 2 A See marc 459
Notices respecting New Books :-—
Baron Rayleigh on the Theory of Sound........ AN 462
A few Magnetic Elements for Northern India, by R. S.
OSB: 0 ctl eRe lel Stee i eal eee carer interne or cou a 464
On Molecular Attraction in its Relations with the Tempera-
merermbonies. by Mo Lévy... be ee cee 466
Dr. T. A. Edison on the Sonorous Voltameter ............ 468
PLATES.
I. Hlustrative of Mr. D. J. Blaikley’s Paper on Brass Wind Instru-
ments as Resonators.
Ii. Hlustrative of Professor Ayrton’s Paper on the Electrical Proper-
ties of Bee’s-wax and Lead Chloride.
III. Illustrative of Mr,.J. E. H. Gordon’s Paper on the Effect of Varia-
tion of Pressure on the Length of Disruptive Discharge in Air.
IV. Illustrative of the Rey. J. F. Blake’s Paper on the Measurement of
the Curves formed by Cephalopods and other Mollusks.
V. Illustrative of Mr. T. Gray's Paper on the Experimental Determi-
nation of Magnetic Moments in Absolute Measure.
VL, VII. Illustrative of Professor S. P. Thompson’s Paper on Mag-
netic Figures illustrating Electrodynamic Relations.
VUI. Illustrative of Prof. K, Ndlund’s Paper on Unipolar Induction,
Atmospheric Electricity, and the Aurora Borealis,
ERRATA,
y
b°
is :
Page 89, line 3 from bottom, for aa dx + — Fs read ei
a
— 90, — 13, for rP=cy” read r= Cy"?
THE
LONDON, EDINBURGH, axp DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
eS
[FIFTH SERIES.]
SUG Vo NSTS,
I. On the Origin of Nebula.
By James Croui, LLD., F.RS.*
ae object of the present communication is to examine
the bearings of the modern science of energy on the
question of the origin of nebulz, and in particular to con-
sider the physical cause cf the dispersion of matter into stellar
space in the nebulous form. In doing so I have studiously
avoided the introduction of mere hypotheses and principles not
generally admitted by physicists. These remarks may be
necessary, as the title of the paper might otherwise lead to the
belief that it is on a speculative subject lying outside the
province of the physicist.
The question of the origin of nebule is simplified by the
theory, now generally received, that stars are suns like our
own, and that nebule are in all probability stars in process
of formation. The problem will therefore be most readily
attacked by considering, first, the origin of our sun, as this
orb, being the one most accessible to us, is that with which we
are best acquainted.
By the origin, of the sun I do not, of course, mean the origin
of the matter constituting the sun—this being an inquiry with
which the physicist has nothing whatever to do—but simply
its origin as a sun, 7. €. as a source of light and heat. Our
first question must therefore be, What is the origin of the
sun’s heat? From what source did he derive that enormous
amount of energy which in the form of heat he has been dis-
* Communicated by the Author.
Phil, Mag. 8. 5. Vol. 6. No. 34. July 1878. B
2 Dr. J. Croll on the Origin of Nebula.
sipating into space during past ages? Difficult as the ques-
tion at first sight appears to be, it is yet simplified and brought
within very narrow limits when we remember that there are
only two conceivable sources. The sun must have derived his
energy either from Gravitation, or from that other source to
which I directed attention several years ago*, Motion in Space.
All other sources of energy put together could not have sup-
plied our luminary with one thousandth part of that which he has
possessed. We are therefore compelled to attribute the sun’s
heat to one or other of these two, or to give up the whole in-
quiry as utterly hopeless. The important difference between
the two is that the store of energy derivable from Gravitation
could not possibly have exceeded 20 to 30 million years’ sup-
ply of heat at the present rate of radiation ; whereas the store
derivable from Motion in Space, depending on the rate of that
motion, may conceivably have amounted to any assignable
quantity. Thus a mass equal to that of the sun, moving with
a velocity of 476 miles per second, possesses in virtue of that
motion energy sufficient, if converted into heat, to cover the
present rate of the sun’s radiation for 50 million years. Twice
that velocity would give 200 million years’ heat; four times
that velocity would give 800 million years’ heat, and so on
without limit.
It is, however, not enough that we should have in the form
of motion in space energy sufficient. We must have a means
of converting this motion into heat—of converting motion of
translation into molecular motion. To understand how this
can be effected, we simply require the conception of Collision.
Two bodies moving towards each other will have their motion
of translation converted into molecular motion (heat) by their
encounter.
To which of these two causes must we attribute the Sun’s
heat? It is certain that gravitation must have been a cause ;
and if we adopt the nebular hypothesis of the origin of our
solar system, then from 20 to 30 million years’ heat may thus
be accounted for. But we know from geological evidence that
the sun has been dissipating his light and heat at about the
present rate for a much longer period. In a paper published
in the ‘ Quarterly Journal of Science’ for July 1877, I have
discussed the geological evidence for the age of the earth at
considerable length, and have pointed out that the time which
has elapsed since life began on the globe cannot have been less
than 60 million years. This estimate is based upon a rough
estimate of the thickness of rock which has been removed by
subaerial denudation since the earliest epoch of which geolo-
* Phil. Mag. May 1868,
Dr. J. Croll on the Origin of Nebula. 3
gists take cognizance. Measuring the rate of the subaerial
denudation by a method which I pointed out several years ago”,
we are able to determine roughly the time required for the
removal of the rock. But the 60 million years thus obtained,
be it observed, are only the inferior limit. We know that a
certain amount of rock has been removed; but how much more
may have been carried away we cannot tell. Consequently,
although we have good grounds for believing that 60 million
years have elapsed since life began on the globe, yet the lapse
of time may really have been very much longer. We are jus-
tified, therefore, in concluding that our globe has been receiy-
ing from the sun for the past 60 million years an amount of
light and heat daily not very sensibly less than at present.
This shows that gravitation alone will not explain the origin
of the sun’s heat, and that a far more effective cause must be
found. Now the only other conceivable cause exceeding that
of gravity is, of course, motion in space.
If the gravitation theory fails to explain the origin of the
sun, it fails yet more decidedly to account for the nebule. In
fact it does not attempt any explanation of the origin of the
latter ; for it begins by assuming their existence, and not only
so, but that they are in process of condensation. This must be
the case, because the theory in question assumes that the par-
ticles of a nebulous mass have, in virtue of gravity, a mutual
tendency to approach one another; and it cannot tell us how
this tendency could exist without producing its effect. The
advocates of the theory are not at liberty to call in the aid of
heat in order to explain why the particles are not mutally
approaching ; because it is this mutual approach which, ac-
cording to the theory, produces the heat, and of course with-
out such approach no heat could be generated. A nebulous
mass with a tendency to condensation could not have existed
from eternity as such; but what the previous condition of a
nebula was, and how it came to assume its present state, the
gravitation theory cannot say. It begins with a star or sun
in process of formation, but does not help us to understand
how the process of formation commenced.
It is quite otherwise, however, with the other theory. This
latter does not, like the former, begin by assuming the exist-
ence of a nebulous mass; on the contrary, it goes back to the
very commencement of physical inquiry, to the very point
where physical investigation takes its rise, and beyond which
we cannot penetrate. The only assumption it makes is that
of the existence of matter and motion—if indeed this can be
called an assumption. How matter and motion began to be,
* Phil. Mag. May 1868, and February 1867.
B 2
4 Dr. J. Oroll on the Origin of Nebulee.
whether they were eternal or were created, are questions wholly
beyond the domain of the physicist. The theory takes for a
fact the existence of stellar masses in a state of motion ; and its
advocate is not required, as a physicist, to account for the ex-
istence either of those masses or of their motions. Neither is
it necessary for him to advance any hypothesis to show how
the masses came into collision; for unless we are to assume
that all stellar masses are moving in one direction and with
uniform velocity (a supposition contrary to known facts), then
collisions must occasionally take place. The chances are that
stellar masses are of all sizes, moving at random in all direc-
tions and with all velocities. We have here therefore, without
any hypothesis, all the conditions necessary for the origin of
nebule. Take the case of the origin of the nebulous mass out
of which our sun is believed to have been formed. Suppose
two bodies, each one half the mass of the sun, approaching each
other directly at the rate of 476 miles per second (and there
is nothing at all improbable in such a supposition), their colli- —
sion would transform the whole of the motion into heat afford-
ing an amount sufficient to supply the present rate of radiation
for 50 million years. Hach pound of the mass would, by the
stoppage of the motion, possess not less than 100,000,000,000
foot-pounds of energy transformed into heat, or as much heat
as would suffice to melt 90 tons of iron or raise 264,000 tons
1°C. The whole mass would be converted into an incandes-
cent gas, witha temperature of which we can form no adequate
conception. If we assume the specific heat of the gaseous
mass to be equal to that of air (viz. 2374), the mass would
have a temperature of about 300,000,000° C., or more than
140,000 times that of the voltaic are.
Reason why Nebule occupy so much Space-—It may be ob-
jected that enormous as would be such a temperature, it would
nevertheless be insufficient to expand the mass against gravity
so as to occupy the entire space included within the orbit of
Neptune. To this objection it might be replied, that if the
temperature in question were not sufficient to. produce the
required expansion, it might readily have been so if the two
bodies before encounter be assumed to possess a higher ve-
locity, which of course might have been the case. But
without making any such assumption, the necessary expan-
sion of the mass can be accounted for on very simple prin-
ciples. It follows in fact from the theory, that the expansion
of the gaseous mass must have been far greater than could
have resulted simply from the temperature produced by the
concussion. This will be obvious by considering what must
take place immediately after the encounter of the two bodies,
Dr. J. Croll on the Origin of Nebule. 3
and before the mass has had sufficient time to pass completely
into the gasecus condition. The two bodies coming into col-
lision with such enormous velocities would not rebound like
two elastic balls, neither would they instantly be converted
into vapour by the encounter. The first effect of the blow
would be to shiver them into fragments, small indeéd as com-
pared with the size of the bedies themselves, but still into
what might be called in ordinary language immense blocks.
Before the motion of the two bodies could be stopped, they
would undoubtedly iaterpenetrate each other; and this of course
would break them up into fragments. But this would only be
the work of a few minutes. Here, then, we should have all
the energy of the lost motion existing in these blocks as heat
{molecular motion), while they were still in the solid state; for
as yet they would net have had sufficient time to assume the
gaseous condition. It is obvious, however, that the greater
part of the heat would exist on the surface of the blocks (the
place receiving the greatest concussion), and would continue
there while the blocks retained their solid condition. It is
difficult in imagination to realize what the temperature of the
surfaces would be at this moment. For, supposing the heat
were uniformly distributed through the entire mass, each
pound, as we haye already seen, would possess 100,000,000,000
foot-pounds of heat. But as the greater part of the heat would
at this instant be concentrated on the outer layers of the blocks,
these layers would be at once transformed into the gaseous
condition, thus enveloping the blocks and filling the inter-
spaces. The temperature of the incandescent gas, ewing to
this enormous concentration of heat, would be excessive, and
its expansive force inconceivably great. Asaconsequence the
blocks weuld be separated from each other, and driven in all
directions with a velocity far more than sufficient to carry
them to an infinite distance against the force of gravity were
no opposing obstacle in their way. The blocks by their mutual
impact would be shivered into smaller fragments, each of which
would consequently become enveloped in incandescent gas.
These smaller fragments would in a similar manner break up
into still smaller pieces, and so on until the whole came to
assume the gaseous state. The general effect of the explosion,
however, would be to disperse the blocks in all directions, ra-
diating from the centre of the mass. Those towards the outer
circumference of the mass, meeting with little or no obstruc-
tion to their onward progress, would pass outwards into space
to indefinite distances, leaving in this manner a free path for
the layers of blocks behind them to follow in their track.
Thus eventually a space, perhaps twice or even thrice that in-
6 Dr. J. Croll on the Urigin of Nebule.
cluded within the orbit of Neptune, might be filled with frag-
ments by the time the whole had assumed the gaseous con-
dition.
It would be the suddenness and almost instantaneity with
which the mass would receive the entire store of energy, before
it had time even to assume the molten, far less the gaseous
condition, which would lead to such fearful explosions and
dispersion of the materials. If the heat had been gradually
applied, no explosions, and consequently no dispersion, of the
materials would have taken place. There would first have
been a gradual melting ; and then the mass would pass by slow
degrees into vapour, after which the vapour would rise in
temperature as the heat continued until it became possessed of
the entireamount. But the space thus occupied by the gaseous
mass would necessarily be very much smaller than in the case
we have been considering, where the shattered materials were
first dispersed into space before the gaseous condition was
assumed.
Reason why Nebule are of such various Shapes.—The latter
theory accounts also for the various and irregular shapes as-
sumed by the nebule; for although the dispersion of the
materials would be in all directions, it would, according te
the law of chances, very rarely take place uniformly in all di-
rections. There would generally be a greater amount of dis-
persion in certain directions, and the materials would thus
be carried along various lines and to diverse distances ; and
although gravity would tend to bring the widely Scattered
materials ultimately together into one or more spherical masses,
yet, owing to the exceedingly rarefied condition of the gaseous
mass, the nebulz would change form but slowly.
Reason why Nebule emit such Feeble Light.—The feeble light
emitted by nebule follows as a necessary result from the theory.
The light of nebule is mainly derived from glowing hydrogen
and nitrogen ina gaseous condition ; and itis well known that
these gases are exceedingly bad radiators. The oxyhydrogen
flame, though its temperature is only surpassed by that of the
voltaic arc, gives nevertheless a light so feeble as scarcely to
be visible in the daytime. Now,even supposing the enormous
space occupied by a nebula were due to excessive temperature,
the light emitted would yet not be intense were it derived from
nitrogen or hydrogen gas. The small luminosity of nebulz,
however, is due to a different cause. The enormous space oc~
cupied by those nebulz is not so much owing to the heat which
they possess, as to the fact that their materials were dispersed
into space before they had time to pass into the gaseous con-
dition; so that, by the time this latter state was assumed, the
Dr. J. Croll on the Origin of Nebule. 7
space occupied was far greater than was demanded either by
the temperature or the amount of heat received.
If we adopt the nebular hypothesis of the origin of our solar
system, we must assume that our sun’s mass, when in the con-
dition of nebula, extended beyond the orbit of the planet
Neptune, and consequently filled the entire space included
within that orbit. Supposing Neptune’s orbit to have been its
outer limit, which it evidently was not, it would nevertheless
have then occupied 274,000,000,000 times the space that it
does at present. We shall assume, as before, that 50 million
years’ heat was generated by the concussion. Of course there
might have been twice or even ten times that quantity; but it
is of no importance what number of years is in the meantime
adopted. Enormous as 50 million of years’ heat is, it yet
gives, as we shall presently see, only 32 foot-pounds for each
cubic foot. The amount of heat due to concussion being equal,
as before stated, to 100,000,000,000 foot-pounds for each
pound of the mass, and a cubic foot of the sun at his present
density of 1:43 weighing 89 lbs., each cubic foot must have
possessed 8,900,000,000,000 foot-pounds. But when the mass
was expanded to occupy 274,000,000,000 times more space,
which it would do when it extended to the orbit of Neptune,
the heat possessed by each cubic foot would then amount to
only 32 foot-pounds.
In point of fact, however, it would not even amount to that ;
for a quantity equal to upwards of 20 million years’ heat would
necessarily be consumed in work against gravity in the expan-
sion of the mass ; all of which would, of course, be given back
in the form of heat as the mass contracted. During the ne-
bulous condition it would not exist as heat, so that only
19 foot-pounds out of the 32 foot-pounds generated by con-
cussion would then exist as heat. The density of the ne-
bula would be only =.= that of hydrogen at ordinary
temperature and pressure. The 19 foot-pounds of heat in each
cubic foot would nevertheless be sufficient to maintain an ex-
cessive temperature ; for there would be in each cubic foot only
stoo0w Of ® grain of matter. But although the temperature
would be excessive, the quantity both of light and heat in each
cubic foot would of necessity be small. The heat being only
7 of a thermal unit, the light emitted would certainly be ex-
ceedingly feeble, resembling very much the electric light in a
vacuum-tube.
Heat and Light of Nebule cannot result from Condensation.—
The fact that nebule are not only self-luminous but indicate
the existence of hydrogen and nitrogen in an incandescent
condition proves that they must possess a considerable tempe-
8 Dr. J. Croll on the Origin of Nebule.
rature. And it is scarcely conceivable that the temperature
could have been derived from the condensation of their masses.
When our sun was in the nebulous condition it no doubt was
self-luminous like other nebule, and doubtless would have
appeared, if seen from one of the fixed stars, pretty much like
other nebule as viewed from our earth. The spectrum would
no doubt have revealed in it the presence of incandescent gas.
At all events we have no reason to conclude that our nebula
was in this respect an exception to the general rule, and es-
sentially different from others of the same class. The heat
which our nebula could have derived from condensation up to
the time that Neptune was formed, no matter how far the
outer circumference of the mass may originally have extended
beyond the orbit of that planet, could not have amounted to
over ——1__ of a thermal unit for each cubic foot ; and the
70000
quantity of light given out could not possibly have rendered
the mass visible. Consequently the heat and light possessed
by the mass must have been derived from some other source
than that of gravity.
We have further evidence that the heat and light of nebulee
cannot have been derived from condensation. If there be
any truth, as there doubtless is, in Mr. Lockyer’s view of the
evolution of the planets, then the nebulee out of which these
bodies were evolved must have originally possessed a very
high temperature—a temperature so high, indeed, as to pro-
duce perfect chemical dissociation of the elements. In short,
“the temperature of the nebule,”’ as Mr. Lockyer remarks *,
“was then as great as the temperature of the sun is now.”
Mr. Lockyer’s theory is that the metals and the metalloids,
owing to excessive temperature, existed in the nebulous mass
uncombined—the metals, owing to their greater density, assu-
ming the central position, and the metalloids keeping to the
outside. ‘The denser the metal the nearer would its position
be to the centre of the mass, and the lighter the metalloid the
nearer to the outside. Asa general rule the dissociated ele-
ments would arrange themselves according to their densities ;
and it is for this reason, he considers, that the outer planets
Neptune, Uranus, Saturn, and Jupiter, are less dense than
the inner planets, since they must have been formed chiefly of
metalloids, while the inner and more dense planets would
consist chiefly of metallic elements.
“‘The hypothesis,” says Mr. Lockyer, “is almost worthless
unless we assume very high temperatures, because unless you
have heat enough to give perfect dissociation, you will not
have that sorting-out which always seems to follow the same
* “Why the Earth’s Chemistry is as it is,” p. 55, 1877,
Dr. J. Croll on the Origin of Nebule. oy)
law.’ But the heat which produced this dissociation previous
to the formation of the planets could not have been derived
from the condensation of the nebula; for the quantity so de-
rived prior to the existence of the outermost planet must have
been infinitesimal indeed. The heat existing in the nebula
previous to condensation must have come from some source ;
and we can conceive of no other save that which we have been
considering.
The Gaseous State the first Condition of a Nebula.—lIf the
foregoing be the true explanation of the origin of nebule, it
will follow that the gaseous state will in most cases be the
first or original condition, and that a nebula giving a con-
tinuous spectrum will only be found after it has condensed to
a considerable extent.
The irresolvable nebulee which exhibit bright lines, in all
probability consist, as Mr. Huggins maintains, of glowing gas
without any thing solid in them. In short they are nebule in
their first stage of development, and have notas yet condensed
sufficiently to become possessed of nuclei. If we adopt the
generally accepted nebular hypothesis, I cannot understand
how we can consistently deny the existence of gaseous nebule;
for, according to the nebular hypothesis, the central nucleus
which constitutes a sun or star, and which exhibits a con-
tinuous spectrum, was formed by condensation as surely as the
planets or the satellites have been. Were we to go back suf-
ficiently far in the past, we should come to a time when not
only our globe but the sun himself consisted of gaseous matter
only. If we admit this, then why not also admit that there
may be nebulz at the present time in a condition similar to
what our sun must formerly have been.
The gaseous condition of nebulze seems to follow as a con-
sequence from Mr. Lockyer’s theory. For in order that the
materials in the formation of a sun or star may arrange them-
selves according to their densities, dissociation is requisite ;
but there can be no dissociation except in the gaseous con-
dition.
Star-Clusters.—The wide-spread and irregular manner in
which the materials would in many cases be distributed through
space after collision, would prevent a nebula from condensing
into a single mass. Subordinate centres of attraction, as was
long ago shown by Sir William Herschel (in his famous memoir
on the formation of stars*), would be established, around which
the gaseous particles would arrange themselves and gradually
condense into separate stars, which would finally assume the
condition of a cluster. 7
* Phil. Trans. for 1811.
10 Dr. J. Croll on the Origin of Nebule.
Binary, Triple, and Multiple systems of stars will of course
be accounted for in a similar manner.
It is conceivable that it may sometimes happen that by the
time the materials are broken up and dissipated into space,
there may not be sufficient heat left to convert the fragments
into vapour. In this case we should have what Professor
Tait has suggested, a nebula consisting of “ clouds of stones.”’
But such nebulz must be of rare occurrence.
Objections considered.—On a former occasion I considered
one or two anticipated objections to the theory that stellar
light and heat were derived from motion in space. But as
these objections have since been repeatedly urged by physicists
both in this country and in America, I shall again briefly refer
to them.
Objection 1st. ‘‘ The existence of such non-luminous bodies
as the theory assumes is purely conjectural, as no such bodies
have ever been observed.’ In reply, it is just as legitimate
an inference that there are bodies in stellar space not luminous
as that there are luminous bodies in space not visible. We
have just as good evidence for believing in the existence of
the one as we have in the existence of the other. Bodies in
stellar space can only be known through the eye to exist. If
they are not luminous, they of course cannot be seen. But
we are not warranted on that account to suppose that they do
not exist, any more than we have to suppose that stars do not
exist which are beyond the reach of our vision. We have,
however, positive evidence that there are bodies in space non-
luminous, as the meteorites and planets for example. The
stars are beyond doubt suns like our own; and we cannot
avoid the inference that, like our sun, they are surrounded by
planets. If so, then we have to admit tlfat there are far more
bodies in stellar space non-luminous than luminous. But
this is not all: the stars no more than our sun can have been
dissipating their light and heat during all past ages; their
light and heat must have had a beginning; and before that
they could not be luminous. Neither can they continue to
give out light and heat eternally ; consequently when their
store of energy is exhausted they will be non-luminous again.
Light and heat are not the permanent possession of a body.
A body may retain its energy in the form of motion undimi-
nished and untransformed through all eternity, but not so in
the form of heat and light. These are forms of energy which
are being constantly dissipated into space and lost in so far as
the body is concerned.
The conclusion to which we are therefore led is that there
are in all probability bodies in stellar space which have not
Dr. J. Croll on the Origin of Nebula. 11
yet received their store of light and heat, while there are
others which have entirely lost it. The stars are probably
only those stellar masses which having recently had an en-
counter have become possessed of light and heat. They have
gained in light and heat what they have lost in motion, but
they have gained a possession which they cannot retain, and
when it is lost they become again what they originally were
—dark bodies.
2nd. “ We have no instances of stellar motions comparable
with those demanded by the theory.” A little consideration
will show that this is an objection which, like the former, can
hardly be admitted. No body of course moving at the rate
of 400 miles per second could remain a member of our solar
system ; and beyond our system the only bodies visible are the
nebulz and fixed stars ; and they are according to the theory
visible because like the sun they have lost their motion—the
lost motion being the origin of their ight and heat. Their
comparatively small velocities are in reality evidence in favour
of the theory than otherwise; for had the stars been moving
with excessive velocities this would have been adduced as
proof that their light and heat could not have been derived
from motion lost, as the theory assumes.
ord. “Ifsuns or stars have been formed by collision of bodies
moving in space, proper motion can be none other than the
unused and unconverted energy of the original components.
And as stellar bodies are likely of all sizes and moving with
all manner of velocities, it must often happen, from the unequal
force of the impinging masses, that a large proportion of the
original motion must remain unconverted into heat. Conse-
quently some of the stars ought, according to the theory, to
possess great velocities—which is not the case, as none of the
stars have a motion of more than 30 or 40 miles per second.”
I freely admit that, if it could be proved that none of the
stars have a proper motion of more than 30 or 40 miles per
second, it would at least be a formidable difficulty in the way
of accepting the theory. Tor it would indeed be strange that
amidst all the diversity of dimensions of heavenly bodies, it
should invariably happen that the resultant movement of the
combined masses should be reduced to such comparatively in-
significant figures. But something more definite must yet
be known in reference to the motion of the stars before tlrs
objection can be urged.
All that we are at present warranted to assume is simply
that, of the comparatively few stars whose rate of motion has
been properly measured, none have a greater velocity than 30
or 40 miles per second, while nothing whatever is known
12 Dr. J. Croll on the Origin of Nebula.
with certainty as to the rate of motion of the greater number
of the stars.
There seems to be a somewhat prevailing misapprehension
regarding the extent of our knowledge of stellar motions.
Before we can ascertain the rate of motion of a star from its
angular displacement of position ina given time, we must
know its absolute distance. But itis only of the few stars
which show a well-marked parallax that we can estimate the
distance; for it is now generally admitted that there is no re-
lation between the apparent magnitude and the real distance
ofa star. All that we know in regard to the distances of the
greater mass of the stars is little else than mere conjecture.
Even supposing we knew the absolute distance of a star and
could measure its amount of displacement in a given time,
still we could not be certain of its rate of motion unless we
knew that it was moving directly at right angles to the line
of vision, and not at the same time receding or advancing
towards us; and this we could not determine by mere obser-
vation. The rate of motion, as determined from its observed
change of position, may be, say, only twenty miles a second,
while its actual velocity may be ten times that amount.
By spectrum-analysis it is true we can determine the rate
at which a star may be advancing or receding along the line
of sight independently of any knowledge of its distance. But
this again does not give us the actual rate of motion, unless we
are certain that it is moving directly to or from us. If it is
at the same time moving transversely to the observer, its
actual motion may be more than a hundred miles per second,
while the rate at which it is receding or advancing, as de-
termined by spectrum-analysis, may not be 20 miles a
second. But in many cases it would be difficult to ascertain
whether the star had a transverse motion or not. A star, for
example, 1000 times more remote than e Centauri (that is,
twenty thousand billion miles), though moving transversely to
the observer at the enormous rate of 100 miles per second,
would take upwards of 30 years to change its position so much
as 1’, and 1800 years to change its position 1’; in fact we
should have to watch the star for a generation or two before
we could be certain whether it was changing its position or
not. And even after we had found with certainty that the
star was shifting, and this at the rate of 1! in 1800 years,
we could not, without a knowledge of its distance, express the
angle of displacement in miles. But from the apparent
magnitude or brilliancy of the star, we could not determine
whether its distance was 10 times, 100 times, or 1000 times
that of « Centauri; and consequently we could form no con-
Dr. J. Croll on the Origin of Nebule. 13
jecture as to the actual velocity of the star. If we assumed
its distance to be 10 times that of « Centauri, this would give
a transverse velocity of one mile per second. If we assumed
its distance to be 100 times that of « Centauri, this would
- give 10 miles a second as the velocity, and if 1000 times, the
velocity of course would be 100 miles per second.
As there are but few of the stars which show a measurable
parallax, and we have no other reliable method of estimating
their distances*, it follows that in reference to the greater
number of the stars, neither by spectrum-analysis nor by ob-
servation of their change of position can we determine their
velocities. There does not, therefore, appear to be the shadow
of a reason for believing that none of the stars has a motion
of over 30 or 40 miles per second: for any thing that at
present is known to the contrary, many of them may possess
a proper motion enormously greater than that.
There is, however, an important point which seems to be
overlooked in this objection, viz. that, unless the greater part
of the motion of translation be transformed into heat, the
chances are that no sun star will be formed. It is necessary
to the formation of a sun which is to endure for millions of
years, and to form the centre of a planetary system like our
own, that the masses coming into collision should be converted
into an incandescent nebulous mass. But the greater the
amount of motion left unconverted into heat, the less is the
chance of this condition being attained. A concussion which
would leave the greater part of the motion of translation un-
transformed, would be likely as a general rule to produce
merely a temporary star, which would blaze forth for a few
years, or a few hundred years, or perhaps a few thousand
years and then die out. In fact we have had several good
examples of such since the time of Hipparchus. Now,
although it may be true that, according to the law of chances,
collisions producing temporary stars must be far more nume-
rous than those resulting in the formation of permanent stars,
nevertheless the number of those temporary stars observable
in the heavens may be perfectly insignificant in comparison
with the number of permanent stars. Suppose there were as
many as one hundred temporary stars formed for one per-
manent, and that on an average each should continue visible
for 1000 years, there would not at the present moment be over
half-a-dozen of such stars visible in the heavens.
4th. “Such collisions as the theory assumes are wholly
* It is true that we may one day be able to determine by spectrum-
analysis the distance of some of the binary stars; but as yet this method >
has not been applied with success,
14 Mr. I. Bayley on the Analysis of Alloys
hypothetical ; it is extremely improbable that two cosmical
bodies should move in the same straight line ; and of two
moving in different lines, it is improbable that either should
impinge against the other.” In reply, if there are stellar
masses moving in all directions, collisions are unavoidable.
It is true they will be of rare occurrence: but it is well that it
is so; for if they had been frequent the universe would be in
a blaze, and its store of energy soon converted into heat.
II. On the Analysis of Alloys containing Copper, Zinc, and
Nickel. By Taomas Bayury, Assoc. R.C.Sc.1.*
HE analysis of these alloys can be very rapidly effected
by a combination of colorimetric and volumetric methods.
The alloy is dissolved in nitric acid, and the solution then eva-
porated to dryness with excess of sulphuric acid to expel nitric
acid, which must not be ieft in the solution. “
Determination of the Copper.—The solution is mixed with
excess of potassic 1odide, which causes the formation of cuprous
iodide, according to the following well-known reaction :—
Z, CuSO, + 4KIT= 2K, SO, se Cu, I, + ie
The solution containing the precipitate is then titrated with a
standard solution of sodic thiosulphate. The free iodine present
is an exact measure of the copper, each gram of copper being
equal to two grams of iodine. The following is the result of
a series of determinations of copper made under various cir-
cumstances by this method :—
Cu taken. Jodine.
GBD Wai iO OUsE IS! Ua Oe eee bees
1250 Cu'(iree HCl present). 303 9) 2-25 00m
aa Sala Grae pa UE ESS ORI A ea ie ee
"1408 Cu (free H, SO, present) - . . . “2740
"1408 Cu (NiSO, present). . er ie (i505.
‘1408 Cu (ZnSO, and free H, SO, present) 2760
The solution, after the titration, is filtered and the precipi-
tate washed. The filtrate is free from copper and contains the
nickel and zinc. The absence of copper was proved in several
experiments by evaporating to dryness and gently heating the
residue, after which it was dissolved in a little dilute sulphuric
acid and excess of ammonia added. In no instance was any
blue colour perceptible.
Determination of the Nickel.—The fact will have been ob-
served by chemists, that solutions of nickel and cobalt salts
* Communicated by the Author.
containing Copper, Zinc, and Nickel. 15
are so far complementary in colour, that when they are mixed
together the resulting liquid, if moderately dilute, is hardly to
be distinguished from pure water. 1 conceived this fact might
be made the basis of a method for estimating nickel and cobalt,
and therefore undertook the following experiments.
A large hollow prism filled with a moderately strong solu-
tion of a nickel or cobalt salt was placed immediately in front
of the slit of the spectroscope ; and the thickness of the liquid
traversed by the light was regulated by moving the prism until
the eye could most clearly determine the dark absorption-band
caused by the metal in solution. On referring to the accom-
panying diagrams, which show the absorption-spectra of the
two metals, it will be seen that cobalt and nickel are almost
exactly complementary in their relations to light. The black
band of cobalt is well defined at the edges, especially at the
end nearest to the red ; while the absorption-bands of nickel
are not so sharply defined, but fade away at each end. If the
Spectrum of light passed through Co.
Spectrum
"i i iti Menta omar. Smt Ee T | 3
Spectrum of light passed through
|
The black parts here represent the bright parts of the spectrum, and vice versd.
spectra were exactly complementary, on superimposing the
nickel spectrum upon the cobalt spectrum, the dark part on
the one would exactly cover the light part on the other. This,
however, though nearly the case, is not exactly so; for the
bright band in the nickel spectrum overlaps the dark cobalt
_ band at the end nearest to the red, although with diminished
brilliancy. Consequently, when we employ a mixture of nickel
and cobalt salts in solution, we do not get a uniformly dark
spectrum, but an excess of light coming through at the part
where the overlapping occurs, as seen in the diagram. ‘This
is why the solution obtained by mixing strong solutions of
nickel and cobalt is not grey, but reddish brown in colour.
Having so far demonstrated the complementary character of
the two metals, I next endeavoured to find in what proportions
they must be mixed in order to neutralize each other. For
this purpose a tall glass cylinder (150 cubic centims. capacity),
16 Mr. T. Bayley on the Analysis of Alloys
in which ammonia is estimated by Nessler’s method, was em-
ployed. Dilute standard solutions of pure nickel and cobalt
having been carefully prepared, a measured quantity of cobalt
solution was placed in the cylinder, and the nickel added from
a burette until the neutral point was reached. It is difficult
by this method to distinguish the exact point of neutrality, but
easy to determine that the colour-coefficient of nickel with
regard to cobalt lies between 3:1 and 3:2. That is to say, if a
quantity of cobalt in solution be mixed with a solution con-
taining 3:1 times its weight of nickel, the cobalt colour will
slightly predominate in the mixture, which will have a reddish
tinge; while if a solution containing 3:2 times its weight of
nickel be added, the nickel colour will be slightly in excess
and the solution will have an olive-green tinge. It is only
with dilute solutions containing not more than about 2°5
grams of the metals per litre that it is possible to determine
the coefficient with this accuracy.
I now sought for some method of indicating more exactly
the neutral point. After several attempts, it was found that
the addition of ammonium carbonate to the solution of the two
metals affords a means of determining whether the slightest
excess of either metal is present.
If we take 25 cubic centims. of solution containing 03125
gram of Co, and add to this 39:25 cubic centims. of solution
containing ‘098125 gram of nickel, the resulting liquid appears
perfectly colourless. If we now dilute the mixed solutions to
100 cubic centims., and transfer 25 cubic centims. of that so-
lution, containing ‘0078125 gram of cobalt and °02453125
gram of nickel, to a tall glass jar, add 25 cubic centims. of
the solution of ammonium carbonate, described hereafter, and
then dilute to 150 cubic centims., the result is a liquid of deep
purple colour. If we repeat this experiment, using in the first
instance ‘03125 gram of cobalt and ‘099375 gram of nickel,
the colour of the 150 cubic centims. is not purple, but of a
distinct blue colour. The ammonium carbonate for this pur-
pose must be neutral, as the excess of either base or acid
destroys the delicacy of the reaction.
The solution of neutral carbonate, (NH,), CO3, was prepared
as follows:—A few ounces of the commercial carbonate having
been dissolved in water, 10 cubic centims. of the solution were
neutralized by standard solution of sulphuricacid. . The quan-
tity of NH; in the 10 cubic centims. was found to be -085
gram. ‘The quantity of CO, in an equal quantity of the solu-
tion was found to be, in two experiments, ‘348 gram and °350
gram (mean ‘349 gram): the amount of CO, required to form
the neutral carbonate with 085 gram of NH; being ‘110, it
17
follows that there was an excess of CO, equal to :259 gram in
every 10 cubic centims. of the original solution of commercial
carbonate. To neutralize this, 18 grams of ammonia were
required to be added to a litre of the commercial carbonate
solution. This was furnished by 61:7 cubic centims. of am-
monia solution (of sp. gr. *880).
I next endeavoured to determine whether the nature of the
salt of nickel or cobalt has any effect on the reaction. For
this purpose the following solutions were prepared:—
containing Copper, Zinc, and Nickel.
CoCl, 1 cubic centim. =*00125 gram Co.
me 1 cubic centim. ="0025" ,,° “Ni.
Ba CNO;), - 1 cubic centim. =-0025. ,, ~—s N1.
ioe = 1 cubic centim. =*0025" ,; “Ni.
Co(NO;), . 1 cubic centim. =:00125 ,, Co.
apes.” : 1 cabic centim: =-00125 ,, .. Co.
The method of proceeding was as follows:—Into each of
five cylinders 25 cub. centims of the standard solution of
cobaltous chloride were placed ; to the first cylinder 39 cubic
centims. of the solution of nickelous chloride were added, to
the second cylinder 39°25 cubic centims., and so on, to the
fifth cylinder 40 cubic centims. of nickelous chloride being
added. Hach cylinder was then made up to 100 cubic centims.,
and 25 cubic centims. out of each 100 cubic centims. placed
in a second series of cylinders. To each of the second series
neutral ammonium carbonate (25 cubic centims.) was added,
and then sufficient water to make 150 cubic centims. The
results are expressed in the following Table:—
; Ratio of
Cylinder. Co used. Ni used. Colour. Ni to Co.
1. .... 03125 grm. 097500 grm. Purpie 3°12
2..... 03125 ,, 098125, ‘Slightly purple. 3:14
B..... 03125 , 098750 , Between2and4, 316
4..... 03125 4, -099375 , Slightly blue 3:18
a 03125 ,, 100000 ;, ~— Blue. 3:20
In two erveriments, using in the first solutions of CoCl,
and NiSO, and in the second solutions of CoCl, and Ni(NOs),,
I obtained exactly the same results; so that the foregoing
Table expresses the results of these experiments. Subsequently
experiments were made with the same quantities of the metals
in the following combinations :—
Co( NOs), with NiSQ,, Ni( NOs). and NiCl,,
CoSQ, with Ni(NO3;),, NiSO, and NiCl,.
The results of these latter experiments were exactly the
same as those of the first experiments, so that the Table also
does equally well to express them.
Phil. Mag. 8. 5. Vol. 6. No. 34. July 1878. C
18 Analysis of Alloys containing Copper, Zine, and Nickel,
If the cylinders, after the addition of the ammonium car-
bonate be allowed to stand, the differences of tint disappear in
a few hours, and a uniform deep purple-red tint is produced.
This is caused by the cobalt absorbing oxygen from the air
to form the double compounds of cobalt and ammonia. <A
small quantity ofa sulphite destroys the reaction, as it changes
the tint to a deep brown. Thiosulphates and some other re-
ducing-agents do not act in this way.
These experiments lead to the conclusion that the colour-
coefficient of nickel with regard to cobalt is 3°16 in all cases,
or, in other words, that the tint of nickel and cobalt solutions
is independent of the acid radical in combination with the
metals, and depends only upon the metal in solution.
It is evident that nickel and cobalt may be estimated by
means of this reaction. As an example of its application to
this purpose, I give the following account of the manner in
which small quantities of nickel may be estimated.
The nickel must be dissolved in an acid and the solution
diluted to any convenient quantity, e. g. 50 or 100 cubic cen-
tims. Into each of three cylinders ‘0078125 grm. of Co as
CoCl, is placed. This amount of cobalt is afforded by 6°25
cub. centims. of the standard CoCl, solution. Calling the
cylinders No. 1, No. 2, and No. 3, we place in No. 1 °024531
erm. of nickel in solution, and in No. 3 ‘0248458 grm. To
the three cylinders we then add 25 cubic centims. of the stan-
dard ammonium carbonate. Cylinder No. 2, which contains
only cobalt solution and ammonium carbonate, is then made
up nearly to 150 cub. centims., and No. 1 and No. 3 are filled
up to that quantity. Cylinder No. 1 has then a purple tinge,
while cylinder No. 3 has a blue tinge. By adding froma
burette the solution whose strength we wish to determine to
No. 2 until its tint is intermediate between No. 1 and No. 3,
we make with great accuracy the required determination. In
all cases the cylinders should be held, whilst under compari-
son, with their lower extremities at some inches distance
above a sheet of white paper. Three experiments that by no
means reached the highest limit of accuracy, gave the follow-
ing results :—
Ni in solution. Ni found.
02469 orm. (1) :02425
” ” (2) °02475
» 9 (8) 102500
‘02466 = mean.
It is evident that a similar plan of estimating cobalt would
be still more accurate on account of the higher colour-efiici-
ency of that metal.
On Picoline and its Derivatives. 19
The partially opaque brown solution obtained by mixing
strong solutions of nickel and cobalt might, I think, be used
for making standards for the purposes of colorimetrical ana-
lysis. For instance, the brown solution mixed with a few
drops of potassic bichromate cannot be distinguished from
Nesslerized ammonia. Probably the tests used to compare
the solutions of steel in Hggertz’s process for the estimation of
carbon might be made in a similar manner. They would
have the advantage of being permanent.
After the determination of the copper and nickel by the
above methods, the zinc is obtained by difference. If lead is
present in the alloy, it is separated by the evaporation with
sulphuric acid.
II. On Picoline and its Derivatives. By Witu1AM Ramsay,
Pu.D., Tutorial Assistant of Chemistry in the Glasgow
University.
Ly my last memoir (Phil. Mag. Oct. 1877, p. 251) I men-
tioned that on oxidizing lutidine with potassium perman-
ganate an acid, or a mixture of acids, was obtained, the silver
salt of which contained 45°82 per cent. of silver, corresponding
to a molecular weight of 257, assuming the acid to be dibasic.
Since that time I have ascertained that the silver salt of the
acid giving the above percentage of silver is not a pure com-
pound, but a mixture of an acid and a neutral salt of at least
two acids of the same formula.
Oxidation of Lutidine—About 100 grams of lutidine,
C,H, N, boiling from 152° to 155° C., were oxidized with
potassium permanganate in a tinned iron vessel in precisely
the same manner as that described for picoline. After com-
plete oxidation the manganese oxide was removed by filtra-
tion, and the filtrate was distilled to recover unoxidized luti-
dine; less had escaped oxidation than was the case with
picoline, probably on account of its higher boiling-point, as
well as of its being more easily oxidized than its lower homo-
logue. The highly alkaline solution of the products of oxi-
dation was then evaporated to dryness, and digested with
absolute alcohol by means of an apparatus which permitted
the hot alcohol continually to drop on the mixture of salts.
After three or four days the insoluble residue consisted of
nearly pure potassium carbonate, the organic salts having
dissolved in the alcohol. The alcohol was then removed by
evaporation. ‘The residue had an extremely persistent bitter
taste, almost comparable with that of strychnine. It was
* Communicated by the Author.
C2
20 Dr. W. Ramsay on Picoline and its Derivatives.
dissolved in water, neutralized, and precipitated while hot with
lead nitrate, less being used than was necessary to combine
with all the acid present. The precipitate was white and
flocculent. When decomposed with sulphuretted hydrogen
it yielded a liquid from which, on concentration, dicarbo-
pyridenic acid separated out in its usual form of hair-like
needles, and when purified by crystallization from water was
obtained in its two other crystalline forms, viz. naphthalene-
like plates and short thick crystals. Its purest form, the
thick crystals were converted into the silver salt, after deter-
mination of the water of crystallization. It contained 10°94
per cent. of water; and the silver salt, on ignition, was found
to contain 56°57 per cent. of silver. Dicarbopyridenic acid,
in the same crystalline form, crystallizes with 9°83 per cent.,
or one molecule of water; and its silver salt contains 56°69
per cent. of silver. The silver salt was almost completely —
insoluble in boiling water, and was gelatinous and very bulky.
The filtrate from a boiling solution deposited a few amorphous
flocks on cooling.
The calcium salt, prepared by addition of calcium chloride
to a hot solution of the ammonium salt, crystallized in thin
plates, usually grouped together in masses. It contained
17:47 per cent. of water, which it lost at 150°, and the an-
hydrous salt 19°96 per cent. of calcium. OC, H; NO,Ca.
24 H,O requires 18-00 per cent. of water, and the anhydrous
salt 19°51 per cent. of calcium. I had not obtained the salt
crystallized with water before; that described in my last
memoir was anhydrous. On evaporation of the solution of
the calcium salt, needles were precipitated which were an-
hydrous and on analysis yielded 19-01 per cent. of calcium.
The formula of this acid is certainly C; H; NO,; and from its
crystalline forms it appears to be identical with the dicarbo-
pyridenic acid discovered by Professor Dewar. The yield
was somewhat more than ten grams. Whether it is derived
from lutidine by oxidation, or from a possible impurity of
picoline in the lutidine, I am unable to decide.
The mother liquor of the dicarbopyridenic acid contained
a mixture from which an acid crystallizing in groups of aci-
cular crystals radiating from a common centre was deposited,
but not in sufficient quantity for complete examination. From
consideration of its crystalline form it is probably identical
with one shortly to be described.
The remainder of the solution of potassium salts, from which
the dicarbopyridenic acid was precipitated in combination
with lead, was treated with excess of lead nitrate. A copious
flocky precipitate came down, from which the acids were
Dr. W. Ramsay on Picoline and its Derivatives. 21
liberated as usual by treatment with sulphuretted hydrogen.
The lead sulphide was well washed with boiling water; the
filtrate and washings were evaporated ; and on cooling, a white
substance deposited mixed with spear-like crystals. After a
long series of fractional crystallizations from water three dis-
tinct acids were obtained, of which I have investigated two ;
the third was unfortunately lost. As these two have the same
percentage composition as Dewar’s dicarbopyridenic acid, I
propose to name that acid a-dicarbopyridenic acid.
The white substance, mentioned above, consisted chiefly of
a sparingly soluble acid, which I shall call 6-dicarbopyridenic
acid.
The acid depositing from the mother liquor of the B-acid,
in groups of spear-like crystals, shall be distinguished as
y-dicarbopyridenic acid.
B-Dicarbopyridenic acid, C;H; NO,=This acid, as has
already been mentioned, separates out as a white crystalline
powder when its aqueous solution is allowed to cool. It was
purified by repeated crystallization from water. When viewed
under the microscope it presents the appearance of truncated
octahedra, grouped together in masses. The acid dried at
100° decomposes at 244—-245°, frothing up, and giving off
gas. It is very sparingly soluble in water; 0°2 gram, dis-
solved by boiling with about 200 cubie centimetres of water,
erystallized out after standing for some hours. It is rather
more soluble in alcohol, and dissolves sparingly in ether.
When heated on platinum-foil it melts, effervesces, and gives
_ off a smell resembling that of pyridine. It was analyzed, with
the following results :—
I. Taken, 0°4012 gram of air-dried acid. oss at 100°,
0:0532 gram; CO, obtained on combustion, 0°6611 gram ;
H,O, 0°1045 gram.
II. Taken, 0°4233 gram of air-dried acid. Loss at 100°,
0:0560 gram; CO,, 0°6935 gram; H, O, 0°1025 gram.
Caleulated for
I. If. C, Hs NO,. 13H, 0.
H, O...13:26 per cent. 13:20 per cent. 13°91 per cent.
For C, H; NO,.
- eG le Be 50:30 per cent.
Se. oan, LOR MN: OOM.
To ascertain if this acid, when heated, splits up into carbonic
anhydride and pyridine, thus,
C, H; NO,=C, H; N+ 2CO,,
its vapour-density was taken at the boiling-point of sulphur
(446° C.) by means of the beautiful arrangement devised by
22. = Dr. W. Ramsay on Picoline and its Derivatives.
Victor Meyer, and described in the Berichte der deutschen
chemischen Gesellschaft, ix. p. 1216.
Results. Taken, 0°0151 gram.
Weight of empty bulb......... 11°6 grams.
Weight of bulb full of alloy... 199°6
Weight of bulb after heating. 583 ,,
Height of barometer ......00- 750 millims.
Height of alloy in tube above
levelin Dull... .ccecsnesss
The formula given by Meyer (Berichte, 1877, p. 2070),
S . 1548500
LP +50 NL (st05) "ors
where D is the vapour-density compared with air;
S the weight of substance taken;
P the height of the barometer;
p the height of alloy in tube, above level in bulb;
a the amount of alloy used;
9:608 the spec. gray. of the ne at 100°;
9:158 446°;
7 the weight of alloy - remaining in the bulb after the
operation is over.
Substituting the numbers found,
00151 x 1548500
J
; 188-0 167
(750-+40)} (Saag) 01— (ae aa :
or, compared with hydrogen, 29:22. The molecular weight
of C;H;N is 79, and of 2COQ, 88. Adding these together
and div iding by 6 we get 27:8. It is therefore clear that the
above equation is correct, and that @-dicarbopyridenic acid
decomposes into pyridine and carbonic anhydride at the
boiling-point of sulphur.
Reactions of B-Dicarbopyridenic acid.—A cold saturated so-
lution gave no precipitate with the following salts:—Ca Cl,
Ba Cl,, Ba H, OP MgSO,, Zn SQ, Cd Gls Ni (NOs),,
Co (NO3)., Hg Cl., alum, chrome-alum, Mn Cl,, Sn Cl,. With
ferric chloride it gave a white flocculent precipitate soluble
in hydrochloric acid ; the precipitate, on addition of ammonia,
turned reddish-brown in colour, and apparently changed to
ferric hydrate. With mercurous nitrate it gives a bulky
white precipitate; with copper sulphate a light blue precipi-
tate, turning darker on drying; with lead ‘nitrate a heavy
Ww ae crystalline precipitate cae some time; and with silver
nitrate white crystalline flocks very sparingly soluble in water.
93
Dr. W. Ramsay on Picoline and its Derivatives. 23
Ferrous sulphate gives a red coloration exactly resembling
that produced by e-dicarbopyridenic acid.
| Salts of B-Dicarbopyridenie acid.
Ammonium salt—This salt was prepared by evaporating
the acid to dryness with aqueous ammonia. It is moderately
soluble, and crystallizes from a hof solution in needles.
Synthesis. Taken, 0°4025 gram of acid.
Gain, on evaporation with ammonia, 0:0925 gram,
= 18°68 per cent. NH;. Calculated, 16°91 per cent.
Calcium salt——Prepared by adding calcium chloride to a
hot solution of the ammonium salt. It forms very thin mi-
croscopic needles, sparingly soluble in water.
Analysis. Taken, 0°3190 gram.
Loss at 150°, 0:0483 gram, =15:14 per cent. H, O.
Ca CO3 ....-. 0°1320 gram, =16°55 per cent. Ca.
Calculated for C; H; NO, Ca.2H, O=14°93 per cent. H, O.
16°91 per cent. Ca.
Iron salt.—The white flocculent precipitate obtained by
-adding ferric chloride to the acid was analyzed, after being
dried at 150°.
Taken, 0°1020 gram.
Fe, O;, 0:0304 gram,=0°0213 gram Fe, or 20°86 per cent.
Calculated for (C; H; NO,)3 Fe, ... Fe, or 18°45 per cent.
The salt is probably basic. On addition of ammonia to the
moist salt it is converted into ferric hydrate.
Lead salt-—A white crystalline precipitate, very sparingly
soluble in water, prepared from the ammonium salt with lead
nitrate.
AKER cn.00s0-s 0°4165 gram.
Loss at 150° 0:0867 gram,= 8°81 per cent. H, O.
Lead sulphate 0°3117 gram,=51°'14 per cent. Pb.
Calculated for C; H; NO, Pb.2H, O, 8°82 per cent. H, O.
50°73 per cent. Pb.
Silver salt.—The silver salt of §-dicarbopyridenic acid,
when precipitated by adding silver nitrate to a solution of
the acid, contains 43°56 per ceat. of silver, and is probably a
mixture of neutral and acid salt. it was this which led me,
in my last paper (Phil. Mag. Oct. 1877), to state that the
molecular weight of the acids from lutidine was higher than
that of the picoline acids. Two analyses of the silver salt
prepared in this manner showed it to contain 43°56 per cent.
and 44:05 per cent. of silver. When prepared by adding silver
nitrate to the ammonium salt,it has the formula C; H; NO, Ags,
as the following analyses prove :—
24 Dr. W. Ramsay on Picoline and its Derivatives.
I, Taken...0°3247 gram.
Nilver...0°1825 gram, =56°23 per cent.
Il. Taken...0°3590 gram.
Silver...0°2031 oram,=56°57 per cent.
C,H; NO, Ags contains 56°69 per cent. of silver.
This silver salt is not nearly so bulky as that of «-dicarbo-
pyridenic acid, but comes down in flocks. Itis very sparingly
soluble in hot water, and crystallizes out on cooling in tufts
of microscopic needles. When heated it evolves the usual
smell of pyridine. It does not blacken on exposure to light.
Methyl ether.—Prepared by cohobating the silver salt with
methyl iodide. It is a very deliquescent white solid, crystal-
lizing in needles, and soluble in water, alcohol, and ether.
Chloride.—One gram of 6-dicarbopyridenic acid was dis-
tilled from a small retort along with 2:7 grams of phosphoric
chloride. The mixture liquefied before heat was applied.
The distillate was fractionated. After the oxychloride had
distilled over at 110° the thermometer rose rapidly to 269-270°,
and remained stationary while the chloride distilled. The
distillate solidified to a mass of white needles, melting at
49°, and remaining liquid long after the ordinary temperature
had been regained.
y-Dicarbopyridenic acid, C,H; NO,—y-Dicarbopyridenic
acid is much more soluble then the $-acid, and crystallizes
out from the mother liquor of the latter. After repeated
recrystallization, to free it from the f-acid, and from a still
more soluble bitter substance, it was obtained in a pure
state. It forms tufts of spear-like crystals springing from a
common nucleus. When its solution in hot water is allowed
to cool, it crystallizes from nuclei which form on the sur-
face of the liquid. After being dried by exposure to air it
has a satin-like lustre. It is moderately soluble in water
at 18°; 100 cubic centimetres of its saturated solution left,
on evaporation to dryness, 1°1580 gram of dry acid. It is
easily soluble in alcohol and ether. Like its two isome-
rides, it decomposes when heated into pyridine and carbonic
anhydride about 241-245°. To ascertain if it decomposed
in the same manner as the f-acid, I determined the vapour-
density of the mixture of pyridine and carbonic anhydride
yielded by the acid at the boiling-point of sulphur. To save
space I shall omit the details of the determination, and shall
merely state that the number found was 28:4, compared with
hydrogen. The number required by the equation
C, inl O— C; H; N+ 260,
Dr. W. Ramsay on Picoline and its Derivatives. 25
is 27°8. The equation is thus proved to represent what
happens when y-dicarbopyridenic acid is decomposed by
heat.
y-Dicarbopyridenic acid gave the following numbers on
analysis :—
Ps lake... ++ 0°3075 gram.
Loss at 100°, 0°0475 gram,= 15-44 per cent. H, O.
The remainder, 0°2600 gram, on combustion gave
Oe 04929 gram,=51°70 per cent. C.
OG Cais 0:0740 gram,= 3°16 per cent. H.
Pe Waken....:: 0°3582 per cent. of dry acid.
COP cies 0°6697 gram,= 50°98 per cent. C.
BO 2.22%. 0:0974 gram,= 3:02 per cent. H.
III. When dried for one night over sulphuric acid,
0°3085 gram of the acid lost at 100° 0:0380 gram,
= 12°31 per cent. of H, O.
IV. After being dried for a long time in air, 0°2290 gram
lost at 100° 0:0235 gram, = 10-26 per cent. H, O.
C, H; NO, contains 50°30 per cent. C. and 3:00 per cent. H.
C,H; NO, .H, O contains 9°73 per cent. H,O; with 14H, O,
13°91 per cent.; and with 2 H, O, 17°78 per cent.
The acid, when dried in air, appears to contain less than
two molecules of water, and when dried over sulphuric acid,
more than one molecule.
Reactions of y-Dicarbopyridenic acidi—A cold saturated
solution of the acid gave no precipitate with the following
salts:—Ca Cl,, even after addition of ammonia; Ba Cly,
MgSO,, Zn SO,, Cd Cl,, Hg Cl,, Ni (NO3)., Co(NOs3). Ferric
chloride causes a white flocculent precipitate, soluble in
hydrochloric acid, and converted into ferric hydrate by am-
monia; mercurous nitrate gives a bulky white precipitate ;
stannous chloride, a flocculent precipitate ; copper sulphate, a
whitish blue precipitate; lead nitrate, a white precipitate,
which disappears at first, probably owing to formation of an
acid salt, but on addition of more lead salt it becomes perma-
nent; silver nitrate gives a white flocculent precipitate,
slightly soluble in hot water. Ferrous sulphate gives a blood-
red coloration.
Salts of y-Dicarbopyridenic acid.
Ammonium salt.—W hite needles.
0°2708 gram of acid gained 0:0575 gram when evaporated
with ammonia, =17°37 per cent. NH3.
Calculated for C; H; NO, (NH,)., 16°91 per cent.
Calcium salt.—Prepared by adding calcium chloride to a
26 Dr. W. Ramsay on Picoline and its Derivatives.
hot solution of the ammonium salt. On cooling, small plates
crystallized out. After being dried over sulphuric acid it was
analyzed.
PARED fesec uss 02530 gram.
Loss at 150°...0°0310 gram, =12°25 per cent. H, O.
The residue, after conversion into CaCQ3, weighed 0:1116
gram,=20'11 per cent. Ca in the dried acid. C,H; NO, Ca
2H, O contains 14:93 per cent. H,O; and C,H; NO, Ca,
19°51 per cent. Ca.
Silver salt——The silver salt comes down on addition of
silver nitrate to a solution of the acid as a flocculent preci-
pitate, closely resembling that of the $-acid, but not nearly
so gelatinous or bulky as that of the eacid. It is very
sparingly soluble in water.
I. Prepared by adding silver nitrate to the acid.
Taken... 0°4475 gram.
ANE Shs 0:2465 gram,=55:08 per cent.
II. and III. Prepared by adding silver nitrate to the
ammonium salt.
Taken... 0°2967 gram.
iD ee 0°1675 gram,=56°38 per cent.
Taken... 0°2305 gram.
ND =o 0°1305 gram,=56°61 per cent.
C,H; NO, Ag» contains 56°69 per cent. of silver.
y-Dicarbopyridenyl chloride.—The chloride was prepared in
the usual manner; it boiled at 265°. On exposure to air it
turns bluish-violet, and liquefies. It solidifies with great re-
luctance at the ordinary temperature ; and yet its melting-
point is at 88-89°. It appears to be much more easily decom-
posed by water than the chlorides of the «- and f-acids, for it
turns liquid at once on treatment with cold water.
Bitter substance-—The bitter substance already menticned
remained in the mother-liquor of the 6- and y-dicarbopyridenic
acids. ‘It was partially separated by adding lead or silver
nitrates to a neutral solution ; for both these salts are soluble
in acid. The lead salt, when decomposed by sulphuretted
hydrogen, gave a solution which was evaporated to a syrup.
The bitter substance does not crystallize from water or alcohol ;
it is extremely soluble in both these solvents, but less easily
soluble in ether. Itis an acid; its barium salt is a syrup,
which dries up to a vitreous mass over sulphuric acid. The
acid, as well as its salts, give off the usual smell of pyridine
when heated, and also give a red coloration with ferrous
sulphate. It was unfortunately lost, after it had been separated
in a nearly pure state.
Dr. W. Ramsay on Picoline and its Derivatives. 27
Theoretical considerations.—If the formula N
proposed for pyridine by Alder Wright, be
accepted as correct, six isomeric acids of the
formula C;H;N (CO.OH), are theoretic HG CH
cally possible. They are as follows :— ~ oh
Pyridine
1 2,
N N
Ls
He C_CO.0H HC” CH
ce Tl
HU (¢-CO.0H HC (¢-CO.0H
GY Sey:
CH C-CO.OH
3, Me
N N
Yipes
mesOoe—-C° 636MM C—-CO.0OH ne raed OH
\|
HC Ou EEC + CE
\% W XX Y
CH C-CO.OH
S 6.
N N
- FERS vin
me - CH Hee eee
\| | |
Ho OC-C . C-CO.OH HO -OG=C = CH
a Nee
CH CH
Kyen if structural formule be discarded, it is evident from
the analogy between pyridine and chinoline, and benzol and
naphthalene, that a number of isomerides are to be expected
when two external groups replace two atoms of hydrogen in
pyridine. In the case of benzol, three isomerides are known
under such conditions ; and it is to be expected that pyridine,
a more complicated substance than benzol, owing to its con-
taining an atom of nitrogen, should yield more than three
isomeric bodies.
Now, that «-, 8-, and y-dicarbopyridenic acids are isomeric,
and not identical, is rendered highly probable by the following
considerations :—the #-acid is much less soluble in water than
the other two modifications ; as a rule its salts are much less
soluble ; its crystalline form is different. Copper sulphate
produces no precipitate with the a-acid, whereas the other two
28 Dr. W. Ramsay on Picoline and its Derivatives.
give whitish biue precipitates. With ferric chloride, the B- and
y-acids give a white precipitate, which is changed to ferric
hydrate on addition of ammonia; the a-acid gives no preci-
pitate with ferric chloride, even after addition of excess of
ammonia, showing that ferric hydrate is soluble in the
ammonium salt of the acid. The methyl-ether of the a-acid
forms thick isolated crystals ; that of the 6-acid consists of
deliquescent needles. The chloride of the a-acid boils at
284°, that of the B-acid at 269-270°, and the chloride of
the y-acid at 265°. The melting-points of the chlorides are
respectively :—a, 60°5-61° ; B, 49°; y, 88-89°.
I may anticipate that the acid obtained by oxidation of
quinine, and since found to result from the four chief alka-
loids of the cinchona-bark, and described by Mr. James Dobbie
and myself in the ‘Journal of the Chemical Society’ for
April of the current year, has the formula C,H; NO,; but,
from its crystalline form and properties, it appears to be dis-
tinct from any one of the acids described in this memoir.
This subject, however, demands a more complete examination
than we have as yet bestowed on it. It is my intention,
should it prove different, to publish a table giving the charac-
ters of the isomeric acids.
It is also possible that the bitter substance, which, like these
acids, gave off pyridine when heated, is also an isomeride ; but
of this I have no proot.
Dipyridine.—In purifying some oils, Sioa k to be de-
scribed, I obtained a considerable quantity of dipyridine,
Cio Hi Ne, and purified it by crystallization from hot water.
It presented the appearance of long hair-like white needles.
As its vapour-density had only been once determined, it was
deemed of sufficient interest to redetermine it, by means of
Meyer’s apparatus.
The amount taken was 0°0247 eran. The formula by which
it was calculated is
0°0247 x 1543500 x 14°47
f( 213° a ey
*Fiaas +(26 x a) t4 (se08 L01—-(Gaes
Reference is made to the previous example for the meaning
of the numbers. The theoretical density of dipyridine vapour
compared with hydrogen is 79.
Isodipyridine.—Some test tubes full of oil, left by the late
Professor Anderson, and labelled “ Bases forced over from the
residue on distillation of dipyridine,” were submitted to ex-
amination. When heated at the ordinary atmospheric pressure,
these bases boiled at a temperature above that at which
76°63
Dr. W. Ramsay on Picoline and its Derivatives. 29
mercury boils ; they were therefore fractionated in a vacuum
produced by a Sprengel’s air-pump. After numerous distil-
lations, a fraction was separated, which boiled in vacuo at
145-155°, and in air at 295-305°. Two determinations of
the vapour-density of this oil gave the following numbers:
1 Decors 8 igs a oe Pe oz 00
These numbers agree sufficiently well with the vapour-den-
sity of dipyridine, 79.
On analysis it gave the following results :— _
I. Taken, 0°3935 gram.
COE is -.i ss 11272 gram,=78°10 per cent. C.
4 eee 0:2362 gram,= 6°67 per cent. H.
Il. Taken, 0°3003 gram.
CO, ....... 0°8750 gram,=79°06 per cent. C.
25d eee 071778 gram,= 6°57 per cent. H.
Ill. Taken, 0°2830 gram.
See 0°8181 gram,= 78°84 per cent. C.
131) See 0°1717 gram,= 6°74 per cent. H.
Dipyridine, Cy) Hy) N, contains 75°94 per cent. C
6°38 per cent. i.
Both carbon and hydrogen in every case are too high; and
I have been unable to conjecture any reason for the excess.
I am inclined to believe, from the vapour-density, as well
as from analyses of some compounds of the base, that it really
has the formula of dipyridine.
Tsodipyridine is a yellow viscid oil, of 1°08 specific gravity.
It boils at 145-155° in a vacuum, and at 295-805° at the
ordinary pressure. It does not solidify on exposure to the
cold produced by a mixture of snow and salt, nor is crystalli-
zation induced by addition of crystals of dipyridine. It
dissolves very sparingly in water, and communicates to it its
characteristic heavy basic smell ; it mixes in all proportions
with alcohol and ether.
Isodipyridine hydrochloride-—W hen a solution of isodipy-
ridine is evaporated to dryness with hydrochloric acid, redis-
solved in alcohol, and allowed to remain over sulphuric acid,
small, hard, white crystals are deposited. With platinic
chloride, the solution of this salt gives a yellow crystalline
precipitate of the platinichloride. A determination of platinum
was made with the following results :—
Taken, 0°3903 gram. Loss at 110°, 0°0085 gram,=2°43
per cent.
1 ee ae 0°1298 gram,=34'34 per cent.
9
30 Dr. W. Ramsay on Picoline and its Derivatives.
Cy Hy) No.2 HCl. Pt Cl, contains 34°51 per cent. of pla-
tinum, and with one molecule of water, 3°07 per cent. H, O.
Isodipyridine methyl-iodide.—W hen isodipyridine is mixed
with excess of methyl iodide, the mixture grows warm, and a
brown oil deposits in drops on the side of the tube. After
the reaction is over, addition of anhydrous alcohol changes
this brown oil into a brilliant red powder. The powder was
analyzed.
Daken 9 deans 0:2015 gram.
Ae ytd ae Soe = 58°14 per cent. of iodine.
Gis Hy) N..2CH3I contains 57:99 per cent. of iodine.
This red powder is insoluble in absolute alcohol and ether.
Tn aqueous alcohol it dissolves slightly with a yellow colour;
and with water it forms a nearly colourless solution.
The methyl-chloride is a yellow syrup, which gives a yellow
precipitate with platinic chloride, of the formula
Cio Hip N.. 2 CH; Cl. Pt Cl.
It decomposes partially at 100°.
diacen" = teen er 03426 gram.
essa Orc 0°1126 gram,=382°86 per cent.
Calculated for Cro Hi N, ae CH. Cl ° Pt Cl,; 32°94 per cent.
The small amount of isodipyridine at my disposal made it
impossible to prepare more salts. In distilling this base at
the atmospheric pressure, the last few drops fell on a red-hot
surface; and on opening the bulb a strong smell of pyridine
was perceived. This base therefore is apparently converted
into pyridine by exposure to a high temperature.
The methyl-iodide of dipyridine, prepared from pure
crystallized base, is also a red powder; I failed entirely to
observe the white needles described by Dr. Anderson in his
account of the base.
Dipicoline, Cy, Hy, No.—Dipicoline was prepared by Dr.
Anderson by allowing picoline to remain in contact with
metallicsodium. A bottle, set aside by him in 1874, contained
a black, tarry mass ; on exposure to moist air, it gradually
became yellow, while the sodium unattacked by the picoline
oxidized. After the whole had become yellow, water was
added, and the oil, which sank to the bottom, was well washed
to remove sodium hydrate. After an attempt to purify it by
distillation with water-vapour (which did not succeed, owing
to the slight volatility of the base), the oil was dried, and dis-
tilled alone. A large quantity of picoline came over at 134°;
the temperature then rose rapidly to 280°. A small fraction
Dr. W. Ramsay on Picoline and its Derivatives. dl
distilled between 280° and 310°; but by far the largest por-
tion distilled between 310° and 320°. There was very little
remaining ; so that the fraction last mentioned constituted the
bulk of the oil. After two more distillations, the portion
boiling at 310-320° being collected separately, the base was
considered sufficiently pure for investigation.
Its vapour-density was determined twice:
0°0420 gram x 1548500 x 14°47
2 221°3 ee 96-1 grams’
760+ (42%5)) (“gage )P0l-( pss) S
= 95°30.
eo
0:0411 gram x 15438500 x 14°47
2 53°9 grams \ _ 134°7 grams
m2+ (45% 3)\ (Gans )19l- (gage)
= 97-99,
The theoretical vapour-density of dipicoline is 93.
Analysis of dipicoline dried over sodium and distilled :—
TteD=
faken .....: 02932 gram.
BOTs ses. 0°8313 gram,=77°32 per cent. C.
BRO 7 eenees 071886 gram,= 7:14 per cent. H.
Cy. Hy, N, contains 77-41 per cent. of carbon, and 7:52 per
cent. of hydrogen.
Dipicoline, Cy, Hy, Ne, is a yellow oil, closely resembling
dipyridine in appearance. Its smell is similar, but slightly
different. It mixes in all proportions with alcohol and ether,
and is sparingly soluble in water, to which it communicates
its taste and smell. Its specific gravity is 1:12, rather more
than that of dipyridine. It boils at 310-820° at the ordinary
pressure. It unites with acids to form salts which have little
tendency to crystallize.
The hydrochloride, after standing in a syrupy condition
over sulphuric acid for some days, showed a tendency to
erystallize at the edge. The platinichloride has the formula
Cio Hy Ne- 2H Cl. Pt Cl,
Analyses :-—
Paylaken +... 05117 gram.
Etre, sakess 0°1692 gram,=33:06 per cent.
Ms Dake) \ 10.6 0°5069 gram.
14 ea eee 0°1684 gram, =383:22 per cent.
The platinichloride contains 33°73 per cent. of platinum.
Dipicoline unites with the iodides of the alcohol-radicals ;
of these compounds, the methyl-iodide was prepared.
32 Dr. W. Ramsay on Picoline and its Derivatives.
Dipicoline methyl-iodide, Cy. Hy, Nz. 2 CH; I.—Obtained by
the action of excess of methyl-iodide on dipicoline, at the
ordinary temperature. It forms a reddish-brown oil, which
solidifies after some time. On treatment with anhydrous
alcohol, it changed to a bright yellow powder, almost insoluble
in alcohol and in ether, but readily soluble in water, giving
an almost colourless solution. It was dried and analyzed.
Taken’ Dieek. 0:2764 gram
AG AY eer rc 0:2638 gram ) _ -,.
Ag AP rad 0:0085 aia =54:29 per cent. I.
C,, Hy, N..2CH; I contains 54:24 per cent. of iodine.
The methyl-hydrate, prepared by addition of silver oxide
and water to the methyl-iodide formed a colourless liquid,
which turned brown and evolved a peculiar smell on evapo-
ration. |
The methyl-chloride, obtained by addition of hydrochloric
acid to the methyl-hydrate, is a white crystalline salt. The
platinichloride is a buft-coloured precipitate, soluble in hot
water, and crystallizing out in yellow crystals when the solu-
tion cools. It was analyzed.
dlakem=: St. 071120 gram.
EG“ paeat 0:03845 gram, = 30°80 per cent.
Cy, Hy, N;.2CH; Cl. Pt Cl, contains 31:47 per cent. of
platinum. |
A strong solution of iodine in alcohol was added to a hot
solution of the methyl-iodide in aqueous alcohol ; brown scales
with coppery lustre separated out on cooling. This compound
was analyzed.
Maken: seosies 0°4125 gram,
Tome aah Rees 0°6245 gram,= 81°81 per cent. of I.
By titration with sodium thiosulphate, this compound was
found to contain 61:25 per cent. of free iodine.
CHL N12 Cher i,
the heaxiodide of dipicoline methyl-iodide, contains 82°46 per
cent. of total iodine, and 61°85 per cent. of additive iodine.
This compound is insoluble in water, but dissolves sparingly
in alcohol with a deep yellow colour. It is insoluble in car-
bon disulphide. .
An aqueous solution of dipicoline, on addition of bromine
water, gave a very bulky buff-coloured precipitate. It was
dried over sulphuric acid and analyzed.
Palen heey! 0°4108 gram.
Ag Brit) o0s4 0°5161 gram, =53°46 per cent. of Br.
Dr. W. Ramsay on Picoline and its Derivatives. 33
C,, Hy, Br; N, contains 56°73 per cent. of bromine.
C,, Hy; Br N,.2H Br contains 55°70 per cent. of bromine.
I am disposed to accept the latter formula as the correct one ;
for one atom of bromine introduced into the molecule of dipi-
coline would probably not destroy its basic property.
Oxidation of Dipicoline—Five grams of dipicoline were
oxidized in the usual manner with potassium permanganate.
The acids when separated from their lead salts, consisted :—(1)
of an acid, almost totally insoluble in water, alcohol, and ether,
and separating in amorphous flocks on evaporation of the
solution containing other acids, in which it dissolves sparingly ;
it gives off a smell of the polymerized bases when heated on
platinum foil; and (2) amixture of acids (certainly containing
no #-dicarbopyridenic acid), of which the quantity at my dis-
posal was too small to admit of fractional crystallization. These
acids also evolved a smell resembling that of dipyridine, when
heated. The lead and silver salts of these acids are white
insoluble precipitates. It is probable, from the fact of these
acids evolving the smell of dipyridine when heated, that
dipicoline, when oxidized, yields a polymeride of dicarbopyri-
denic acid.
General Conclusions.
1. Bases of the series C, Ho»-5.N are tertiary bases; they
are not attacked by nitrous acid; nor do they unite with more
than one molecule of a halogen compound of an alcohol
radical.
2. They are unsaturated compounds, but have no great
tendency to form addition-compounds. ‘The addition-com-
pounds are divisible into three classes :—(a) compounds in
which the base combines directly with an acid to form a salt ;
(6) compounds in which the base unites with two atoms of a
halogen, e. g. picoline chloriodide, C,H,N.Cl1I; and (e)
those in which a salt combines with two atoms of a halogen,
in the pyridine series, as, for example, the diniodide of picoline
methyl-iodide, C,H; N.CH;1.1,, and with six atoms of a
halogen, as in the case of the hexiodide of dipicoline methyl-
iodide, Cie et Ns (CH; I). Ig
3. Like the paratiins, ea. are not attacked by acid oxidizing
agents in the cold. They ditter from parattins by withstanding
such action even at a high temperature ; and this is probably
owing to the increased stability given to the molecule by
nitrogen, which renders them basic, and imparts to them the
property of forming salts. The heat of formation of these bases
is doubtless very high ; and when a still greater amount of
heat is evolved by their combination with acids, the sum of
Phil. Mag. 8. 5. Vol. 6. No. 34. July 1878. D
34 Dr. W. Ramsay on Picoline and its Derivatives.
heat-units evolved by the union of the carbon, hydrogen, and
nitrogen, plus that evolved by the formation of their salts, is
probably greater than that evolved by their oxidation.
4. It is consequently only in alkaline solution that they can
be oxidized. In this case, the amount of heat evolved by the
acid formed by oxidation uniting with the alkali increases the
sum of thermal units evolved by their oxidation to a number
larger than that evolved during the formation of the base.
The amount of heat evolved, moreover, is not increased by
that arising from a union of the base with an acid.
5. At least three isomerides are formed by replacement of
two atoms of hydrogen in pyridine by carboxyl, COOH. From
analogy with benzol, and consideration of the greater com-
plexity of the molecule of pyridine, it is highly probable that
more than three exist. These acids are produced by oxidizing
picoline and its higher homologues, and probably also by
oxidizing pyridine. This behaviour is analogous to that of
benzol ; for benzol yields acids containing more than six atoms
of carbon when oxidized. From picoline, C, H, N, it was to
be expected that monocarbopyridenic acid, C; H, N.COOH,
should be produced ; this acid has been obtained only by the
oxidation of nicotine ; a-dicarbopyridenic acid is the only one
produced in large quantity by the oxidation of picoline.
When lutidine, C; Hy N, is oxidized, a mixture of at least three
isomeric acids of the formula C; H;N(CO.OH), is formed.
This would imply the existence of as many different isomeric
lutidines: and indeed it is highly probable that such iso-
merides exist ; for great difficulty is experienced in separating
isomeric liquids, especially (as in this case) when the presump-
tion is that their boiling-points are almost identical.
6. These isomerides may be represented in graphic formule
as on page 27. A closed chain appears best suited to express
the behaviour of the bases and the isomeric compounds de-
rived from them. I failed in several attempts to convert the
dicarbopyridenic acid into its alcohol (from which I had hoped
to obtain a base), owing to the instability of the acid at a high
temperature and the small yield of aldehyde when the acid
was distilled with calcium formate. I had hoped to achieve
the formation of the base by the following stages :—
C;H;N(CO.OH); C;H;N (CHO), ; OC; H; N(CH; OH), ;
C; H,;N.(CH,Cl),; and C; H; N (CHs3)>. 7
From similar reasons, an attempt to prepare lutidine,
C,H, N, by distilling the methyl ether of the e-acid proved
abortive ; in every case, pyridine was formed. In spite of
these failures, it appears to me probable that picoline is methyl-
pyridine, latidine dimethyl-pyridine, etc.,—the presence of
On Salt Solutions and Attached Water. 35
nitrogen, as conjectured in (3), giving stability to the
molecule, and preventing the oxidation of the methyl-groups
to carboxyl.
7. On treatment with sodium, these bases are polymerized,
no hydrogen being evolved by the action of the sodium on
the base. An addition-product is consequently formed,
probably by two atoms of sodium being taken up by each mole-
cule of base ; on coming into contact with a fresh molecule
of base, the sodium leaves the first molecule, which has thereby
its affinities free for union with another similarly placed. I
am very doubtful if any compound of picoline and sodium is
formed. Certainly sodium does not combine with dipicoline ;
for that base can be freed from water by heating it to a high
temperature with metallic sodium.
8. In conelusion, I would remark the analogy between the
furfurol and pyridine groups. ‘That they are closely related
appears very probable. An attempt to effect the conversion
of furfurol, C;H,0O,, into pyridine through the following
series of reactions, failed owing to the instability of furfuryl
chloride.
Pie; eee. ©, C,H,OCL C, H,O NH, C,H, N.
Farfurol, Furfuryl Furfuryl Furfuryl amine Pyridine.
alcohol. chloride (unknown).
(unknown).
The furfurol group, from its unstable nature, is probably
analogous to the higher homologues of acetylene, and is best
represented by an open chain ; whereas the pyridine group,
from its stability, and from the number of isomeric deriva-
tives obtained from it, is, like benzol, best pictured by a closed
chain.
In closing this research, I have to express my deep indebt-
edness to Professor Ferguson for placing at my disposal the
material which belonged to the late Professor Anderson.
IV. On Salt Solutions and Attached Water.
By FREDERICK GUTHRIE*.
(Continued from vol. ii. p. 226. ]
VI.
Further Examples of Cryohydrates and Cryogens.
§ 167. PY XPLATE of Barium.—On cooling a saturated
solution of this salt, the well-known recognizable
erystals are continually deposited until the temperature reaches
* Communicated by the Physical Society.
36 Frederick: Guthrie on Salt Solutions
—0°5. At this temperature the cryohydrate is formed, the
temperature remaining constant until solidification is complete.
The barium was estimated by adding carbonate of ammonium
and gently igniting.
grams. BaO CO,,. BaO. BaO per cent.
22°1204 gave 04271 or 0°3381707 or 1°4995
19°6436 ,, 03790 ,, 0°29435 ,, 1:4984
14°7921 °°, 0°2924° 5. "022709" ,) ito oes
The above analyses are of three separate liquid residues after
the separation of two crops of cryohydrate in each case.
‘The water-worth calculated on the whole three of these
results is 565.
As a cryogen the same temperature (—0°5) was obtained.
§ 168. Hydrate of Strontiwn.—On lowering the tempera-
ture of a saturated solution of this hydrate, crystals of the same
separated until the temperature —O0°1 was reached ; the cryo-
hydrate then formed.
orams. SrO CO, SrO. SrO percent.
17°2620 gave 0:0944 or 0°5468 or 0°3838
13°5124 ,, O-0774 ,, 0°5728 ,, 04020
The analyses were of different liquid residues after two crops
of cryohydrate had been separated from each. The water-
worth derived from the mean of these two analyses appears to
be 1463. As eryogens, SrO H,O or SrO when mixed with
ice did not lower the temperature below 0°. A very slight fall
to —0°09 was obtained on slaking SrO with water and allow-
ing it to assume the normal temperature before mixing with
ice. Such a fall, however, can scarcely be recognized.
§ 169. Hydrate of Calcium.—This body, as is well known,
presents the very interesting peculiarity of being moresoluble
in cold than in hot water. On further cooling the solution
saturated at a certain temperature above O°, one gets an im-
perfectly saturated solution; and on still further cooling, ice
appears. But if the solution be kept saturated during cooling,
which can be well effected by continued stirring with some hy-
drate precipitated by rise of temperature in another quantity,
the cryohydrate appears at —0°'15.
prams. Ca0C0, — Ca. B30
er cent.
22°1094 gave 0°1030 or 0:057630 or 0:26
28°3498 ,, 071222. ,, 0:0684382 ,, 0:29
The analyses were of different liquid residues after two crops
of cryohydrate had separated: the mean of these two results
corresponds to the relation
CaO + TENG EH QO.
and Attached Water. BAT |
Employed as a cryogen, —0°:18 was the lowest temperature
reached. The only data I can find of the solubility of lime at
different temperatures are those of Dalton; from whose expe-
riments it appeared that lime-water saturated at
100° C. contains 0:1050 per cent. of CaO H, O
wee. i871 *,,
eee OO -
From my results it appears that, the mean CaO being 0°275 per
cent, (the mean of two analyses of the cryohydrate at —0°15
gave 0°3634 per cent. of CaO H, QO), lime is 3$ times more
soluble in water at —0°15 C. than at 100 C.
With regard to these water-worths,
W.W.
Hydrate of barium . . «+ . 565
45 strontium...) '. 1463
95 calerum sp. al ay fet kL
it is not only noteworthy, but imperatively demands notice,
that here calcium lies between barium and strontium. They
who are engaged with the spectra of these metals will scarcely
need a further hint.
The melted cryohydrates of SrO H, O and CaO H, O, which
had been solidified in an ice and NaCl freezing-mixture, did
not exhibit the characteristic opacity of eryohydrates. They
became milky in a carbonic acid and ether cryogen, but did
not seem even then to assume the characteristic opacity. A
trace of this true opacity appeared with BaO H, O.
§ 170, Hydrate of Potassium.—A concentrated solution,
namely a solution resulting from the deliquescence of the
solid hydrate in moist air free from carbonic acid, did not
solidify on being subjected to a cryogen of CQ, and ether: it,
however, became syrupy. A dilute solution (indefinite) soli-
dified wholly within the range of an ice-and-NaCl cryogen.
The solid was transparent and resembled ice; it sank in water
at 0° C.
Asa cryogen, caustic potash gave a temperature of —19°2(C.,
But, as will appear subsequently (and this is an important
point), a salt which evolves heat on mixing with water makes
a more powerful cryogen with ice if previously cooled ; not
so those which do not.
§ 171. Permanganate of Potassium.—On cooling a saturated
solution of this salt, crystals of the permanganate separated
out down to 0° C. The cryohydrate was formed at —0°57;
and the temperature then ceased to sink. ‘The estimation of
the water was by evaporation at 100°. The samples are from
38 Frederick Guthrie on Salt Solutions
different preparations. In each case several crops of the solid
eryohydrate had been removed. |
grams. Anhydrous salt. Per cent.
204024" aa. a aeons 2°871
196134) 6. cen een (ODOED 3°013
1D7115 |. eS ee eee 2°663
19°74760° 4. ee ees 2°693
12°6520" 0°3718 2°943
The mean of these rather discordant results shows a water-
worth of 608°3 (K, MnQg).
As a cryogen, permanganate of potash gives a temperature
of —0°52. |
§ 172. Acetate of Lead.—The cryohydrate of acetate of lead
forms at —1°-4 C. After the separation of several crops, in each
ease the residual liquids, after weighing, were repeatedly eva-
porated with an excess of nitric acid and gently heated. Itis
found that the acetate is thereby completely converted into
the nitrate.
orams. Nitrate. ne
14°8195 gave 2°7906 = 18°4
679029 4 1°2401 = £73
74904 = 1:3700 = 18:0
The water-worth, calculated on the mean of these three
results, is 82°3. The temperature of the acetate-of-lead cryo-
gen is —1°7,
§ 173. Sulphate of Zine and Potassium.—The cryohydrate
forms at —1°25. The analyses are, as before, of different
residual liquids. The liquid eryohydrate was evaporated to
dryness at 100° and heated to incipient fusion.
orams. ZuS8O,+K,80,. Per cent.
91020 yielded 0°7274 or 7-992
90954 e .ONiad Tae Noam
The mean of these results gives the water-worth 167°4. As
a cryogen, the same double salt gives —1°-01. The tempera-
ture of solidification of this cryohydrate and the percentage of
salt it contains are approximately those of K,SQ,, its least-
soluble constituent (see §§ 22, 71).
Temperature of Per cent.
cryohydrate. of salt.
Ko SO nk eee 7-8
ZOD OL,| <2 tee ae 30°84
K,, 80O,9-2nbOs a ke a eee 8°25
Comparing this fact with those developed in §§ 109-120,
and Attached Water. 39
where mixtures of salts were employed, we find that while
with such mixtures the more powerful cryogen governs the
temperature, here it is the less powerful cryogen which does so.
§ 174. Ferrocyanide of Potassium—tThe cryohydrate of this
salt forms at —1°-7. Two analyses of the same residual liquid
were made by evaporating at 100°, and subsequent stirring
with free exposure to the air at the same temperature.
grams. K,FeCy,. Per cent.
6°6510 gave 0-7987 or 12
macau 2. Orrons oo Lis
The mean indicates the formula
K, FeCy,+ 151-6 H, O.
The temperature of the cryogen is —1°°61. If this body had
been the first to be experimented on in the direction which
has led to the discovery of the cryohydrates, it is possible that
the whole class might have escaped notice, because, when the
eryohydrate is allowed to meit, a considerable quantity of yel-
low salt (terhydrate or subcryohydrate) falls down unless the
liquid is kept well agitated. ‘Though not peculiar to this salt,
it is perhaps more marked with it than with any other. To
be viewed almost as a corollary to the above fact is the follow-
ing one concerning the same salt. When a solution of the
strength of the cryohydrate is cooled, there may be a simul-
taneous formation of ice and some hydrated or anhydrous
ferrocyanide: the one floats; the other sinks. As before
pointed out in other cases, this independent separation of the
constituents of the cryohydrate is entirely prevented by pla-
cing in the solution a fragment of previously formed cryohy-
drate.
§ 175. Ferricyanide of Potassium.—At a temperature of
—3°-9 a saturated solution of this salt began to give up its
eryohydrate, having previously given up a less hydrated salt.
Though several determinations of the amount of salt in the
residual liquid were made both by evaporation over a water-
bath and drying in vacuo over sulphuric acid, the results dif-
fered from one another by several per cent. The lowest was
19-8 per cent., the highest 24 per cent. The temperature of
the cryogen is —3°9 C. The ambiguity in the amount of
water in the cryohydrate finds its counterpart in the similar
ambiguity in the water of crystallization of the ordinary salt.
§ 176. Nitrate of Urea. —The cryohydrate first appears at
—4°, on cooling a saturated solution. The residual liquids
from two preparations, after about the same quantity of cryo-
hydrate had separated, were very gently evaporated on a water-
40 Frederick Guthrie on Salt Solutions
bath only just to complete dryness. Ifthe substance be further
heated, minute iridescent crystals begin to appear at that part
of the residue where the basin is in contact with the bath. As
soon as these began to appear the further heating was stopped.
grams. Nitrate. Per cent.
66889 gave 0°5693 or 8:64
61616". 5,, O0844 EL ieron
The water-worth is accordingly 72°83. As a cryogen the
temperature of —4°5 is obtained.
§ 177. Ovalate of Potassium.—The temperature at which
the cryohydrate formed was found to be —6° 38. On evapo-
rating 3°2862 grams in a platinum capsule, igniting, and
quickly cooling on a metal slab, 0°5790 of the carbonate was
obtained (=17°62 per cent.).
In another analysis, 3°1500 grams, on evaporation to dry-
ness on a water-bath, gave ()°6684 oxalate (21:22 per cent.).
This gave on ignition 0°5531 of carbonate (17°56 per cent.),
which by treatment with hydrochloric acid gave 0°5958 of
chloride of potassium (18°88 per cent.). The percentage of
carbonate agrees closely with that of the first analysis. The
percentage of chloride differs only by 0-07 from that required
on the conversion of 17°56 of carbonate. Hence it would
seem that with due care oxalate of potassium may safely be
estimated as carbonate, notwithstanding the hygroscopic cha-
racter of the latter salt. It also appears (contrary to state-
ments sometimes made) that oxalate of potassium does. not
retain any of its water of crystallization when its solution is
evaporated to dryness at 100° C.; for the 17°56 per cent. of
carbonate obtained is equivalent to 21:12 per cent. of oxalate,
which only differs by 0:1 per cent. from 21:22, which was
found. The water-worth (deduced from the chloride of potas-
sium) is 17-3. :
The temperature of the cryogen is —6°2.
§ 178. Fluoride of Sodium.—This salt, like several other
salts of sodium, is troublesome when attacked from the side of
saturated solutions, because there appears to be a suberyohy- |
drate. ‘This salt also exhibits the very rare property of being
almost equally soluble at all temperatures between 100° and
—3°9. On cooling a hot saturated solution to —2°, nothing
separates. Between —2° and —4° an ice-like body is formed.
The true cryohydrate appears to be formed at —5°68; for this
temperature is preserved till the whole is solid and opaque.
Fluoride of sodium, as a cryogen, gives —3°2. The eryohy-
drate has not been further examined.
§ 179. Cyanide of Mercury.—A concentrated solution gaye
and Attached Water. 4l
up the anhydrous salt until —0°45 was reached; then the
cryohydrate was formed. The amount of salt was determined
by evaporation over sulphuric acid im vacuo.
erams. Cyanide.
3°8835 gave 0°2892 or 7°45 per cent.
| 5-0238 ,, 0:3738 or 7-44 _,,
This percentage exhibits the water-worth of 174. The same
salt as a cryogen reaches the temperature —0°'6.
§ 180. Acetate of Zine.—A boiling saturated solution was
allowed to cool to the atmospheric temperature (+15°). The
residual liquid was drained from the separated crystals and
introduced, together with a few crystals, into a stoppered
bottle. After keeping in ice for nine hours with frequent agi-
tation, all sign of further crystallization ceased. The zinc was
estimated by precipitation with carbonate of sodium. It was
thus found that the strength at 0° was 23 per cent. This so-
lution, when artificially cooled, yields fern-like crystals at
—5°-9; these gradually became opaque, the opacity forming
in a frond-like manner; the whole became dry at the above
temperature. An analysis of the residual liquid, after two
crops of cryohydrate, showed that the cryohydrate had sensibly
the same composition as the solution saturated at 0° C.; for
erms. Oxide.
5:9980 gave 0°6103 or 23 per cent. anhydrous acetate,
-§ 181. Ayposulphite of Soda.—tThe following are the tem-
peratures at which solidification begins in solutions of varying
strengths of this salt :—
TABLE XX XIX,
Wy ,,0,, Temperature,
by weight. Centigrade. poset
per cent. =
i — 01 Ice.
2 — 04 29
3 — 0°65 \.
5 — 12 Fe
6 — 15 Appearance of ice, but sinks
10 — 25 in water 2t U°. Perhaps
15 — 39 due to interstitial solution.
20 — 5-45 More probably a suberyo-
30) — 95 to —110 7 hydrate.
30 —l1 Cryohydrate.
33°5°5 0-0 (Kr Ordj Beas
4} 420 remers). rdinary hydrate.
A 30-per-cent. solution does not always give up a solid at
—9°:5. Sometimes the temperature sinks to —12°4; then
42 Frederick Guthrie on Salt Solutions
the true eryohydrate i is formed, and the temperature rises to
—11° and remains constant till all is solid.
The solubilities at 0° and 20° are those given by Kremers.
These and the determination for —11°, when plotted in the
usual way, are found to lie on the same straight line. H. Schiff
found at 19°°5 a saturated solution to contain 638°5 per cent.
five- hyd andy or 45:8 per per cent. anhydrous salt. As a
cryog ey the temperature —10° was reached.
6 182. Citric Acid.—This body presented many difficulties ;
but as ae difficulties occur again with most organic acids
fo)
of high molecular weight, a special study was made of it. It
is peculiarly lable in aqueous solution to supersaturation of
the most persistent kind, especially when the solution is at a
low temperature. At temperatures and under conditions
which are capable of evolving the cryohydrate, the solution.
assumes sometimes an almost colloidal form, and shows no signs
of eliminating solids unless other means besides mere lowering
of temperature are employed.
From solutions ranging from 10 to 40 per cent. of anhy-
drous acid, ice is liberated; and this continues to 42°26 per
cent., from which solution a cryohydrate separates at —9°-2.
The following is a somewhat detailed account of the behaviour
of solutions containing a greater percentage of acid than 40.
Two grams of a solution gave 0°8525 of citric acid, or 42°28
per cent. This gives a solid at —9°2, which at first floats on
the residual liquid. The solid consists of massive white ag-
glomerated crystals. The crystals are hexagonal, but pre-
sent thomboidal elements, causing the edge of each crystal
to be deeply and regularly serrate. When they melt, the
rhomboidal crystals are themselves resolved into long slender
prisms. A large quantity of such a solution retained its com-
position when nine tenths of it had been removed by solidifi-
cation, nevertheless, if such a solution be kept perfectly still
for many hours at —9°, a few ice spicula may be formed.
Other solutions, containing respectively 45, 45:9, 50, 50°7,
and 51°5 per cent. of the anhydrous acid, were examined. It
is only this latter which yields, on cooling g, distinct quantities
of the original salt: this it does at —6°, but only if a particle
of the original salt be introduced and by piece: stirring.
When undisturbed, this 51:5 solution may be cooled to —19°5
without any solidification. So prone is this acid to exhibit
supersaturation, that solutions both weaker and stronger than
the 42°62 may be enriched on partial solidification. Thus a
50-per-cent. solution, though already stronger than the ery o-
hydrate, may become still stronger by the separation of ice at
—17°. There is therefore a large region of double supersa-
and Attached Water. 43
turation; the ice-curve crosses the acid or subcryohydrate-
curve, both continuing their courses for an exceptionally long
distance.
For the solubility at 0° C., a solution saturated above 0° C,
was kept at 0° surrounded by ice and placed in an ice-safe for
three days.
Anhydrous
acid.
2°0962 gave 1:0755 or 51°80) __ 54.92%
Bess ., 10912, F187 fo
Crystallized citric acid when added to water has a consider-
able cooling effect. Thus
110-9 grams of crystallized acid at 20°°5 C., added to
89 Bs Wael Ath s wit ait NOs
lowered the temperature to . 275;
Solution. Per cent. Mean.
while
51°5 grams of anhydrous acid cooled to 0° C. and added to
48-5 Pe water cooled ta,.>.. ,. ,.0°
gaveatemperature of . . —6°.
The chief results may be summarized in the following
Table :— |
TaBLe XL.
Citrie acid (anhydrous).
| ! ., | Temperature at
Anhydrous acid, Sirah sake | Bodtiomed
Boca cation begins. |
10 — 11 Tee
20 — 28 6
30 — 5 -
40 — 895 E
42°62 — 92 Cryohydrate.
nee a \ Vat these temperatures
47-06 _ 19-2 | ordinary hydrate, sub-
50-7 13-7 cryohydrate, or even
5-3 Ly j ice may be formed.
As a cryogen, the lowest temperature attainable is —9°3 ;
and this confirms the composition of the cryohydrate which
had been deduced synthetically. Neither cooling the acid to
0° C. nor cooling the two separately to —9° C. had any effect
upon the temperature ; but, of course, the more nearly the
initial temperature is to the final one the less is the quantity
of liquid formed. 3
44 Prof. Hughes on the Physical
Miscellaneous Notes.
§ 183. The following notes of salts which have not yet been
fully examined may be useful.
Cyanide of Potassium, as a cryogen, gives a temperature of
—21°1. The cryohydrate forms at —33°, with a carbonic-
acid and-ether eryogen. Compare § 170.
Oxalate of Sodium forms a eryohydrate at —1°7 C.
Employed as cryogens, the following temperatures were
obtained from the corresponding salts :—
O
Chloride of'cadmium, x. ~\) 3) — 8 -3nG?
es mickel. °,).\ je). aa llaoe
Citrate of sodium. > 0° PS eS
Acetate of calcium “.°-° > =e
Chloride’ of cobalt «5 1” 2, —fos30
¥, Maw eanese wee. aoa)
Those of these bodies which evolve heat on mixture with water
would, when cooled, depress the temperature more. Thus the
chloride of manganese scarcely showed signs of a cryohydrate
at —40° C.
Formate of Sodium, as a eryogen, gives —14°°3, A con-
centrated solution becomes semisolid at —14°, but does not
become opaque or completely solid in a salt-ice cryogen
(—22°). |
Tae Acid, as a cryogen, gives —1°5.
Sulphurous Acid gives a cryohydrate at —1°5.
Boracic Acid, as a cryogen, gives —0°'8, The cryohydrate
forms at —O0°7.
Arsenious Acid.—The cryogen stands at —0°3; the cryo-
hydrate formed at —0°:5, Two samples of the melted and
liquid cryohydrate were sealed hermetically. After two or
three days it was found that a considerable quantity of a fine
white powder had exhibited itself.
[To be continued. |
the paper read on the 9th of May before the Royal
Society, I gave a general outline of the discoveries I had
made, the materials used, and the forms of microphone em-
ployed in demonstrating important points. I have made a
great number of microphones, each for some special purpose,
varying in form, mechanical arrangement, and materials. It
* Communicated by the Physical Society, having been read June 8, 1878.
Action of the Microphone. 45
would require too much time to describe even a few of them ;
and as I am anxious in this paper to confine myself to general
considerations, I will take it for granted that some of the forms
of instrument and the results produced are already known.
~The problem which the microphone solves is this—To in-
troduce into an electrical circuit an electrical resistance, which
resistance shall vary in exact accord with sonorous vibrations
so as to produce an undulatory current of electricity from a
constant source, whose wave-length, herght, and form shall
be an exact representation of the sonorous waves. In the mi-
crophone we have an electric conducting material susceptible
of being influenced by sonorous vibrations; and thus we have
the first step of the problem.
The second step is one of the highest importance: it is es-
sential that the electrical current flowing be thrown into waves
of determinate form by the sole action of the sonorous vibra-
tions. I resolved this by the discovery that when an electric
conducting matter in a divided state, either in the form of
powder, filings, or surfaces, is put under a certain slight pres-
sure, far less than that which would produce cohesion and
more than would allow it to be separated by sonorous vibra-
tions, the following state of things occurs. The molecules
at these surfaces being in a comparatively free state, although
electrically joined, do of themselves so arrange their form,
their number in contact, or their pressure (by increased size
or orbit of revolution) that the increase and decrease of elec-
trical resistance of the circuit is altered in a very remarkable
manner, so much so as to be almost fabulous.
The problem being solved, it is only necessary to observe
certain general considerations to produce an endless variety of
microphones, each having a special range of resistance.
The tramp of a fly or the cry of an insect requires little range
but great sensitiveness ; and two surfaces, therefore, of chosen
materials under a very slight pressure, such as the mere weight
of a small superposed conductor, suffice ; but it would be un-
suitable for a man’s voice, as the vibrations would be too
powerful, and would, in fact, go so far beyond the legitimate
range that interruptions of contact amounting to the well-
known “ make and break ” would be produced.
A man’s voice requires four surfaces of pine charcoal, as is
described in my paper to the Royal Society, six of willow
charcoal, eight of boxwood, and ten of gas-carbon. The
effects, however, are far superior with the four of pine than
with either the ten of gas-carbon or any other material as yet
used. It should be noted that pine wood is the best resonant
material we possess; and it preserves its structure and quality
46 Prof. Hughes on the Physical
when conyerted into the peculiar charcoal I have discovered
and described.
It is not only necessary to vary the number of surfaces and
materials in accordance with the range and power of the vibra-
tions, but these surfaces and materials must be put under more
or less pressure in accordance with the force of the sonorous
vibrations. Thus for a man’s voice the surfaces must be
under a far greater pressure than for the movements of insects.
Still the range of useful effect is very great, as the boxes
which | have specially arranged for man’s voice are still sen-
sitive to the tick of a watch.
In all cases it should be so arranged that a perfect.undu-
latory current is obtained from the sonorous vibrations of a
certain range. Thus, when speaking to a microphone trans-
mitter of human speech, a galvanometer should be placed in
the circuit, and, while speaking, the needle should not be de-
flected, as the waves of + and — electricity are equal, and
are too rapid to disturb the needle, which can only indicate a
general weakening or strengthening of the current. If the
pressure on the materials is not sufficient, we shall have a con-
stant succession of interruptions of contact, and the galvano-
meter-needle will indicate the fact. If the pressure on the
materials is gradually increased, the tones will be loud but
wanting in distinctness, the galvanometer indicating interrup-
tions; as the pressure is still increased, the tone becomes
clearer, and the galvanometer will be stationary when a maxi-
mum of loudness and clearness is attained. If the pressure be
further increased, the sounds become weaker though very
clear; and as the pressure is still further augmented the
sounds die out (as if the speaker were talking and walking
away at the same time) until a point is arrived at where there
is complete silence.
When the microphone is fixed to a resonant board, the lower
contact should be fixed to the board, so that the sonorous vi-
brations act directly on it. The upper contact, where the
pressure is applied, should be as free as possible from the in-
fluence of the vibrations, except those directly transmitted to
it by the surfaces underneath ; it (the upper surface) should
have its inertia supplemented by that of a balanced weight.
This inertia I find necessary to keep the contact unbroken by
powerful vibrations. No spring can supply the required
inertia ; but an adjustable spring may be used to ensure that
the comparatively heavy lever shall duly press on the contacts.
The superposed surfaces in contact may be screwed down
by an insulated screw passing through them all, thus doing
away with the lever and spring; but this arrangement is far
Action of the Microphone. 47
more difficult to adjust, and the expansion by heat of the screw
causes a varying pressure. It is exceedingly simple, however,
easily made, and illustrates the theoretical conditions better
than the balanced lever I have adopted in practice.
In order to study the theoretical considerations, and that with
the most simple form of microphone freed from all surrounding
mechanisms, let us take a flat piece of charcoal 2 millims. thick
and 1 centim. square, and, after making electrical contact by
means of a copper wire on the lower surface, 2 glue that to a
small resonant board or, better for the purpose of Pobserv ation, t
a block of wood 10 centims. square. Upon this superpose one
or more similar blocks of charcoal, the upper surface in com-
munication with a wire, the lowermost surface resting flat, or as
nearly so as possible, on the lower block.
The required pressure is
put on the upper block ; and
while in this state the two _
may be fastened together
with glue at the sides, or,
better, by an insulated screw. OB
The pressure can then be A
removed, as the screw or
glue equally preserves the
force. Let the lower piece be called A and the upper B:
when we subject this board to sonorous vibrations, we can-
not imagine an undulatory movement of the actual waye-
length in such a mass, that is a length comparable with the
real wave-length of the sonorous wave, which may be several
feet. Nor can we imagine a wave of any length without
admitting that the force must be transmitted from molecule to
molecule throughout the entire length: thus any portion of a
wave, of which this block represents a fraction, must be in
molecular activity. The lower portion of the charcoal A,
being part of the block itself, has this molecular action
throughout, transmitting it also to the upper, block. How is
it that the molecular action at the surfaces of A and B should
so vary the conductivity or electrical resistance as to throw it
into waves in the exact form of the sonorous vibrations ?
It cannot be because it throws up the upper portion, making
an intermittent current, because the upper portion is fastened
to the lower, and the galvanometer does not indicate any in-
terruption of current whatever. It cannot be because the
molecules arrange themselves in stratified lines, becoming
‘more or less conductive, as then surfaces would not be re-
quired—that is, we should not require discontinuity between
the blocks A and B; nor would the upper surface be thrown
48 Prof. Hughes on the Physical
up if the pressure be removed, as sand is on a vibrating glass.
The throwing-up of this upper piece B when pressure‘is re-
moved proves that a blow, pressure, or upheaval of the lower
portion takes place : that this takes place there cannot be any
doubt, as the surface, considered alone (having no depth),
could not bodily quit its mass. In fact, there must have been
a movement to a certain depth; and I am inclined to believe,
from numerous experiments, that the whole block increases
and diminishes in size at all points, in the centre as well as
the surface, exactly in accordance with the form of the sono-
rous wave. Confining our attention, however, to points on
A and B, how can this increased molecular size or form pro-
duce a change in the electrical waves? This may happen in
two ways :—jirst, by increased pressure on the upper surface,
due to its enlar gement ; or, second, the molecules themselves,
finding a certain resistance opposed to their upward move-
ment, spread themselves, making innumerable fresh points of
contact. Thus an undulatory current would appear to be pro-
duced by infinite change in the number of fresh contacts.
I am inclined to believe that both actions occur : but the latter
seems to me the true explanation; for if the first were alone
true, we should have a far greater effect from metal powder,
carbon, or some elastic conductor, such as metallized silk, than
from gold or other hard unoxidizable matter ; but as the best
results as regards the human voice were obtained from two sur-
faces of solid gold, Iam inclined to view with more favour
the idea that an infinite variety of fresh contacts brought into
play by the molecular pressure affords the true explanation.
{t has the advantage of being supported by the numerous
forms of microphone I have constructed, in all of which I can
fully trace the effect.
I have been very much struck by the great mechanical
force exerted by this uprising of the molecules under sonorous
vibrations. With vibrations from a musical box 2 feet in
length, 1 found that one ounce of lead was not sufficient on a
surface of contact 1 centim. square to maintain constant con-
tact; and it was only by removing the musical box to a dis-
tance of several feet that I was enabled to preserve continuity
of current with a moderate pressure. 1 have spoken to forty
microphones at once ; and they all seemed to respond with
equal force. Of course there must be a loss of energy in the
conversion of molecular vibrations into electrical waves ; but
it is so small that I have never been able to measure it with
the simple appliances at my disposal. J have examined every
portion of my room—wood, stone, metal, in fact all parts—and
even a piece of india-rubber: all were in molecular movye-
Action of the Microphone. 49
ment whenever I spoke. As yet I have found no such insu-
lator for sound as gutta-percha is for electricity. _Caoutchouc
seems to be the best; but I have never been able by the use of
any amount at my disposal to prevent the microphone report-
ing all it heard.
The question of insulation has now become one of necessity,
as the microphone has opened to us a world of sounds, of the
existence of which we were unaware. If we can insulate the
instrument so as to direct its powers on any single object, as
at present I am able to do on a moving fly, it will be possible
to investigate that object undisturbed by the pandemonium of
sounds which at present the microphone reveals where we
thought complete silence prevailed.
I have recently made the following curious observation :—
A microphone on a resonant board is placed in a battery-cir-
cuit together with two telephones. When one ‘of these is
placed on the resonant board, a continuous sound will emanate
from the other. The sound is started by the vibration which
is imparted to the board when the telephone is placed on it ;
this impulse, passing through the microphone, sets both tele-
phone-disks in motion; and the instrument on the board,
reacting through the microphone, causes a continuous sound
to be produced, which is permanent so long as the indepen-
dent current of electricity is maintained through the micro-
phone. It follows that the question of providing a relay for
the human voice in telephony is thus solved.
The transmission of sound through the microphone is per-
_ fectly duplex; for if two correspondents use microphones as
transmitters and telephones as receivers, each can hear the
other, but his own speech is inaudible; and if each sing a dif-
ferent note, no chord is heard. The experiments on the deaf
have proved that they can be made to hear the tick of a watch,
but not, as yet, human speech distinctly ; and my results in
this direction point to the conclusion that we only hear our-
selves speak through the bones and not through the ears.
However simple the microphone may appear at first glance,
it has taken me many months of unremitting labour and study
to bring to its present state through the numerous forms each.
suitable for a special object. The field of usefulness for it
widens every day. Sir Henry Thompson has succeeded in
applying it to surgical operations of great delicacy ; and by its
means splinters, bullets, in fact all foreign matter, can be at
once detected. Dr. Richardson and myself have been experi-
menting in lung- and heart-diseases ; and although the applica-
tion by Sir H. Thompson is more successful, I do not doubt
that we shall ultimately succeed. There is also hope that
Phil. Mag. 8. 5. Vol. 6. No. 84. July 1878. E
50 Mr. R. Meldola on a Cause for the Appearance
deafness may be relieved. For telephony articulation has
become perfect, and the loudness increased. Duplex and mul-
tiplex telegraphy will profit by its use ; and there is hardly a
science, where acoustics has any direct or indirect relation,
which will not be benefited. And I feel happy in being able
to present this paper on the results obtained by a purely phy-
sical action to such an appropriate and appreciative body as
the Physical Society.
In conclusion, allow me to state that throughout the whole
of my investigations I have used Prof. Bell’s wonderfully sen-
sitive telephone instrument as a receiver, and that it is owing
to the discovery of so admirable an appliance that I have been
enabled to commence and follow up my researches.
VI. On a Cause for the Appearance of Bright Lines in the
Solar Spectrum. By RAPHAEL MELpoLa, /. RAS. £.CS.,
Gc.
iG July 1877 Professor Henry Draper showed that oxygen
and (probably) nitrogen are present in the sun’s atmo-
sphere, the spectral lines of these gases appearing as bright
lines in the solar spectrum.
The photograph accompanying Professor Draper’s paper T
shows that the oxygen-lines are bright, although not conspi-
cuously so, upon a less-luminous background.
The discoverer of this most important fact in solar chemistry
does not offer any complete explanation of the exceptional
behaviour of the lines of these elements, but remarks that “it
may be suggested that the reason of the non-appearance of a
dark line may be that the intensity of the light from a great
thickness of ignited oxygen overpowers the effect of the pho-
tosphere, just as, if a person were to look at a candle-flame
through a yard thickness of ignited sodium-vapour, he would
only see bright sodium-lines and no dark absorption-lines.
Of course such an explanation would necessitate the hypo-
thesis that ignited gases such as oxygen give forth a relatively
large proportion of solar light.”
The oxygen-spectrum referred to in the above-mentioned
paper is the well-known “line spectrum ”’ seen when powerful
disruptive sparks pass through the gas. Dr. Schuster has
recently succeeded in obtaining a second or “compound”
spectrum of oxygent, the fundamental lines of which he has
* Communicated by the Author.
Tt Nature, vol. xvi. p. 364, August 50, 1877.
t Nature, vol. xvii. p. 148, December 20, 1877.
of Bright Lines in the Solar Spectrum. 51
shown with considerable certainty to be present as dark lines
in the solar spectrum.
Since the publication of Professor Draper’s discovery, I
have given much attention to the consideration of a cause for
the apparently anomalous brightness of the cxygen-lines ; and
in the present paper I venture to advance an explanation
which has recommended itself as-being worthy of notice, not
only because it offers a reconciliation of the known solar spec-
trum with the generally accepted views of the constitution of
the sun’s atmosphere, but likewise because it furnishes a sug-
gestive hypothesis for the attack of many other obscure prob-
lems in solar physics.
1. I shall throughout this paper consider it to be established
_ that the gaseous envelopes surrounding the sun succeed each
other in the following order, commencing with the lowest :—
1. Photosphere.
2. Reversing layer.
3. Chromosphere.
4, Coronal atmosphere.
I also assume the truth of the hypothesis, first advanced by
Johnstone Stoney *, who showed, from purely theoretical con-
siderations, that in the sun’s atmosphere the various elements
must extend to heights which are, broadly speaking, inversely
as their vapour-densities. This view has, in my belief, been
substantially confirmed by subsequent observation. Thus ni-
trogen and oxygen, having the respective densities 14 and 16
(H=1), would extend to a great height in the solar atmo-
sphere, rising above sodium, calcium, and magnesium, and
having exterior to them the unknown substance giving the D;
line (helium), hydrogen, and the element giving the coronal
line “ 1474.”
2. Two suppositions can be made concerning the sun’s tem-
perature. In the first place, it may be assumed that the
temperature is so enormously elevated that no chemical com-
pound is anywhere capable of existing in his atmosphere ; in
other words, dissociation may be considered to be complete.
In the next place, it may be supposed that the temperature
falls off sufficiently at some region of the outer portion of the
sun’s atmosphere for certain chemical combinations to take
place.
3. lict us first assume that the temperature of the sun is so
* Proc. Roy. Soc. xvi. p. 25, and xvii. p. 1; Phil. Maz. August 1868 ;
Monthly Notices Roy. Astr. Soc. Dec. 1867; Lockyer, Phil. Trans. 1873,
vol, elxiii. p. 265,
EQ
52 Mr. R. Meldola on a Cause for the Appearance
ereat that there is perfect dissociation throughout his whole
atmosphere. Under these circumstances free oxygen would
exist in the presence of electro-positive elements ; and, in ac-
cordance with Stoney’s hypothesis, both this element and
nitrogen (if present) would extend to a considerable height in
the sun’s atmosphere, rising as a necessary consequence, into
regions which are cooler than that stratum which is cool
enough to reverse the spectral lines of those metals having the
smallest molecular mass, viz. Na, Ca, and Mg*.- Professor
Draper’s suggestion that the enormous thickness of incan-
descent oxygen may overpower the light of the photosphere,
ean only hold good, when considered in connexion with this
hypothesis, if the temperature of the upper portions of the
oxygen atmosphere does not differ to any great extent from
that of the lower and hotter portions. When, however, we
bear in mind the comparatively low vapour-density of oxygen,
and consider at the same time to what an enormous height the
hydrogen atmosphere extends, it appears probable that the
height reached by oxygen would be such that the temperature
of the upper portions of this gas would be considerably lower
than that of the subjacent layers; so that any excess of radia-
tion over that of the photosphere given out by the hottest
portions of the incandescent oxygen would be obliterated by
the absorption of the cooler portions above.
| The same reasoning can be applied if we suppose that the
temperature of the oxygen falls off at some particular level ;
so that above this boundary the state of molecular aggregation
of the gas corresponds to Dr. Schuster’s “ compound-line ”’
spectrum, while below this boundary the greater heat of the
gas resolves its molecules into the atoms giving the ordinary
line-spectrum. The effect of this state of affairs is practically
the same as would be brought about by annihilating a certain
portion of the upper oxygen layers, since the two different
molecular states of the gas give totally dissimilar spectra. We
are thus reduced to an oxygen atmosphere of smaller extent,
and, the foregoing reasoning obtains. |
Angstrom suggested f that the non-appearance of the lines
* Stoney has shown (Proc. Roy. Soc. xvii. p. 14) that a gas or vapour,
even when present in only small quantity, will nevertheless extend to
nearly its full height in the solar atmosphere.
+ He remarks (Recherches sur le spectre Solaire, Upsal, 1869, p. 37) that
it is ‘‘ trés-probable que la température élevée du soleil ne suffit pas pour
produire les raies brillantes de l’oxygéne et de l’azote, et que par consé-
quent, méme en supposant que ces corps existent actuellement dans le
soleil, ils ne doivent pourtant pas occasioner de raies obscures dans le
spectre solaire,” He further suggests that oxygen and nitrogen may exist
in the corona,
of Bright Lines in the Solar Spectrum. D3
of oxygen and nitrogen in the solar spectrum might be ac-
counted for by supposing that, at the temperature of the sun,
the specific absorptive power of these gases may be insufficient
to reverse their spectra. This view, however, equally fails to
account for the brightness of the lines in question.
4. Let us now make the not improbable assumption that the
temperature of the sun’s nucleus, photosphere, and reversing
layer is so great that dissociation is perfect throughout these
regions, but that somewhere in the higher regions, or above
the chromosphere*, the temperature falls off sufficiently for
some kinds of chemical combination to take place—say, in the
present instance, for oxygen to combine with hydrogen.
Under these circumstances we should have, concentric with
and exterior to the chromosphere, a zone of combustion where
oxygen and hydrogen, already at a very elevated temperature,
enter into combination and become thereby raised to a state
of more vivid incandescence ft. All elements which, by virtue
of their small vapour-density, extended into the region of com-
bustion, would be raised to incandescence by contact with the
flaming gases, if not actually taking part in the combustion.
Thus, according to the present hypothesis, we should not ex-
pect to find in the solar spectrum the bright lines of elements
having a high vapour-density.
5. The possibility of combination taking place in the higher
regions of the sun’s atmosphere is admitted by Stoney t, who
states that “gases in the solar atmosphere which are kept
asunder by the temperature of its lower strata may be able to
combine in the cooler regions above.” Such combination,
although arising from the cooling-down of gases previously at
a temperature of dissociation, would nevertheless be attended
with the evolution of heat, and would possess the character of
true combustion. Professor Draper also remarks, in the paper
* It is generally admitted that the true height of the chromosphere is
considerably greater than that seen by means of the telespectroscope,
since the amount of dispersion necessary to weaken the scattered light of
our atmosphere must weaken and shorten the hydrogen-lines by which
the chromosphere is revealed.
T It is well known that the oxyhydrogen flame does not show the
lines of either of the burning gases. In the sun, however, the conditions
are probably very different. The combining gases may be largely diluted
with other inactive gases. Furthermore the pressure, as shown by the
researches of Frankland and Lockyer (Proc. Roy. Soc. xvii. p. 288), is
apparently far less in the upper regions of the chromosphere than in ovr
own atmosphere. Doth these causes would conspire to raise the point cf
ignition of the gases in question, so that a much higher temperature would
be necessary to bring about combination than if they were undiluted and
under greater pressure.
{ Proc. Roy. Soc. xvii. p.
54 Mr, R. Meldola on a Cause for the Appearance
before referred to*, that “diffused and reflected light of the
outer corona could be caused by such bodies (oxygen com-
pounds) cooled below the self-luminous point.”
6. The following considerations appear to give support to
the yiew that oxygen extends into regions sufficiently reduced
in temperature for combustion to take place :—
The region which is called the chromosphere is distinguish-
able as such through what may be called an optical accident:
it is that zone of incandescent hydrogen which is rendered
visible by the telespectroscops ; the true boundary of the hydro-
een atmosphere lies far above the visible chromosphere; and
from this latter zone outwards the temperature falls off rapidly.
Now it has been well established by observation, that metals
of great molecular mass, such, for example, as those of the iron
group, are frequently thrown high up into the chromospheref.
‘Thus, if gases of great vapour-density are occasionally injected
into the chromosphere, gases composed of molecules of com-
paratively small mass, such as those of oxygen and nitrogen,
would probably extend permanently into regions far above the
chromosphere, and which are therefore at a much lower tem-
perature than that zone.
The elements chiefly concerned in producing selective ab-
sorption in sun-spots, as shown by the local thickening of their
spectral lines, are all elements of high vapour-density com-
pared with oxygen—viz. Na, Mg, Ca, Ba, Fe, Ni, Cr, and Ti:
from this it appears that the disturbances producing these
phenomena must extend low down in the chromosphere. The.
band-spectra occasionally seen in the nuclei of sun-spots{
appear to indicate that in these regions the temperature is
sometimes sufficiently reduced to admit of the formation of
* Loe. cit. p. 366.
+ Lockyer, Proc. Roy. Soc. xviii; Young, Journ. Frank. Inst. Sept.
1869 and Oct. 1870; also ‘Nature,’ vol. ii. p. 111, and vol. vu. p. 17;
Respighi, Atti d. Real. Accad. d. Linc. 1872; Tacchini, Comptes Rendus,
Ixxvi. p. 829; H.C. Vogel, Leobuchtungen, 1872; and numerous other
observers.
t Professor Young states (‘ Nature,’ vii. p. 109) that in the spectrum of
a sun-spot he observed “between C and D some very peculiar shadings,
terminated sharply at the less refrangible limit by a hard dark line, but
fading out gradually in the other direction at a distance of 5 or 4 Kireh-
hoff’s scale-divisions.” This answers in all respects to the spectrum of a
compound hody: indeed this excellent observer subsequently suggests
that these bands “seem to point to such a reduction of temperature over
the spot-nucleus as permits the formation of gaseous compounds by ele-
ments elsewhere dissociated.” In the spectrum of a sun-spot recently
observed at the Royal Observatory, Greenwich (Monthly Notices Roy.
Astr. Soc. Nov. 9, 1877), a dark-shaded band was seen at about wave-
length 6380, “sharp towards the blue and shaded off towards the red.
Nothing seen on the sun to correspond with it.”
of Bright Lines in the Solar Spectrum. dd
compounds. If therefore the temperature of the solar atmo-
sphere above the spot layer is low enough to permit of che-
mical combination taking place“, even when the portions of
the atmosphere concerned are swept down into the subjacent
spot-cavity, it follows that the layer into which oxygen ex-
tends (which, as we have seen, must be far above the spot
layer) would likewise be cool enough to allow of the formation
of compounds.
7. it will help to give greater precision to the hypothesis
of a zone of combustion, if we follow the course of a ray of
light supposed to be emitted by the photosphere and received
in the spectroscope of a terrestrial observer. Passing through
the reversing layer, the ray undergoes that selective absorption
which gives rise to the Fraunhofer lines ; and if its spectrum
could be examined immediately after its emergence from this
layer, the oxygen- (and nitrogen-) lines would appear dark,
but less conspicuous than the metallic lines, for reasons which
will be entered into later on in this paperf. After traversing
the chromosphere the ray reaches the zone of combustion, in
which region, owing to the increased temperature, the lines of
all elements which extend so far would tend to be reversed
into bright lines of radiation f.
| I say “tend to be reversed,’ because whether they would
actually become so depends upon the specific absorptive power
of the elements concerned for the rays in question. Thus, let
there be two gases, A and B, of which the spectral lines are
A, Ag, A, and B,, Bz, B, respectively ; and let the specific
absorptive power of A be greater at a given temperature than
* If these band spectra are regarded as the spectra of elements in the
stage of molecular complexity corresponding to the molecule giving the
band spectrum of iodine, or Roscoe and Schuster’s new spectra of Na and
K (Proc. Roy. Soc. xxii. p. 362), the argument remains unaffected, since
these band-spectrum-giving molecules are spectroscopically equivalent to
the molecules of compound bodies.
Tt The question here arises as to what order of oxygen-spectrum we
should expect to find at the temperature of the reversing layer. Dy.
Schuster seems inclined to believe that the temperature may be such as
to give the “compound” spectrum of this gas (‘ Nature,’ vol. xvii. p. 148).
The recent observations of Lockyer upon the calcium-spectrum (Proce.
Roy. Soc. xxiv. p. 352) tend to show that the temperature of this layer
is intermediate in dissociation-power between that produced by a small
coil with jar and a large coil with jar, a temperature which I am disposed
to believe would produce a state of molecular dissociation corresponding
to the line-spectrum of oxygen.
{ It is possible that the temperature of the chromosphere may fall off
at some particular level, so as to give above such boundary the “ com-
pound” oxygen-spectrum. Should this be the case, the higher portion of
the chromosphere may obviously be left out of consideration, so far as re-
lates to its absorbing action on the line-spectrum of oxygen,
56 Mr. R. Meldola on a Cause for the Appearance
that of B. Imagine A and B to be raised to incandescence,
and placed in front of a source of white light at a higher tem-
perature, and let this combination be called the “ first system.”
On examination we should see the continuous spectrum crossed
by dark lines, A,, Ag, A,, B,, Bg, and B,, of which the first
series would be darker than the second. Now conceive the ra-
diation of the whole system to be weakened by general absorp-
tion or by removal to a distance. ‘The lines of B would first
disappear ; so that if we imagine a mixture of A and B (‘second
system’) to be heated to incandescence and placed between
the first system and the observer, the B lines might appear .
bright on a background of continuous spectrum, while the A
lines remained dark, although weakened by the radiation of
the second layer of mixed gases. |
Thus, if the sun’s envelopes exterior to the zone of combus-
tion could be stripped off, we should see the solar spectrum
with the lines of oxygen (and nitrogen) bright, and the hy-
drogen-lines probably dark but much fainter than now seen.
8. The reversal of the oxygen- (and nitrogen-) lines into
bright lines by the increased temperature of the region of
combustion is rendered possible, even with the intense light of
the photosphere as a background [and if, as most probably
would be the case, the temperature of the said region of com-
bustion is lower than that of, the photosphere], because the
light radiated by the latter has undergone almost its maximum
amount of weakening before reaching the zone of combustion,
not only on account of the distance of this last region from the
photosphere, but also because of the absorption, both selective
and general, which the light has undergone in passing through
the intervening reversing layer and chromosphere.
9. We have next to turn our attention to that part of the
sun’s atmosphere exterior to the zone of combustion, in order
to account for the fact that the hydrogen-lines appear so in-
tensely dark while the oxygen-lines are bright. The explana-
tion which I venture to suggest is based upon a wide survey
of the general spectroscopic characters of the elements.
10. At the temperature of incandescence, the characteristic
lines in the spectra of any elements which are compared may
be of very different intensities. Thus Cappel has shown”, by
aseries of quantitative determinations made at the temperature
of a Bunsen burner and of an induction-spark, that very dif-
ferent amounts of the metals experimented upon can be de-
tected by means of the spectroscope. The characteristic lines
of an element are those which Lockyer has shown to be the
longest. Interpreting such facts by the aid of the molecular
* Poge, Ann, cxxxix. p. 628 (1870).
of Bright Lines in the Solar Spectrum. 57
theory of gases (and making due allowance for the fact that
the characteristic lines of the spectra being compared may
occur in parts of the spectrum not visually comparable so
far as regards intensity), we should say that some kinds of
molecules can have certain internal vibrations more readily
excited than is the case with other kinds. From the relation-
ship which exists between radiation and absorption, it follows
that molecules which have the most sensitive radiative orga-
nization have likewise the most sensitive absorptive organi-
zation. |
11. The non-metals are distinguished, as a group, from the
metals by the greater complexity of their spectra (which more
resemble the band spectra of compound bodies), and also by
their comparative insensitiveness to the spectroscope. Many
of the metals are known to give band spectra at low tem-
peratures ; but these break up into line spectra at high tem-
peratures. On the other hand, the band spectra of many
non-metals bear temperatures high enough to break up the
band spectra of metals without being resolved into line spectra.
We might thus have a mixture of two vapours, one metallic and
the other non-metallic, at the temperature of incandescence,
the former giving a line spectrum and the latter a band spec-
trum. If we imagine the temperature of such a mixture of
yapours to be raised to the point at which the band spectrum
of the non-metal breaks up, we should get a line spectrum
from both elements ; but the metallic lines would be more
intense* than those of the non-metal, owing to the greater
sensitiveness of the metallic molecule. We should thus have
realized the conditions laid down in a former paragraph (7),
where A would then represent the metallic, and B the non-
metallic vapour.
12. It now remains to show the applicability of the fore-
going principles to the case under consideration.
The oxygen and hydrogen of the sun’s atmosphere will, for
the sake of simplicity, be exclusively considered. These gases
represent the metallic and non-metallic vapours of the last
paragraph. The photosphere, reversing layer, and chromo-
sphere represent the “ first system” of paragraph 7—1. e. the
* “Jn a tube containing both nitrogen and aqueous vapour, the lines of
hydrogen (spectrum II order) made their appearance at the same time as
the spectrum of bands (I order) of nitrogen, whence it follows that the
lines of hydrogen are visible in a temperature in which the lines of ni-
trogen do not appear” (Schellen’s ‘ Spectrum-Analysis,’ p.171). So also
Frankland and Lockyer found that in a tube containing hydrogen and
nitrogen, the lines of the latter gas under certain conditions of pressure
could be made to disappear entirely, while the hydrogen-lines under all
conditions remained yisible (Proc, Roy. Soc. xvii. p. 454),
58 Mr. R. Meldola on a Cause for the Appearance
source of white light, with the mixture of two vapours of dif-
ferent specific absorptive powers in front. The oxygen and
hydrogen of the zone of combustion represent the second layer
of incandescent gases of paragraph 7, supposed to have been
placed in front of the first system, the total radiation of which
is imagined to have been weakened by general absorption or
by removal to a distance. It has been shown in paragraph 8
that the total radiation of the photosphere has probably under-
gone a great amount of weakening from both these causes.
Thus the spectrum of a ray which reaches the zone of com-
bustion would exhibit (supposing the zone of combustion and
all exterior to it to be stripped off) the lines of oxygen and
hydrogen dark, but those of the former much fainter than those
of the latter. The action of the incandescent gases of the -
zone of combustion upon such a spectrum would be to reverse
the oxygen lines and to weaken those of hydrogen.
The temperature of the region outside the zone of combus-
tion must fall off, so that any oxygen which might there exist *
would be in the state of molecular aggregation corresponding
to the compound spectrum, and would thus be without action
on the bright-line spectrum of this gas, but would give rise to
the dark lines of its compound spectrum. The hydrogen of the
region now under consideration by further absorption inten-
sifies the lines of this gas. Thus the solar spectrum as now
known is shown to be in complete accordance with the hypo-
thesis here advanced.
The hypothesis of a zone of combustion in the higher regions
of the sun’s atmosphere, as already stated, furnishes sugges-
gestions for the explanation of many observed facts in solar
physics hitherto unaccounted for.
I will first call attention to the intense brilliancy of the line
D, in the spectrum of the chromosphere, and the extreme
faintness of the corresponding dark line in the solar spectrum].
If we consider to what an enormous height this element ex-
tends, bearing also in mind that it must consequently reach
into comparatively cool regions, and that its radiative (and
therefore absorptive) powers are very great, it seems impro-
* It may be supposed that the oxygen atmosphere terminates with the
zone of combustion, in which case Dr. Schuster’s new oxygen-spectrum
must be produced by the absorptive action of the gas in the upper regions
of the chromosphere (see also note to paragraph 7).
+ This line was seen in July 1877 by H. C. Russell at Sydney. The
observer states that “it isa difficult line to see, and only to be made out
with high powers.” The greatest dispersion of the spectroscope em-
ployed was equal to eighteen 64°-prisms (Month, Not. Roy. Astr. Soe.
Noy. 9, 1877, pp. 30-32).
~ i. ee
of Bright Lines in the Solar Spectrum. 59
bable that the vast thickness of this gas which must be tra-
versed by a ray of light emitted by the photosphere should be
barely sufficient to reverse its spectrum. If the existence of
a zone of combustion be granted, however, this region becomes
the source of radiation of all gases which extend so far. Thus
in the case of the D; element, which reaches nearly the same
level in the sun’s atmosphere as hydrogen, the stratum of gas
exterior to the zone of combustion is, on the present view,
alone concerned in reversing the line under consideration; and
this stratum may be of insufficient thickness to produce any
marked absorption. The “1474” substance, however, which
rises far above hydrogen, appears to exist in sufficient quan-
tity exterior to the supposed region of combustion (or its spe-
cific absorptive power is sufliciently great) to produce a
marked reyersal in the solar spectrum”™.
The hypothesis advanced in the present paper does not ne-
cessarily imply (at least under existing solar conditions) the
production and accumulation of large quantities of compound
bodies in the higher regions of the sun’s atmosphere. The
zone of combustion may be, so to speak, only a local pheno-
menon confined to a thin shell of the sun’s outer envelopes ;
and compounds formed would be rapidly decomposed both by
dissociation and chemical reduction by being swept down into
the underlying hotter regions by the convection-currents which
take place on such an enormous scale in the sun’s atmosphere.
The heat of the zone of combustion may also contribute to
the dissociation of compounds formed therein f.
* Lockyer has recently shown (Compt. Rend. Ixxxvi. 519; Proc. Roy.
Soc. xxvil. 282) that the blue line of lithium (w.-l. 4603) is represented
in the solar spectrum, while the red line (w.-l. 6705) has not hitherto
been detected. The question suggests itself whether the absence of this
last line may not also be connected with the existence of a region of com-
bustion. The low atomic weight of lithium would lead to the belief that
this element extends to a great height in the solar atmosphere. Thusthe
zone of combustion might be the source of lithium-radiation, and at the
temperature of the sun the blue line may be the longest (as appears pro-
bable from the fact that this line requires a high temperature for its de-
velopment) ; so that the vapour above the region of combustion may be
sufficient to reverse the blue, but insufficient to reverse the shorter red
line. Iwould here ask whether the bright red line so frequently seen in
the spectrum of the chromosphere by Lockyer (Phil. Trans. 1869, pp.
428 and 429), and described as being less refrangible than C, may not be
the missing lithium-line? I may add that a line less refrangibie than C
has also been frequently seen by Respighi at the base of prominences. It
is highly significant that during the eclipse of 1868 a blue line between F
and G was seen by Rayet in the spectrum of a prominence. This is the
position that would be occupied by the lithium-line w.-l. 4605.
+ See Bunsen’s experiments on the combustion of different mixtures of
CO and H with O (Poge. Ann. exxxi. 161); also Berthelot “On the
Chemical Equilibrium of C, H, and O” (Bull, Soe, Chim. [2] xiii. 99),
60 Mr. R. Meldola on a Cause for the Appearance
It is well known to spectroscopists that the solar spectrum
is never absolutely free from the so-called “ telluric” lines,
which have been shown to owe their existence to the aqueous
vapour of our atmosphere. It is possible from the present
point of view that these lines may be partly caused by aqueous
vapour in the higher regions of the sun’s atmosphere*. Should
there be any connexion between the activity of combustion
and the formation of sun-spots, a rigorous comparison of the
“¢telluric’’ lines in the solar spectrum carefully observed (or
still better, photographed) at different periods of the spot-
cycle would be of the highest possible interest. Thus it may
be suggested that the solar combustion varies periodically in
activity—combination being in excess of dissociation during
one half of the cycle, and dissociation being in the excess
during the other half, when the heat resulting from the com-
bustion, having reached its maximum, tends to decompose the
compounds formed. This view points to the belief that the
connexion between the sun-spot period and the period of va-
riation of magnetic declination may be due to a common
cause—the activity of combustion in the sun’s atmosphere and
the resulting variation either in the amount of free oxygen, or
in the magnetic characters of this gas consequent on variation
of temperature.
Sir William Thomson’s theory of the dissipation of energy
leads to the belief that the sun, like other stars, is gradually
cooling down. Thus we should be led to infer @ priora that
there must be a period in the life of a star when compounds
can begin to form. Such combination would begin in the
outer and cooler portions of the star’s atmosphere, as required
by the present hypothesis, and would be attended with the
development of the heat representing the energy of chemical
separation. As the star goes on cooling down, the zone of
combustion, at first a mere shell, would gradually encroach
upon the central regions, and a star having permanently
bright lines in its spectrum would result. In the earlier
stages of what may be called the “‘ chemical period ”’ of a star’s
history—a period into which our sun may be supposed to have
entered—the lines of the non-metallic elements would alone
appear bright, for the reasons detailed in the foregoing por-
tions of this paper (paragraph 11), and, owing to their compa-
rative faintness, would be lost at the enormous distances which
* I may here recall the much-discussed observation of Secchi, who
asserted the existence of water-vapour in the neighbourhood of sun-
spots (Compt. Rend. \xyiil. p. 238). Janssen also, in 1864, observed aque-
ous vapour in the atmosphere of Antares, and, in 1868, in the atmosphere
of many other stars (Compt. Rend. Ixvili. p. 1845).
of Bright Lines in the Solar Spectrum. 61
the light of the star has to traverse before reaching our spec-
troscopes. When, however, the region of combustion had
encroached sufficiently to reverse the metallic lines, these
would shine out with much greater brilliancy than the non-
metallic lines, and we should have a background of continuous
spectrum crossed by the bright lines of the metals of smallest
vapour-density. Such stars would only be expected among
those which are, so to speak, in the latest phase of their ‘‘ che-
mical period.” It is significant that y Cassiopeie, 6 Lyre,
and 7» Argo, three stars which show bright lines in their
spectra, all have sufficiently complex spectra to warrant the
belief that they have entered upon a late phase of their exist-
ence. Before the actual reversal of the metallic lines there
must exist a period in the life-history of many stars when the
temperature and extent of the zone of combustion is such as
to obliterate the dark lines of those metals which will ulti-
mately appear as bright lines. Such appears to be the case
with the hydrogen in e Orionis; and according to the present
views it might perhaps be predicted that this star will sooner
or later show a permanent hydrogen-spectrum of bright lines.
It is conceivable that in certain cases the composition of a
star’s atmosphere may be such as to permit a considerable
amount of cooling before any combination took place among
its constituents; under such circumstances a sudden catas-
trophe might mark the period of combination, and a star of
feeble light would blaze forth suddenly, as occurred in 1866
to t Coronz Borealis. In other cases, again, it is possible
that the composition of a star’s atmosphere may be of such a
nature as to lead to a state of periodically unstable chemical
equilibrium ; that is to say, during a certain period combina-
tion may be going on with the accompanying evolution of
heat, till at length dissociation again begins to take place. In
this manner the phenomena of many variable stars may per-
haps be accounted for. On the whole, the possibility of actual
combustion taking place in the atmosphere of a slowly cooling
star previously at a temperature of dissociation does not seem
to me to have had sufticient weight attached to it; and in
concluding, I would point out the important factor which is
thus introduced into calculations bearing upon the age of the
sun’s heat in relation to evolution.
London, June 6, 1878.
fp Wie Y
VIL. Notice of Researches in Thermometry.
By Epuunv J. Miurs, D.Se., £RS.*
N the course of some researches, commenced some years
since, which required a series of accurate measurements
with the mercurial thermometer, I had occasion to make a
somewhat minute inquiry into the properties of that instrument.
The publication of the completely reduced results has been de-
layed by ill-health and pressure of other work ; my present
wish is to indicate them, as they may be of interest to those
who are engaged in observations of temperature.
I. If an old thermometer be immersed in boiling water, its
zero descends. In the course of two or three years, at the
ordinary heat of the air, the zero may attain its original posi-
tion, subject to some slight oscillations according to the season
of the year. If w represent the time in months, y the remain-
ing depression, and (A+B) the total depression, the equation
to the ascent is
y= Act + BB;
Aa depending on the diameter, BG on the length of the bulb.
In the case of a spherical thermometer, A is very nearly equal
to B. The probable error of a single comparison of theory
with experiment, in a fairly favourable instance, does not ex-
eced 0°01 C. :
II. For other temperatures than that of boiling water, other
depressions occur ; the connexion between these depressions
and the temperature seems to follow a compound-interest law,
similar to the preceding.
III. If, however, a considerable elevation of temperature
be effected, then the zero no longer falls, but rises. In various
lead-glass thermometers this phenomenon usually commences
at 120°-150°, the bulb collapsing to such an extent as to raise
the zero sometimes 8°, At some point, which we may take
roughly as not less than 100° higher than the last, the zero is
again depressed,—as might, in fact, be expected from the then
sensible tension of mercury vapour, aqueous vapour, residual
air, and other foreign bodies in the tube.
IV. I have made a large number of comparisons of the
mercurial with the air-thermometer. ‘The maximum difference
between the two, between 0° and 100°, is at about 33°; neg-
lecting Poggendorff’s important correction (as is usually
done), it lies at about 50°. It is convenient to use a glass
helix, instead of a bulb, for the body of the air-thermometer ;
in this way convection of air is avoided.
* Communicated by the Author.
Relation between the Notes of Open and Stopped Pipes. 63
V. The effect of external pressure on a thermometer’s bulb
is directly proportional to the pressure as far as about 140
atmospheres. The ascent of the zero of a thermometer on
keeping is consequent on a change of state in the glass, being
the same whether the thermometer be open or closed, and
therefore independent of atmospheric pressure.
VI. When all corrections are made, every individual ther-
mometer has specific characters whereby it differs from all
other thermometers.
VIL. A number of bodies have been rigorously purified,
and their fusion-points determined, with a good second place
of decimals, in terms of the air-thermometer: these points
range from about 35° to 121°. The possession of these bodies,
which can always be preserved without risk, will enable any
observer to obiain standard points within that distance, and
save a vast amount of tedious experimentation.
Anderson’s College, Glasgow.
VIII. On the Relation between the Notes of Openand Stopped
Pipes. By R. H. M. Bosanquet, Fellow of St. John’s
College, Oxford.
To the Editors of the Philosophical Magazine and Journal.
GENTLEMEN,
T has long been known to practical men that, if an open
pipe be stopped at one end, the note of the stopped pipe
is not exactly the octave below the note of the open pipe, as it
should be according to Bernouilli’s theory, but the stopped
pipe is somewhat less than an octave below the open pipe; in
ordinary organ-pipes the difference is said to be about a major
seventh instead of an octave. It has occurred to me lately
that the theory of this phenomenon is not generally known ;
and the following account of it, with some of its applications,
may be of interest. I should mention that the investigations
were made some time ago, before the publication of my Notes
on the Theory of Sound, in the Philosophical Magazine last
year; and they were not mentioned there only because the
methods depending on them proved of insufficient accuracy
for the purpose then in view.
Consider a cylindrical tube open at both ends. Let its
length be J, and its diameter 2R. Then the effective (or re-
duced) length of the pipe is 1+2«; where « is the correction
for one open end, which formed the subject of the investiga-
tions contained in Nos. 5 and 6 of my “ Notes” (Phil. Mag.
LV.]| vol. iv. pp. 25, 125, 216).
Gf Mr. R. H. M. Bosanquet on the Relation between
Now suppose a flat stopper, fitting airtight, to be applied at
one end of the tube. It may then, according to the ordinary’
theory, be regarded as equivalent to the half of an open pipe
whose middle point, or node, coincides with the face of the
stopper, the effective length measured from the node being
l+a. The length of the corresponding open pipe would be
double of this, or 2(/+a). The ratio of the notes is conse-
quently (J+ 2a) : 2(¢+«), which may be put in the form
ly [+22
2 PEE
that is to say, the interval in question differs from an octave
by the interval whose ratio is (J+ 2a): (+a).
The following experiment was made with an iron cylindrical
tube, 4°9 inches in length and 2 inches in diameter. The
notes were determined, as in my former investigations, by
blowing short jets of air against the edges. The tube was
stopped by standing it upright on a flat surface, and applying
a little oil round the edge in contact with the surface. The
notes of the pipe, open and stopped, made with one another
the interval of a minor seventh; 7. e. they deviated from the
octave by a whole tone. The ratio (9: 8) was determined
with some slight accuracy by comparison with the notes of
my enharmonic organ. ‘The tuning of this instrument is not,
however, sufficiently stable to base very accurate work on.
Then
colder
Gram eee
or
Leen ae
ge baa?
a —— ee
And l==A4-9 im,,
TNT aia
and = 110...
sir In
The value of « for this tube was formerly determined at °635 R
(Phil. Mag. vol. iv. p. 219). The tube has been shortened by
about ‘1 inch since; but this cannot affect the correction. Jt
appears then that the present process presents general cor-
respondence with the result of the former investigation ; but
the numerical values of « do not coincide very exactly.
When I originally investigated this subject some time ago,
I anticipated that I should be able, by observation of the in-
ithe Notes of Open and Stopped Pipes. 65
terval between open and stopped pipes, to determine e in an
accurate manner. Jor this purpose I constructed many pipes,
in which the interval in question was as nearly as possible of
definite magnitude, generally a semitone less than the octave ;
but the method proved too inaccurate to be of any real use.
An excellent and perfect tonometer is required to measure the
intervals accurately ; and if we have that, it can be applied to
the solution of the problem with greater advantage in other
ways. The present method, however, is quite sufficient for the
approximate demonstration of the value of a.
There are difficulties in the way of the exact application of
these principles to ordinary organ-pipes. Tirst, it is impos-
sible to blow an open and stopped pipe in a similar manner
with the same mouthpiece. The pitch varies considerably
with the force of the blowing ; and the two notes produced
with different blowing are not comparable. Again, there isa
considerable correction of unknown amount to be taken ac-
count of, due to the closing-in of the mouth-end of the pipe.
We may, however, par ily get over these difficulties. In the
first place, it is possible to arrange a pipe so as to blow the
fundamental when open and the twelfth when stopped, without
variation of the wind. Secondly, the correction due to the
closing-in of the parts round the mouth can be determined for
pipes of given shape by sawing one of them across so as to
leave a plain circular end. The correction due to the differ-
ence in pitch +. (correction for circular end) gives the total
yalue of the correction for the mouth.
The following is an example :—Organ-pipe 9°5 inches from
upper lip to open end; diameter *95 inch. When arranged so
as to blow the fundamental when open and twelfth when
stopped, the twelfth was 2 commas of the enharmonic organ
sharper than the note corresponding to the fundamental.
Taking these to be true commas, which they are very nearly,
we may take the resulting interval to be 40: 41.
The correction for the mouth was determined by sawing
across a similar pipe; it is roughly
l
N=
Then
41 _l+A+e
Aun ice
l+r=40a,
a= Ao iis
Phil. Mag. 8. 5. Vol. 6. No. 84. July 1878. i
66 Notices respecting New Books.
and sinee
2R="95 in.,
a='59 R nearly.
This is closer than could be expected considering the ex-
tremely rough measurement of the two commas. It will be
remembered that the value of a is known to be gener ally about
‘do KR to 6K.
IX. Notices respecting New Books.
An Elementary Treatise on Spherical Harmonics and Subjects con-
nected with them. By the Rev. N. M. Ferrers, M.4., hRS.,
Fellow and Tutor of Gonville and Caius College, Cambridge.
London: Macmillan and Co. 1877. Crown 8vo, pp. 160.
pee author’s object in this treatise is “‘to exhibit, in a concise
form, the elementary properties of the expressions known by the
name of Laplace’s functions, or Spherical Harmonics.” More than
two fifths of it, comprised in chapters i. and iii., are devoted to
the discussion of the particular case in which the spherical Surface
Harmonie (P,) is a function of » only. This function Mr. Ferrers
calls a Zonal Surface Harmonic; it is the same function as that
which Mr. Todhunter calls a “‘ Legendre’s Coefficient.” The author
investigates briefly and elegantly the chief properties of P,, and then
applies them to determine the potential of various forms of attract-
ing matter. Of these the last which he considers is the followin
comprehensive case :—to find “ the potential of a spherical shell of
finite thickness whose density is any solid zonal harmonic.” These
investigations serve as a foundation for those contained in the
following chapters. Thus, in the fourth chapter the subject of
General, Tesseral, and Sectorial Spherical Harmonics is somewhat
briefly treated. It is well known that the general Surface Har-
monic of the degree 7 consists of 274-1 terms of the form
C cos a sin? g PPCH) S sin o¢ sine 9 UPAe) ,
due dpe
to these terms individually Mr. Ferrers gives the name of Tesseral
Surface Harmonics of the degree 7 and order c; and the last of these
terms, viz. those for which «=, he calls Sectorial Surface Harmonies
of the degree z. In the fifth chapter he notices very briefly the
Spherical Harmonics “of the second kind ;” and in the sixth chapter
he treats of Ellipsoidal Harmonics, a name which he proposes to
give to the functions called by Mr. Todhunter “‘ Lamé’s functions.”
It is well known that one of the standing difficulties of this sub-
ject resides in the proof of the theorem that “any function which
does not become infinite between the limits of integration can be
expanded in a series of Spherical Harmonics.” Thus, Mr. Todhunter
notices four or five proofs, and is not, to all appearance, completely
Notices respecting New Books. 67
satisfied with any one of them. It may therefore be of some in-
terest to give a sketch of the proof adopted by Mr. Ferrers. The
principal discussion takes place with reference to Zonal Harmonics,
though a proof of the general case is given on pp. 93-95. ‘The
method, then, is as follows :—He jirst obtains an expression for the
potential of a spherical shell of uniform small thickness, whose
density is A for the part corresponding to the value of p from 1 to
A, and B for the part corresponding to the value of » from A to —1.
He then extends the same method to the case in which the densities
are A from p=1 to p=),, B from p=), to p=d,, and C from
p=, top=—1. His next step is to take \,=X and A,=A+ dA,
and thus arrives at the result that
ZANMI+...4+(214+1)PA)P(e)+...}
has the value unity from p=dA to p=A+dX, and zero for other
values of p. Nowif we suppose X,, A,,... to be continuous values
of X ranging from 1 to —1, it is evident that the expression
ZO FA) {I+ serie + (20+ 1)P,A,)Pi(e) + ane $ =e
mae Oe a. (22-1 )yP(L)PAu) + . 2.) +...
will equal /(\,) when p=A,, f(A,) when p=d,...; and consequently
the whole expression must be f(z). But it is also plain that
{FO JPAA) + FOP) +. F}a= { APA
and consequently that j(u) can be expressed as a series whose
general term is
1
E+ 1)PKq) { Pad sy) de
the theorem to be proved.
Instructions to Meteorological Observers in India, being the First
Part of the Indian Meteorologist’s Vade Mecum. By Henry F.
Buanrorp, Meteorological Reporter to the Government of India.
Calcutta, 1876.
Meteorology of India, being the Second Part of the Indian Meteoro-
logists Vade Mecum. By Henry F. Branrorp. Calcutta,
1877.
Tables for the Reduction of Meteorological Observations in India. By
Henry F. Buanrorp. Calcutta, 1876,
The works above mentioned constitute a complete Meteorological
Jabrary, and, although written expressly for India, are by no means
restricted in interest to the Indian Peninsula, as they contain re-
marks of general application, especially relative to the instruments
employed in Meteorological research. In the “ Instructions ” each
instrument, including its varieties, is fully described ; and the reader
will find many valuable hints on the use of the Barometer, Ther-
mometer, Actinometer, Hygrometer, Rain-gauge, Wind-vane, and
Anemometer ; also interesting articles on Cloud and Weather obser-
2
6S Geological Society:—
vations, with ITours and Reduction of Observations, the latter
treating very fully of the most recent and exact methods employed.
In the “ Notes on Registration” and “ Rules for Observers” the
amateur will find much important information.
The second part of the Vade Mecum is a very valuable produc-
tion : the portions of greater interest treat of the physical properties
of air and vapour a and the physical geography of India ; the peculiar
conformation of the surface of India, which is lucidly described,
renders the country in relation to Meteor ology an epitome of atmo-
spheric physics. Students will derive much useful information from
their conjoint study. The succeeding portions, on Temperature,
Pressure, Wind and Rain, are full of important information ; and
the concluding part, on Storms, contains the most recent develop-
ment of the Theory of Cyclones, especially the incurvature of the
wind’s motion in storms.
X. Proceedings of Learned Societies.
GEOLOGICAL SOCIETY.
{Continued from p. 475. ]
March 20, 1878.—Henry Clifton Sorby, Esq., F.R.S., President,
in the Chair.
HE following communications were read :—
1. “On the Chronological Value of the Triassic Strata of the
South-western Counties.” By W. A. E. Ussher, Esq., F.G.S.
The author maintained that the general thinning-out of the Trias
in the South-Devon and West-Somerset area as it is traced north-
ward, of which he adduced evidence, proves that this area was not
connected with that of Gloucestershire and the midland counties
until the later stages of the Keuper; and endeavoured to show by a
comparison of sections that the area east of Taunton and south of
the Mendips was not submerged before the deposition of the Lower
Keuper Sandstone, and probably not until the later stages of its
formation, the Quantocks acting as a barrier dividing the Bridge-
water area from the Watchet valley. He thought that a subsidence
progressing from south to north led to carlier deposition in South
Devon, and to a consequent attenuation of the lower beds towards
Watchet and Porlock. Hence the lowermost beds of the Trias of
the south coast are much thicker than their more northerly equi-
valents, and probably were still thicker where the English Channel
now flows, some beds perhaps dating as far back as Permian times.
The presence of numerous fragments of igneous rocks (quartz-
porphyries) in the basement-beds of the South-Devon Trias, and
the absence of known corresponding rocks in the county, led the
author to infer that the cliffs and beds of the early Triassic sea were
composed of such rocks, any undestroyed portions of which would
probably occur cither under the Triassic beds near Dartmoor and
between Newton and Seaton, or in the area now occupied by the
On the so-called Greenstones of Cornwall. 69
English Channel. As continuity is evident only in the upper
division of the Trias, between the area of Devon and Somerset and
that of the midland counties, and there is no unconformity in the
former, the author maintained that the upper marls, upper sand-
stones, and probably the conglomerate and pebble-bed subdivision
of Devon and Somerset, are equivalent in time to the Keuper series
of the Midland counties, and that deposition took place in Devon
and Somerset between Keuper and Bunter times, bridging over the
hiatus marked by unconformity in the Midland counties.
2. «Note on an Os articulare, presumably that of Jquanodon
Mantelh.” By J. W. Hulke, Esq., F.RS., F.G.S.
3. * Description of a new Fish from the Lower Chalk of Dover.”
By EH, Tulley Newton, Esq., F.G.S.
4, “Further remarks on adherent Carboniferous Productide.”
By R. Etheridge, jun., Esq., F.G.S.
5. “The Submarine Forest at the Alt Mouth.” By T. Mellard
- Reade, Esq., F.G.S.
April 3.—Henry Clifton Sorby, Esq., F.R.S., President, in the
Chair.
The following communications were read :—
1. “Onan Unconformable Break at the base of the Cambrian
Rocks near Llanberis.” By George Maw, Esq., F.L.S., F.G.8.
In a paper read before the Society on December 5, 1877 (Q. J. G.
S. vol. xxxiv. p. 137), Prof. Hughes referred to an observation
made by the author in 1867 as to the occurrence near Llanberis of
an unconformable break, indicating the base of the Cambrian, and,
while accepting the asserted existence of pre-Cambrian rocks in
North Wales, placed the base of the Cambrian in a very different
position, and maintained that the appearances described by
Mr. Maw might be accounted for by lateral pressure acting upon
beds of dissimilar texture and unequal hardness. The author had
reexamined the section in question, and maintained his original
interpretation of the phenomena, which he regarded as the
earliest indication of the existence of a pre-Cambrian series. He
accounted for differences observed in the supposed pre-Cambrian
rocks at Moel Tryfaen and Llanberis by regarding them as having
undergone different degrees of metamorphism.
2. “On the so-called Greenstones of Central and Eastern Corn-
wall.” By J. Arthur Phillips, Esq., F.G.S.
In this paper the author extended his investigations of the rocks
formerly mapped as greenstones, from the western (see Q. J. G. 8.
vol. xxxii. p. 155) into the central and eastern districts of Cornwall.
He described in detail various rocks from different parts of these
districts, the examination of which had led him to the following
conclusions. The numerous lavas which occur here, in addition to
the rocks met with in Western Cornwall, are so interbedded with
the slates and schists as to lead to the conviction that they are con-
70 Geological Soctety:—
temporaneous; and, although much altered, they closely resemble
lavas of more modern date. Sometimes they assume a distinctly
schistose character. The crystalline greenstones are more varied
and instructive than those of the western portion of the county ;
some of them are typical dolerites, while others are so altered as to
consist only of a granular indefinite base, traversed by indistinct
microlitic bodies. Their pyroxenic constituent is augite; and
although many would call them diabases or melaphyres, the author
regards it as more logical to regard them as ancient dolerites.
Where these rocks are altered the augite is usually changed into
hornblende and viridite, while the felspar becomes cloudy, and
finally merges into a granular base. The crystals of augite are
often gradually replaced by an assemblage of felted microlites; in
other cases their outlines are preserved whilst their substance is
replaced by hornblende, the rock being thus converted into a wralite-
dolerite or uralite-diabase. When these rocks do not contain augite,
and are to a great extent composed of long bacillary hornblendic
crystals made up of parallel belonites, the ends of which are fre-
quently curved outwards, it is probable that hornblende was an
original constituent of the rock, which is therefore a true diorite.
Slaty or schistose greenstones are less frequent than in the western
districts; but on St.-Cleer Down the “ hornblende-slates ” graduate
imperceptibly from crystalline dolerites into clay-slate: these are
not improbably of igneous origin. Some of the slaty blue elvans
- are identical in chemical composition with the dolerites, and may be
highly metamorphosed ash-beds, although, from some of their cha-
racters, it seems more probable that they are true igneous rocks.
The felspar in the brecciated slates is almost entirely plagioclase,
and is derived from the disintegration of greenstones. With regard
to the age of the rocks described, the author states that they are
generally older than the granite ;. for the vesicular lavas and many
slaty hornblendic bands are evidently contemporaneous with the
slates among which they are bedded, while the latter are often dis-
placed by the granite or traversed by granitic ves; and, further,
the eruptive doleritic rocks which break through the sedimentary
beds never traverse the granite, but are often interrupted by it.
3. “The Recession of the Falls of St. Anthony.” By N. H.
Winchell, Esq. Commiunicated by J. Geikie, Esq., F.R.S., F.G.S.
The author’s purpose in this paper was to arrive at an estimate of
the date of the last glacial period from the rate of recession of the
Falls of St. Anthony, near the junction of the Minnesota and Mis-
sissippi rivers. He stated that the country is covered with deposits
of glacial origin, that between the present falls and Fort Snel-
ling, a distance of eight miles, the existing river-gorge has been
formed since the deposition of the newer Boulder-clay, and that the
old river-valley is filled up with glacial deposits. The gorge is of
very uniform character, being cut through hard limestones resting
on soft sand rock, both lying quite horizontally. The country was
settled in 1856; and the recession of the falls has since been very
On the Geological Results of the Polar Expedition. 1
rapid, its rate having been accelerated by the erection of saw-mills,
dams, &c. From the accounts of various travellers who have visited
the falls in the last 200 years, the author endeavoured to obtain an
estimate of the true rate of recession. Between the visit of Father
Hennepin in 1688 and that of Carver in 1766 he finds a recession at
the rate of 3-49 feet annually, between Carver’s visit and 1856 a mean
annual recession of 6°73 feet, and between Hennepin and 1856 one
of 5-15 feet. The time-estimates for the cutting of the gorge would
be, according to the above means, 12, 103, 6, 276 and 8202 years.
The author considers the data upon which the second of these
numbers is founded the most reliable.
April 17.—Henry Clifton Sorby, Esq., F.R.S., President, in the
Chair.
The following communications were read :—
1. “On the Geological results of the Polar Expedition under
Admiral Sir George Nares, F.R.S.” By Capt. H. W. Feilden, R.A.,
F.G.8., and C. E. De Rance, Esq., F.G.S.
The authors describe the Laurentian gneiss that occupies so large
a tract in Canada as extending into the Polar area, and alike
underlying the older Palzozoic rocks of the Parry Archipelago, the
Cretaceous and Tertiary plant-bearing beds of Disco Island, and the
Oolites and Lias of East Greenland and Spitzbergen. Newer than
the Laurentian, but older than the fossiliferous rocks of Upper
Silurian age, are the Cape-Rawson beds, forming the coast-line
between Scoresby Bay and Cape Cresswell, in lat. 82° 40'; these
strata arc unfossiliferous slates and grit, dipping at very high
angles.
From the fact that Sir John Richardson found these ancient rocks
in the Hudson’s-Bay territory to be directly overlain by limestones,
containing corals of the Upper Silurian Niagara and Onondaga
group, Sir Roderick Murchison inferred that the Polar area was dry
land during the whole of the interval of time occupied by the
deposition of strata elsewhere between the Laurentian and the
Upper Silurian ; and the examination by Mr. Salter, Dr. Haughton,
and others of the specimens brought from the Parry Islands have
hitherto been considered to support this view. The specimens of
rocks and fossils, more than 2000 in number, brought by the late
expedition from Grinnell and Hall Lands have made known
to us, with absolute certainty, the occurrence of Lower-Silurian
species in rocks underlying the Upper Silurian; and as several
of these Lower-Silurian forms have been noted from the Arctic
Archipelago, there can be little doubt that the Lower Silu-
rians are there present also. The extensive areas of dolomite of a
ereamy colour discovered by M‘Clintock around the magnetic pole,
_ on the western side of Boothia, in King William’s Island, and in
Prince-of-Wales Land, abounding in fossils, described by Dr.
Haughton, probably represent the whole of the Silurian era and
possibly a portion of the Devonian.
The bases of the Silurians are seen in North Somerset, and
72 Geological Society.
consist of finely stratified red sandstone and slate, resting directly
on the Laurentian gneiss, resembling that found at Cape Bunny and
in the cliffs between Whale and Wolstenholme Sounds. Above these
sandstones occur ferruginous limestones, with quartz grains; and
still higher in the series the cream-coloured limestones come in.
The Silurians oceupy Prince-Albert Land, the central and western
portion of North Devon, and the whole of Cornwallis Island. The
Carboniferous Limestone was discovered, rising to a height of 2000
feet, on the extreme north coast of Grinnell Land, in Feilden and
Parry Peninsulas, and contains many species of fossils in common
with the rocks of the same age in Spitzbergen and the Parry
Archipelago, being probably continuously connected with the lime-
stone of that area, by way of the United-States range of mountains.
The coal-bearing beds that underlie the Carboniferous Limestones of
Melville Island are absent in Grinnell Land; but they are represented
by true marine Deyonians, established in the Polar area for the first
time, through the determination of the fossils, by Mr. Etheridge.
In America a vast area is covered by Cretaceous rocks. The lowest
division, the Dakota group, contains lignite seams and numerous
plant-remains indicating a temperate flora; overlying the Cretaceous
series are various Tertiary beds, each characterized by a special flora,
the oldest containing subtropical and tropical forms, such as various
palms of Eocene type. In the overlying Miocene beds the character
of the plants indicates a more temperate climate; and many of the
species occur in the Miocene beds of Disco Island, in West Green-
land, and a few of them in beds associated with the 30-feet coal-
seam discovered at Lady-Franklin Sound by the late expedition.
The warmer Eocene flora is entirely absent in the Arctic area; but
the Dakota beds are represented by the ‘‘ Atane strata” of West
Greenland, in which the leaves of dicotyledonous plants first appear.
Beneath it, in Greenland, is an older series of Cretaceous plant-
bearing beds, indicating a somewhat warmer climate, resembling
that experienced in Egypt and the Canary Islands at the present
time. In the later Miocene beds of Greenland, Spitzbergen, and
the newly discovered beds of Lady-Franklin Sound, the plants belong
to climatal conditions 30° warmer than at present, the most northern
localities marking the coldest conditions. The common fir (Pinus
abies) was discovered in the Grinnell-Land Miocene, as well as the
birch, poplar, and other trees, which doubtless extended across the
polar area to Spitzbergen, where they also occur.
At the present time the coasts of Grinnell Land and Greenland are
steadily rising from the sea, beds of glacio-marine origin, with shells of
the same species as are now living in Kennedy Channel, extending
up the hillsides and valley-slopes to a height of 1000 ft., and
reaching a thickness of from 200 to 300 ft. These deposits, which
have much in common with the “ boulder-clays” of English geo-
logists, are formed by the deposition of mud and sand carried down
by summer torrents and discharged into fiords and arms of the sea,
covered with stone- and gravel-laden floes, which, melted by the
heated and turbid waters, precipitate their freight on the mud
Intelligence and Miscellaneous Articles. (a
below. As the land steadily rises these mud-beds are elevated
above the sea. The coast is fringed with the ice-foot, forming a
flat terrace 50 to 100 yards in breadth, stretching from the base of
the cliffs to the sea-margin. This wall of ice is not made up of
frozen sca-water, but of the accumulated autumn snowfall, which,
drifting to the beach, is converted into ice where it meets the sea-
water which splashes over it.
2. “On the Paleontological results of the recent Polar Expedition
under Admiral Sir George Nares, K.C.B., F.R.S.” By Capt. H. W.
Feilden, R.A., F.G.S., and Robert Etheridge, Esq., F.R.S., F.G-.S.
XI. Intelligence and Miscellaneous Articles.
AMMONIO-ARGENTIC IODIDE. BY M. CAREY LEA.
0 Eee silver iodide is exposed to ammonia-gas it absorbs 3°6 per
cent., and forms, according to Rammelsberg, a compound in
which an atom of ammonia is united to two of AgI. Liquid ammonia
instantly whitens AgI; every trace of the strong lemon-yellow
colour disappears. The behaviour of the ammonia iodide under
the influence of light differs singularly from that of the plain
iodide, and will be here described.
The affinity of Agl for ammonia is very slight. If the white
compound be thrown upon a filter and washed with water, the
ammonia washes quickly out, the yellow colour reappearmg. If
simply exposed to the air, the yellow colour returns while the
powder is yet moist; so that the ammonia is held back with less
energy than the water. So long, however, as the ammonia is pre-
sent, the properties of the iodide are entirely altered.
Agl precipitated with excess of KI does not darken by exposure
to light even continued for months. But the same iodide exposed
under liquid ammonia rapidly darkens to an intense violet-black,
precisely similar to that of AgCl exposed to light, and not at all
resembling the greenish-black of Agl exposed in presence of excess
of silver nitrate. (This difference no doubt depends upon the
yellow of the unchanged AgI mixing with the bluish-black of the
changed, whereas in the case of the ammonia iodide the yellow
colour has been first destroyed.)
When the exposure is continued for some time, the intense
violet-black colour gradually lightens again, and finally quite dis-
appears ; the iodide recovers its original yellow colour, with perhaps
a little more of a greyish shade. This is a new reaction, and differs
entirely from any thing that has been hitherto observed. It has
been long known that darkened Agl washed over with solution of
KJ and exposed to light, bleached. This last reaction is intelli-
gible enough ; for K1in solution exposed to light decomposes, and
in presence of AgI darkened by light gives up iodine to the Agel,
and so bleaches it. The above experiment is quite different. The
darkened substance may be washed well with water (during which
74. Intelligence and Miscellaneous Articles.
operation it passes from violet-black to dark brown), and may then
be exposed to light either under liquid ammonia or under pure
water: in either case the bleaching takes place, though in the latter
case more slowly.
If the experiment be performed ina test-tube, the bleaching
under ammonia requires several hours, under water from one to
three days. But if the iodide be formed upon paper, and this
paper be exposed to light, washing it constantly with liquid
ammonia, the darkening followed by the bleaching requires little
more than a minute. In this case, however, the bleaching is not
so complete, perhaps because of the ‘influence of the organic matter
present. The bleaching appears to depend upon the escape of
ammonia; forif the darkened ammonia iodide is covered with strong
liquid ammonia and the test-tube well corked, the bleaching does
not take place.
It became a matter of interest to know whether the darkening
under ammonia was accompanied by any decomposition—whether
the ammonia took up iodine from the silver salt under the action
of ight. For this purpose AgI was precipitated with excess of
KT, and subjected to a long and thorough washing; it was then
exposed for several days to light under strong liquid ammonia.
As AglI is not wholly insoluble in ammonia, the mother- water was
first evaporated to dryness at a heat but little over ordimary tem-
peratures. The traces of residue were washed with water; and
this water gave distinct indications of iodine. The icdine present
is In so small a quantity that it may easily be overlooked; but itis
certainly there. The washing given to the Agi was so thorough
that it seemed impossible to admit that traces of KI remained at-
tached to the AgI; but in order to leave no room for doubt, the
experiment was repeated, using an excess of silver nitrate in
making the precipitation, followed by thorough washing. Iodine
was still found in combination with ammonia; and under these
conditions there could be no doubt that AgI had been decom-
posed.
When Agel is blackened under ammonia in a test-tube, and the
uncorked test-tube is set aside in the dark for a day or two, the
AgI assumes a singular pinkish shade. It thus appears that AgI
under the influence of ammonia and of light gives indications of
most of the colours of the spectrum. Starting with white, it
passes under the influence of light to violet, and thence nearly to
black: this violet-black substance washed with water passes to
brown. The brown substance covered with ammonia and left to
itself in an open test-tube becomes pinkish in the dark, yellow in
sunlight. These curious relations to colour which we see in the
silver haloids, from time to time exhibiting themselves in new ways,
seem to give hope of the eventual discovery of some complete
method of heliochromy.—Silliman’s American Journal, May 1878.
Philadelphia, March 25, 1878.
Intelligence and Miscellaneous Articles. 1D
ON THE PRODUCTION OF PLATEAU ’S FILM-SYSTEMS.
BY A. TERQUEM.
M. Plateau, by the use of a mixture of soap-water and glycerine,
has produced liquid films of a certain extent, and has thus been
able to verify most of the Jaws respecting the form of the surfaces
which constitute the boundaries of liquids whose molecules are
subjected only to their reciprocal actions.
I pomted out, some years since, that for the glyceric liquid a
mixture of soap-water and sugar might be substituted, the latter
substance having, especially, like glycerine, the effect of augmenting
the viscosity of the liquid, and preventing it from flowing away too
rapidly. The production of the film-systems of M. Plateau de-
mands the employment of a great quantity of liquid if polyhedra be
used the edges of which are of large dimensions.
I have thought that large films of liquid might be easily obtained
by bounding them in part by flexible threads instead of using for
the purpose rigid wires only.
Thus, if two horizontal rods be joined by two vertical and equi-
distant flexible threads, on dipping the system in the saponaceous
. liquid and slowly lifting it out again, we get a vertical plane film
bounded above and below by the two rods, and laterally by the
flexible threads, which take the form of arcs of a circle. The radius
of the circle evidently depends on the stretching weight. It is
easily demonstrated that, if we designate by / the distance between
the two threads, by R the radius of the are constituted by them,
by ¢ the angle made with the vertical by the tangent of the arc at
the poimt of attachment of the thread to the lower rod, by f the
superficial tension of each of the two surfaces of the liquid film,
and by p the stretching weight, we have the relation
p=2f(l+25 cos #).
Eyery thing happens, therefore, as if the distance between the
threads were equal to that between the centres of the two ares, the
tension of the threads being omitted.
I of course submitted this formula to a series of experimental
verifications, by measuring with the cathetometer the diminution of
the vertical distance between the two horizontal rods produced by
the existence of a liquid-film between them.
If H is the initial length of the threads, and H’ the new vertical
distance of the horizontal rods, to find the radius of the circle and
the angle ¢ we haye only to solve the two equations
H’=2RK sin ¢ and 2R¢=H,
whence we derive
H'¢=H sin 9.
As the angle ¢ is generally very small, this transcendental equa-
tion can be solved with sufficient approximation by substituting
, .
o— e for the sine.
76 Intelligence and Miscellaneous Articles.
Proceeding thus, I have obtained, as the mean of a number of
determinations, the number 2°79 milligrams for the yalue of f. On
the contrary, measuring the sseae al tension by employing the
drop-counter, I obtained the value 3°47 milligr., considerably higher
than the preceding. This difference, which “surprised me at first,
too great to be attributed to errors of experiment, would need to
be bane led by other similar determinations made upon other
liquids, of which there are but few capable of forming films of large
extent. It may have been due, according to M. Duclaux (to whom
I submitted the difficulty), to the circumstance that in a very thin
film like that of soap-solution, the superficial tension has a lower
yalue than in the free surface of the same liquid in indefinite mass
—which would indicate that the thickness of the liquid layer in
which the molecules have the abnormal arrangement which produces
superficial tension exceeds half the thickness of the soap-film.
Thanks to the same arrangement, I have been able to execute
other experiments suitable for showing the superficial tension of
liquids. Moreover, on replacing, in Plateau’s polyhedra (such as the
tetrahedron, the cube, the octahedron, &c.), a certain number of
rigid rods by flexible threads, we can produce with great facility,
and with a minimum quantity of liquid, laminar systems of consi-
derable dimensions and a certain number of surfaces possessing the
characteristic property that their mean curvature is ntl.—Comptes
Rendus de Académie des Sciences, April 29, 1878, tome lxxxvi.
pp. 1057, 1058.
ON THE MAGNETIC ROTATION OF THE PLANE OF POLARIZATION
OF LIGHT UNDER THE INFLUENCE OF THE EARTH. BY HENRI
BECQUEREL.
In the course of my investigations on magnetic rotatory polari-
zation, I have been led to the direct estimation of the action of ter-
restrial magnetism upon various substances. This action can be
very neatly made evident by an experiment which seemed to me
sufficiently interesting to be communicated to the Academy.
Between a Jellet polarizer and an analyzer furnished with a tele-
scope and mounted on a divided circle is placed a tube of half a
metre length, terminated by parallel glass plates and containing
bisulphide of carbon. At the two ends of the tube, plane mirrors
arranged as Faraday arranged them gave several successive reflec-
tions of the luminous ray, and thus augmented the observed rota-
tion. In the present experiment the second reflection could be
viewed; the ray had therefore traversed the tube five times, corre-
sponding to a thickness of 2°5 metres of bisulphide of carbon. The
source of light was a pipe with oxyhydrogen gas. A great amount
of light was lost by absorption and by the successive reflections ;
and the rays transmitted to the eye were chiefly the yellow rays.
The entire system was firmly fixed to a horizontal copper rule, and
Intelligence and Miscellaneous Articles. 77
could turn about a vertical axis so as to orient the luminous beam
in various directions.
With this arrangement it is ascertained that, if the system be
made to coincide in direction with the plane of the magnetic meri-
dian, the same position of the polarization-plane is not obtained
whether we look towards the south or towards the north; a great
number of closely concordant measurements gave an angular differ-
_ ence of about 6"5 between the two positions. On the contrary,
if we place ourselves in a position perpendicular to the magnetic
meridian, we get the same direction of the plane of polarization
whether we look towards the east or towards the west; and this
position is the bisectrix of that which we have in viewing towards
magnetic north and south.
It may hence be concluded that the angular difference observed
is a rotation of the plane of polarization of the light, due to the
action of the earth; the number 65 measures the double of the
rotation for yellow light and in the special conditions of the experi-
ment. The direction of this rotation is the same as that of the
rotation of the earth; it is the direction of an electric current
which, on the hypothesis of Ampere, would give rise to the pheno-
mena of terrestrial magnetism.
It must be remarked that the number we have given only refers
to observations made in the laboratory of the Muséum d’Histoire
naturelle, in proximity to more or less considerables masses of iron.
To ascertain with more precision the action of the globe, and to
utilize this method for estimating the intensity of the earth’s mag-
netism, it would be necessary to use the same precautions as for
ordinary observations of terrestrial magnetism, and to amplify the
phenomenon by taking a longertube. This is what I am at present
engaged in.
The system arranged as above indicated exhibits remarkable sen-
sitiveness to the action of magnetism: an ordinary bar magnet,
held in ‘the hand, and brought parallel near to the tube, first in one
direction, then in the other, is sufficient to make manifest a rotation
of the plane of polarization that may attain to upwards of 1°.
It is interesting to compare this direct measurement with an esti-
mation, made by Mr. Gordon*, of the magnetic rotation produced
by 1 centim. of bisulphide of carbon under a magnetic action equal to
unity. The result found by calculating from this number the action
of the terrestrial horizontal component is, that 2-5 metres of bisul-
phide of carbon should give, with yellow light, a single rotation of
3'-8—instead of 3°25, which results from our direct observation.
The difference may be due to exterior perturbations. If we adopt
the latter number, we see that, under the conditions in which we
have placed ourselves, the double rotation of 1 metre of bisulphide
of carbon would be 26, and that of 1 metre of water 0"8.— Comptes
Rendus de VAcadémie des Sciences, April 29, 1878, tome ]xxxvi.
pp. 1075-1077.
* Philosophical Transactions, 1877, Part I,
78 Intelligence and Miscellaneous Articles.
ON THE CRYSTALLIZATION OF SILICA IN THE DRY WAY.
BY P. HAUTEFEUILLE.
In 1868 M. vom Rath described, in a trachyte, some small lamelli-
form crystals, of which he made a new species, tridymite. The
observations of that accomplished mineralogist prove that tridymite
is silica crystallized under a form different from that of quartz, and
possessing a lower density than that species. Like sulphur, arse-
nious acid, flowers of antimony, &c., silica crystallizes under two
incompatible forms. It can be prepared, as I shall prove, in the
dry way, under both these forms.
The only known process for crystallizing silica in the dry way we
owe to M. G. Rose; it is based on the employment of the phos-
phorus-salt, and permits only tridymite to be prepared. The alka-
line tungstates can, with advantage, be substituted for the phos-
phates ; for they permit crystallized silica to be obtained, at pleasure,
either under the form of tridymite or under that of quartz.
Reproduction of Tridynite—Amorphous silica, kept at the melt-
ing temperature of silver in tungstate of sodium, crystallizes in a
few hours. After the cooling, treatment with water dissolves the
alkaline tungstate and lays bare a crystalline sand, the weight of
which is, within a few thousandths, that of the silica employed.
The principal crystallographic and optical characters of tridymite
are easily verified in the crystals obtamed by this process. They
are thin hexagonal scales, mostly piled one upon another to the -
number of three or four*. Upon the most regular scales one or two
half-scales are frequently lodged.
By the long-continued action of tungstate of sodium at a nearly
constant temperature of 1000° C., the tridymite can be obtained in
thick scales. These crystals, mixed with large lamellae grouped
according to one of the two laws alluded to, are hexagonal tables
with faces free from strie?.
A. pencil of parallel-polarized light is not depolarized when it
passes quite perpendicularly through these hexagonal scales, what-
ever the thickness.
The density of the crystals prepared in platinum vessels, with
pure tungstate of sodium, and with silica contaming neither alu-
mina, nor oxide of iron, nor magnesia, 1s 2°30 at 16° C.; Vom
Rath, operating on some crystals containing about 2 per cent. of
oxides, found 2°326, 2°312, and 2°296 for the density at 16°. The
determination made upon an absolutely pure product proves that
silica in the form of tridymite possesses a density certainly inter-
mediate between those of quartz (2°65) and fused silica (2°20).
Tridymite is more readily attacked than quartz by reagents both
in the wet and the dry way. Tunegstate of sodium itself can
destroy the tridymite. Thus, at a temperature much above 1000°,
* These scales are often partly corroded, like those met with in the tra-
chytes of Mont Dore.
+ The ratio : appears to be constant and equal to 5
Intelligence and Miscellaneous Articles. 79
there is formed at the expense of the lamelliform crystals a silicate
disseminated in droplets in the fused salt. This destruction of the
tridymite is only temporary, if the silicate be maintained in the
liquid bath formed by the acid tungstate, at a temperature between
900° and 1000°; for this silicate then undergoes a decomposition
which regenerates the tridymite. This sort of precipitation in the
dry way demands much more time than the crystallization of amor-
phous silica. This is why it is more advantageous to heat silica
with tungstate of sodium than to decompose an alkaline silicate by
tungstic acid.
_ he destruction of tridymite, and subsequent precipitation of
silica in the form of lamelle, permit the part played by the tungstate
of sodium in the act of crystallization to be analyzed. The alkali
of the tungstate attacks the silica, producing an alkaline silicate ;
and the tungstic acid retakes at a lower temperature the alkali
which the silica had taken from it. These two reciprocally inverse
actions take place successively when the temperature oscillates be-
tween certain limits. They suffice to explain the crystallization,
without it being necessary to invoke the solubility of silica in the
fused salt; for these reactions are perfectly comparable with those
which determine the crystallization of the sesquioxide of iron when
it is heated in gaseous hydrochloric acid.
Although I cannot at present compare the results furnished by
the method I have just made known with those which can be ob-
tained by a judicious application of M. G. Rose’s method, I will
notice this fact, that the preparation of tridymite by means of tung-
state of sodium does not require a temperature so elevated as that
which is necessary when acid phosphate of sodium is employed.
The phosphoric salt and the tungstate of sodium are both minerali-
zers of silica; but the latter salt exerts a more energetic action than
the former, even at a less-elevated temperature—which permits it
to be employed for reproducing the numerous more or less fusible
silicates which are associated with silica in the rocks.—Comptes
Rendus de VAcadémie des Sciences, May 6, 1878, tome Ixxxyi.
pp. 1133-1135.
OUTLINES OF THE ACTINIC THEORY OF HEAT.
. BY PROF. C. PUSCHL.
In the present form of the mechanical theory of heat, and spe-
cially in the kinetic theory of gases, the sum of the vires vive of
the ponderable atoms of a body in motion among themselves is re-
garded as the quantity of heat of the body; while the sum of the
vires vive of the ether contained in the body is neglected, and it is
assumed that this medium exerts no sensible influence on the
motions of the atoms. ‘This presentation the author holds to be
inadequate. Itis remarked that a hot body may be cooled not
merely by contact with colder bodies, but also by radiation, and
that the velocity of such a cooling is not always inconsiderable, but
under fayourable circumstances is so great that many physicists
80 Intelligence and Miscellaneous Articles.
occasionally note it as astonishing. It is evident that the atoms
of a heated body give up vis viva to the wther ; in other words, the
wther takes from the moving atoms of the body a part of their
velocity ; it therefore, indeed, exerts upon them an influence which
acts as a resistance checking their velocity, and is by no means in-
considerable, but of relatively great intensity. Conversely, a body
ean receive heat not merely by contact with warmer bodies, but
also by radiation from without. Its atoms then take vis viva from
the ether ; that is, the ether imparts to the atoms an increase of
velocity. Consequently, in a body cooled by radiation outwards,
the motions of its atoms are rendered slower by the eether ; in one
erowing warmer through radiation from without the motions of its
atoms are accelerated ; in a body which under equal radiation out-
wards and inwards maintains a constant temperature the forces of
the ether retarding and accelerating the motions of its atoms must
on the whole maintain equilibrium; and in consequence of the
rapid change of atom-motion into radiant heat, and of radiant-heat
into atom-motion, these forces must, for every temperature that
occurs, possess great intensity. The Aietic theory, which takes no
account of such forces, is, according to the author, incapable of
anyhow rendering intelligible a rapid annihilation or generation of
atomic velocities by mere generation or annihilation of ether-undu- _
lations, whereas to him the actinic theory, touched upon in the
present memoir, appears to correspond perfectly with the above
conclusion. According to it an essential portion of the heat of a
body consists of radiating heat, which is accumulated by diffusion
between the atoms, and, from the extreme minuteness of the mean
radiation-distance, is concentrated to an enormous intensity. The
cether, thus put into most vehement vibration, exerts at the same
time, upon the atoms floating in it, through the relative differences
of radiation (7. ¢. through the difference of its elasticity-forces on
the average existing on opposite sides of the opaque atoms irradi-
ating one another, and changing with their positions), proportion-
ally intense motive forces, by which they are alternately retarded
and accelerated according to their momentary positions ; and conse-
quently their vires vive are to a corresponding amount expended on
the production of sther-undulations, by the consumption of which
they are again replaced.
According to Pouillet’s determination of the intensity of the
solar radiation, it is calculated that the mean square of the velocity
of the ether for direct sunlight is to that of the ether in water at
0° C. approximately as 1: 273,000,000,000,000; and accordingly
it appears to the author possible that the atoms of a body recipro-
cally exert very intense accelerative forces (according to the hypo-
thesis, in the sense of attractions) by the heat-rays which they
emit to one another; while the corresponding force which any
available source of heat exerts upon a body irradiated by it is under
all circumstances immeasurably little.—Kaiserliche Akademie der
Wissenschaften in Wien, mathematisch-naturwissenschaftliche Classe,
April 4, 1878.
THE
LONDON, EDINBURGH, axp DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FIFTH SERIES.]
ARGUS T 1878.
; XII. On the Figure of the Earth.
By Colonel A. R. CrarKke, C.B., F.R.S.*
HE fraction s},, which, in round numbers, is taken to
express the ellipticity of the earth, has apparently a ten-
dency, as far as it is deduced from the measurement of terres-
trial arcs, to increase as the data of the problem are added to.
The =4,, obtained by Airy and Bessel from the very imperfect
data of forty years back, was replaced, on the completion of
the Russian and English arcs in 1858, by 54,3; and the geo-
detic work recently completed in India indicates a further
increase of the fraction, and so an assimilation to that obtained
from pendulum observations. The data of the Indian are of
21°, as used in 1858, were vitiated by a serious uncertainty as
to the unit of length used by Colonel Lambton in the mea-
surement of the southern half of that arc. It appears from
the Annual Reports of Colonel Walker, C.B., F.R.S., Surveyor-
General of India, who has been for many years Superintendent
of the Great Trigonometrical Survey of India (reports which
are replete with scientific interest), that this southern portion
of “the Great Arc,’ as Colonel Everest delighted to call it,
has been completely remeasured and the latitudes of a great
number of stations in it determined. A complete meridian
chain of triangles has also been carried from Mangalore on the
west coast, in latitude 12° 52’ and longitude 75° H., to a point
in latitude 32°. As this triangulation is rigidly connected
with the are from Cape Comorin to Kaliana, in 78° EH. longi-
tude, it may be considered that the Indian Arc is now 24° in
length.
* Communicated by the Author.
Phil. Mag. 8. 5. Vol. 6. No. 35. Aug. 1878. G
82 Colonel A. R. Clarke on the Figure of the Earth.
Colonel Walker’s last Report contains the details of eleven
determinations of difference of longitude by electro-telegraphy,
with the corresponding geodetic differences. The differences
of longitude are between Mangalore and Bombay on the west
coast, Vizagapatam and Madras on the east coast, and Hydra-
bad, Bangalore, and Bellary in the interior. Bellary holds a
somewhat central position in the polygon formed by the other
points ; Mangalore and Madras are very nearly in the same
latitude ; and Bangalore is midway between them. These dif-
ferences of longitude have been determined with every refine-
ment of modern science, and, taking into account the uncer-
tainty of local attraction, may be considered little, if at all,
inferior to latitude-determinations. ‘‘ When the operations
were commenced,” says Colonel Walker, “ I determined that
they should be carried on with great caution and in such a
manner as to be self-verificatory, in order that some more satis-
factory estimate might be formed of the magnitudes of the
errors to which they are liable than would be afforded by the
theoretical probable errors of the observations....... The
simplest arrangement appeared to be to select three trigono-
metrical stations A, B, C, at nearly equal distances apart on a
telegraphic line forming a circuit, and, after having measured
the longitudinal arcs corresponding to AB and BOC, to mea-
sure A C independently as a check on the other two ares.”
The eleven determinations of difference of longitude between
the seven points named above give thus five equations of con-
dition among themselves, which enable us to assign a system
of minimum corrections to the several determinations. The
following Table contains the observed differences, together
with the computed corrections, half-weight being given to the
first two determinations, which were the earliest made, and
which are affected with some slight defects, then undiscovered,
in one of the transit-instruments :—
Electro-telegraphic
be}
tae)
©
-
Are. difference of lon- Corrections.
gitude.
Oo U di
1872-73. | Madras—Bangalore. 2 39 45°63 +9-010
\ Bangalore—Mangalore. 2 44 11°54 +1:690
1875-76. | Hydrabad—Bombay. 5 42 12°74 —0°452
i Bellary—Bombay. 4 6 44:39 —0'393
Hydrabad—Bellary. 1 35 28:25 +0-040
" Madras—Hydrabad. 1 43 40°38 —0:412
; Madras—Bellary. 319 8:45 —0°192
E Bangalore—Bellary. | 0 39 20:46 +0:160.
| 1876-77. | Vizagapatam—Madras. 3 2 26°78 +0:401
- Vizagapatam—Bellary. 6 21 35°84 —0-401
2 1 50°54 +0°845
23 Mangalore—Bombay.
Colonel A. R. Clarke on the Figure of the Earth. 83
The following Table contains in the second column the geo-
detic longitudes as given by Colonel Walker, computed on
Kverest’s elements ; viz. equatorial semlaxis a’ = 20922932,
MS oo a? ho semiaxis ¢ =20853375 :—
Geodetic longitudes
Geodetic longitudes on
a on Everest’s spheroid. rena |Sgitiajongines| Gendt logins on | spheroid.
3°
Vizagapatam ......... 83 19 47-00 43-05—2:320 w—2-401 v
Phydieiad.:........... 78 33 38°50 37°51 —0°580 w—0°600 v
BOWbay®..3........00.. 72° 51 16°23 18°80+1°511 w+ 1-563 v
Mangalore............ 74 53 10: : 11:444.0°742 w+0°768 v
Bangalore ............ CE 3T, 20-7 27-32 —0:234u—0°242 0 |
SOPs)... 2.2... | 80 17° 21° 87 19°85 —1:184 u—1:226 0 |
EMA voce se secss. | 76 58 697 Pete | oer pe
The third column contains (omitting degrees and minutes).
the same longitudes on the supposition that the elements are
— 20855500 (1 + jaum
ons i +vsin 10”,
ata 590
which I take for the undetermined elements of the spheroid
most nearly representing the mean figure of the earth. -The
terms in uw and v added to the longitudes in the above Table
are thus obtained:—Let A be the central point Bellary, B
one of the other stations, Q the point in which the normal at
A meets the axis of revolution; let @ be the angle subtended at:
Q by the curve distance A B, this curve being the intersection
of the spheroid with the vertical plane at. A. passing through
B; then, if A B=s, and ¢, be the latitude of A, and & the
azimuth of B at A,
_§ 1—
~ e(1+ny tay
Thus for any variations-of m and e¢ a determinate variation .
arises for @ which may be expressed in the above wu and v.
Again, the variation of 0 gives rise to a variation of w, the
longitude of B computed from A, viz. do=sin B sec p. 08,
where B is the azimuth of the curve A B-at-B, and ¥ is the
inclination of the line QB to the equator.
Let us suppose the easterly component of the local attraction
at A is 7,; then, longitudes nae measured positively towards
2
(1+2n cos 26, + n)*(1 + 2n@? cos” d; cos” a).
84 Colonel A. R. Clarke on the Figure of the Earth.
the east, the observed or astronomical longitude of A must
receive the correction 7; sec ¢; ; so that of B receives a corre-
sponding correction v2 sec @, ; and the difference of longitude
as observed (i. e. of B east of A) must receive the correction
yg sec dy—y, sec dy. The astronomical difference of longitude
thus corrected is to be equated to the corresponding difference
of geodetic longitudes as expressed in terms of wu and v; then
multiplying by cos d2, we get an equation of the form
Yo=Y1 Sec Py Cos ho +au+ Buty.
The above data afford six such equations. Properly speaking,
as a direct check upon these equations, we should add to them
the six equations of a similar character which would result
from a comparison of the observed directions of the meridian
at the seven stations we are considering. I have not, however,
the quantities for forming these equations.
Besides the data contained in his last annual report, Colonel
Walker has kindly given me provisional results for his great
ares (or arc, for we may consider them as one)—not final
results, but yet not likely to be materially altered. The Indian
Triangulation contains a vast number of astronomical stations ;
but in the problem of the figure of the earth it is not de-
sirable that the latitude-points in one of the arcs should be
very much more numerous than in the others. The Russian
arc of 25° has thirteen astronomical stations ; the English has
thirty-four ; but only fifteen are used in this investigation,
this number including those of the French arc: the length of
the conjoined English and French ares is 22°.
Taking fourteen evenly distributed latitudes in the Indian
arc, they require the corrections shown in the following Table
(the column on the left gives the approximate latitude of each
station) :—
oO /
Oo eras hid —4°14—8°562u+5:102v+0°997 a
30 29 tee Ae —0°25—7:969u+4°988v+0°998 z
4.4 aes 0 ee +3°37—7°662u+4°9120+0°998 a
ABS 1 a —1°98—7:092u+4°742v+0°998 x
7 RAS Ia oe + 2°22 —6°312u+4°446v+0:998 a
7 NS (SSSR a —0:°98—3°725u+4179v+0:999 x
OT heii tag Me —2:17—4:970u+ 3° 7830 +0:°999 «
2 AA a ~~ +5'°51—4:511u+3°5140+0°999 &
LS eoiemaeee: + 2°65 —3'°545 ut 2°886v+0:999 &
LG AO ss ee + 6°09 —2°865 u+ 2°397v +0°999 x
TA Do eee — 1°75 —2°418u+2:057v + 1:000 x
dG hake ae +5°18—1°726u+1'502v+1:000 x
LG Poe sere + 0°43 —1:005 w+ 0°893v + 1:000 a
Bie ae ATA 0:00 0:000u 0:000v+ 1-000 a
Colonel A. R. Clarke on the Figure of the Earth. 85
It is interesting to consider the influence of each of the
three great arcs in determining the semiaxes of the earth.
The northern ten degrees from 60° to 70° of the Russian are
determine 3a—43c; the ten degrees in England from 50° to
60° determine a; the ten degrees in France from 40° to 50°
determine 4a+43c; the ten degrees in India from 10° to 20°
determine —11a+24c. Or, more precisely, taking the arcs
in combination, suppose each arc to have six astronomical sta-
tions, equidistant, 5° apart in the Russian and 4° apart in the
two other ares ; and let these arcs be combined by the method
of least squares to determine the mean figure of the earth.
Let 0,...0, be the latitudes of the stations in the Russian arc,
numbered from north to south ; ¢,...¢, those of the Anglo-
French; y,..., those of the Indian ; then, supposing these
expressed in seconds, a involves, in feet,
Russian. Anglo-French. Indian.
—117°6 0, —76°2 py —d Avy,
63-7 0, —40°7 b, +0°3%b,
— 14-56; — 88¢5 +3-0Ws
4+ 29:30, +1914, 43-2,
+ 67°36; +432 ds + 1:2,
+ 99°36, + 63-4 de —2-3 Wr,
and ¢ involves
Russian. Anglo-French. Indian.
—26°5 6, —39°6 dy —112°5 Why
—23-0 0, — 28-9 b, — 711,
—14°5 0, —14:6 ds — 26:7 abs
a 0'6 Ga sm Bes, dy ae 20°3 Wry
+19°36; + 26:3 d; + 69°55
+45-4 0, + 52:8 de +1203,
From which we see at a glance the effect that would result
from an alteration of any one of the latitudes.
It seems unnecessary to give here the expressions for the
corrections to the stations of the Hnglish, the Russian, Cape-
of-Good-Hope, and Peruvian arcs, which are to be found in
a paper on the Figure of the Earth, in the Memoirs of the
Royal Astronomical Society for 1860, pp. 34, 35. It is only
necessary to remark that the sign of u in those expressions is
to be changed, and that I have now added three points to
the Anglo-French are as there used. Making now the sum
of the squares of the corrections, or local attractions, at the
forty-nine latitude stations and the seven longitude stations
86 Colonel A. R. Clarke on the Figure of the Earth.
a minimum, the resulting equations in w and v are
O= +56°6615 +301°7624 u + 126°9252 v,
O= —16°9677 + 126°9252 w+ 221:4307 0;
* u=—0°2899; v= +0°2428.
From these we have, in feet of the standard yard,
a= 20926202,
c= 20854895, (E)
bh Pate | .
a 293-465
And this is the spheroid most nearly representing the mean
figure of the earth.
But the Indian observations are not well represented by this
figure. The southern station of the arc requires a large ne-
gative correction of —3’"14, and the northern station a still
larger negative correction of —3’"55. Among the longitude
stations, there is left at Bombay a westerly deflection of
4-05, and at Madras an easterly deflection of 4-50. The
longitudes, in fact, require a larger value of a and a larger
value of the ellipticity: while the form of the meridian-are
requires a smaller equatorial radius and a smaller ellipticity.
In other words, so far as the observations we have at present
to consider indicate, the surface of India does not seem to be-
long to a spheroid of revolution: if it does, we must admit
large deflections towards the sea at Cape Comorin, at Bombay,
and at Madras. |
But we may obtain more strictly the form of the Indian are
from the sixty-six latitude stations it contains. Not to confine
the arc to an elliptic form, let it be such that its radius of cur-
vature in latitude ¢ is expressed by the equation
p=A’+2B’cos 26+ 2C’ cos 4¢,
a curve which includes the ellipse as a particular case. In
order to determine A, B,C, we must apply symbolical correc-
tions to the observed latitudes, and make the sum of the
squares of these corrections a minimum. As the result of a
very long calculation, the actual equation is found to be
p=20932184:1—167963'6 cos 26+ 28153:2 cos4g. . (H’)
The correction to the latitude of the southern point is +161,
and to the northern —0/’"81; and, generally, the residual cor-
rections or apparent local attractions are free from any appear-
ance of law, so that the above equation may be taken as very
closely representing the form of the sea-level along the meri-
dian of India, The geodetic operations give us the form of the
Colonel A. R. Clarke on the Figure of the Earth. 87
curve in the shape of its intrinsic equation; and the absolute
direction of the curve with reference to the polar axis is given
by observing that, at its southern extremity, the actual direc-
tion of the surface of the sea makes an angle of 1/61 with the
curve. Now, the observed latitude of the southern point being
8° 12’ 10-44, the direction of the normal to our curve (H’)
at the same point makes the angle 8° 12’ 12/05 with the plane
of the equator, which determines the curve as to its absolute
direction. So also, on referring the Indian meridian to the
ellipse (E), determined above as representing the mean figure
of the earth, this ellipse at the southern point of the Indian are
has its normal inclined to the equator at an angle equal to
observed latitude —3’’:14, or 8° 12’ 7°30. We can now trace
the difference of the forms of the curves (H, EH’) by making
them coincide at the southern point of the are. The selection
for this purpose of the southern point is quite arbitrary; any
other station would have done equally well. Multiply the
expression for p, the radius of curvature, by —sing@d®@ and
then by cos¢dd, and integrate; thus we get the following
values of the coordinates of the curve (H’) in the meridian
plane, parallel and perpendicular to the equator :—
x = (A’—B’) cos 6+14(B/—C’) cos 86+4C' cos564+H, (B’)
y =(A/ +B’) sind + 4(B/ + C’/) sin864+1C' sindd+K,f
when H and K are disposable constants. The corresponding
coordinates of the ellipse (EH) may also be written in the form
z=(A—B) cos ¢+4(B—C) cos 86+4C cos 5¢, (E)
y= (A+B) sin¢d+4(B+C)sin364+1C'sindd.J -
The values of H and K are now to be determined by put-
ting @=8° 12’ 12”:05 in the expressions for 2 and y’, and
o=8° 12’ 7-30 in those for # and y; then putting r=2’,
The normal distance between the curves (H, E’) in latitude
@ is C=(«/—2x) cos$+(y'—y) sind: this expresses the dis-
tance by which a point in (B’) is further from the centre of
the earth than the corresponding point of (E). Put A/—A=E,
B/—B=F, C’—C=G;; then
C= E—2F cos 26— Geos4¢6+Heos¢+Ksin ¢.
The following Table shows, according to this formula, the
departure of the curve best representing the Indian meridian
from that best representing the earth asa whole. I add also
similar quantities for the Russian and Anglo-French ares ; the
only difference is that, in the case of these last arcs, the local
88 Colonel A. R. Clarke on the Figure of the Earth.
curve is simply that elliptic curve which best represents the
observations.
Indian. Anglo-French. Russian.
Lat. &. Lat. Ge Lat. G:
ft. Z ft. a ft
10 —11°8 40 + 8&1 48 —2:7
12 —18°5 42 +15:7 50 —37
14 —19-6 44 +18°9 52 —40
16 —16-7 46 +18°8 54. —37
18 —111 48 +16:1 56 —2°9
20 — 43 50 +118 58 —18
22 + 21 52 + 68 60 —05
24 + 69 54 + 1:9 62 +08
26 + 9:3 56 — 18 64 +2:0
28 + 83 58 — 36 66 +3]
30 + 38 60 — 2:7 68 +38
32 — 42 70 +41
Here we see the local form of the meridian sea-level in
India with reference to the mean figure of the earth. Sup-
posing that there is no disturbance of the sea-level at Cape
Comorin, then from that point northwards a depression sets in,
attaining a maximum of nearly 20 feet at about 14° latitude ;
thence it diminishes, disappearing at about 21°. An elevation
then commences, attaining at 26° about nine feet; then this
elevation diminishes, and becomes a small depression at 32°.
This deformation may or may not be due to Himalayan attrac-
tion; at any rate we have here an indication that that vast
tableland does not produce the disturbance that might a priori
have been anticipated. This is in accordance with the fact
that there is an attraction seaward at Mangalore and Madras,
and slightly also at Bombay: and I think we have here a cor-
roboration of Archdeacon Pratt’s theory, that where the crust
of the earth is thickest there itis least dense ; and where thin-
nest, as in ocean-beds, there it is most dense.
The Anglo-French are shows a deformation nearly as great
as the Indian—though, after all, the linear magnitude in either
case is certainly as small as could be expected. One cannot
help remarking here, that the remeasurement of the French
meridian-are, with all modern refinements of observation and
calculation, with a considerable increase in the number of lati-
tude stations, would be a vast service to science.
With the elements of the earth’s spheroidal figure at which
we have arrived above (E) the following results are obtained.
The radii of curvature in and perpendicular to the meridian in
latitude ¢ being p, p’, their values in standard feet are,
p =20890564 — 106960 cos 26 + 228 cos 4¢,
p'=20961932— 35775 cos26+ 46 cos 4¢.
Colonel A. R. Clarke on the Figure of the Earth. 89
The lengths of one degree in and perpendicular to the meri-
dian, viz. 5, 6’, are
5 =364609-12 —1866°72 cos 26 + 3:98 cos 4¢,
6’ =365854:72— 624:40 cos 26+ 0°80 cos 4¢.
Also the following :—
log Eg
p sin
=7°994477820 + °002223606 cos 26—°000001897 cos 4¢,
log qn
p sin
= 7°992994150 + 000741202 cos 24 —°000000682 cos 4¢.
Having seen that the surface of India cannot be represented
by a spheroid of revolution, it is necessary now to inquire
what ellipsoid best represents all the observations as the figure
of the earth. On this hypothesis, the equator being no longer
a circle, the ellipticity of a meridian is not a constant, but isa
function of the longitude—say J, from Greenwich. We have
consequently to replace our previous v by v+w cos 2/+ 2 sin 21;
and the longitude /’ of the greater semiaxis of the equator will
be given by the equation wsin 2//—zcos 2l’/=0. But this
substitution cannot be made in the longitude-equations—they
no longer hold good, having been formed on the distinct sup-
position of the earth being a surface of revolution, and they
must now be put aside. If the earth should be found to be
really ellipsoidal, this circumstance will involve a considerable
‘increase of the labours of the geodetic computer. The “ meri-
dian”’ on an ellipsoid is somewhat vague. If it be taken as the
locus of points of constant longitude , its equation in combi-
nation with that of the ellipsoid is
Casinea—a7y cos.@=0. 214 vy. x 1 C1)
But it may also be defined as a line on the ellipsoid whose
direction is always north and south. Suppose that a point
2 2
on the surface of the ellipsoid - + =
towards a given fixed point a’y/z’, and let it be required to
determine the nature of the curve traced by the moving point.
Two consecutive points on the curve having coordinates 2, y, z,
a+tdz, y+dy, 2+dz give the condition
poy ede 0. Pa)
z
eae 1 moves always
The equation of a plane passing through 2, y, z and 2’, y’, 2’ is
A(a' —a) + Bey’ —y) + C(e’ —z) =0.
90 Colonel A. R. Clarke on the Figure of the Earth.
This plane is to contain the normal at z,y,z, and the point
vt+dz,y+dy, ¢+dz, which conditions give two other equations
in A, B, C; and eliminating these symbols we have the dif-
ferential equation of the required curve expressed by the de-
terminant
Saat > / ee (peer
A north-and- south line 1 is a particular case of this curve,
viz. when «’=0, 7/=0, 2’= ; then the equation becomes
Cy da—biady=Q, |... sion gees
of which the integral is
ita 1)
This is nota plane curve ; and at each point its direction makes
a definite angle with the meridian as expressed
by (1). Let 8 be any point on the surface of pag
the ellipsoid, say in that octant where «, y, 2 are
all positive; let M be a point indefinitely near S
on the same meridian (1), N a point on the north
line (5), Pa point on the parallel of latitude ~=——!
through 8, of which, ¢ being the latitude, me :
equation i is
Pe ane
Sse es a 2 ce a re
The differential equation of the meridian is
— 6 sin o dat cosiodye Os 12. «1? ee
And if from this equation, with (2), we determine the ratios of
dw, dy, dz, they are found to be proportional to
—avccoso : —bzsinw : P(ecosw+ysinw) . (6)
And these are proportional to the direction-cosines of SM.
So also, getting the ratios of dx, dy, dz. from (2) and (8), we
find the direction-cosines of SN to be proportional to
2
— ae 2, Wye. (Cr+Se), ye
ee for the ee of SP; they are as
1 cok: Ls
neh 9): Ba 44 8) :en(h 2).
These enable us to determine bi pee between the lines SM,
Colonel A. R. Clarke on the Figure of the Earth. aL
SN, and SP. Let the semiaxes of the equator be expressed
by the relations
C=h(1+i); P=h1—2),
where 7 is a very small quantity whose square is to be neg~
lected. Then the coordinates x, y, z of any point, as 8, are
proportional to
2
(1+7)cosw: (1—i) sino: jtan gp.
Substitute these in (6), (7), (8), and we get finally the fol-
lowing results for the angles between the lines in question :-—
ae C
MSP= —isin @ sin 20(1+ Se
2
7 ., ce singsin2o
= 2" @ sinh + cosh
MSN = isin ¢ sin 20.
In the figure of the earth, as determined in the paper in the
‘Memoirs of the Royal Astronomical Society’ for 1860, there
is a difference of a mile between the greatest and least radii of
the equator. Although this seems but a small departure from
the form of a circle, yet 1=52/"33 (in parts of radius unity),
and the angles expressed above become somewhat large quan-
tities. Supposing 8 to be on a meridian midway between the
greatest and least radii of the equator, the angle between the
“meridian ’’ and the “north line” is 52/33 sing; and the
defect of MSP from a right angle is about double this quan-
tity. So large an angle as this should be detected by firstrate
geodetic observations, though it would require a somewhat
long measurement of meridian and parallel. It is to be re-
membered that, SM, SN being directed towards the north, and
SP towards the minor axis of the equator, SM lies between
SP and SN.
And in an ellipsoidal earth the direction of the principal
sections of the surface (that is, of maximum and minimum
curvature) are no longer coincident with meridians, north lines,
or parallels. Supposing that S is not in a very high latitude,
one of the lines of curvature, as SR through 8, will lie some-
where in the direction of SP, and the second line of curvature
will be perpendicular to SR. Itmay be shown that the angle
Ce
Poe 4
an expression which does not hold in high latitudes; for in
the vicinity of the umbilics, the lines of curvature are approxi-
mately confocal conics having the umbilics as foci. The defect
lites E = —isin 2@ sin ¢ sec? d
92 Colonel A. R. Clarke on the Figure of the Earth.
of RSN from a right angle might, with the value of 7 we have
been supposing, amount to some degrees without going to any
high latitudes.
t appears, then, that it would not do to take the longitude-
equations which we have used for the determination of a sphe-
roidal figure for the earth also for the determination of an
ellipsoidal figure. The only thing that can be done under the
circumstances is to take simply the longitude-are between
Bombay and Vizagapatam, as these points are nearly in the
same latitude, and to reduce it according to the expression for
the length of an arc of parallel on the surface of an ellipsoid,
given in the before-mentioned paper on the Figure of the
Earth, page 43.
Then, with fifty-one equations I get the following :—
u= —0°4908 ;
v= +0°2842 ;
w= +0°3599 ;
z= —0°1067.
From these quantities the following values finally result :—
a= 20926629 ;
b= 20925105 ;
c= 20854477.
If by the word “ ellipticity ”’ of an ellipse we mean the ratio
of the difference of the semiaxes to half the sum of the same,
the ellipticities of the two principal meridians of the earth are
1 1
2895 205i
The longitude of the greater axis of the equator is 8° 15/
west of Greenwich—a meridian passing through Ireland and
Portugal and cutting off a portion of the north-west corner of
Africa; in the opposite hemisphere this meridian cuts off the
north-eastern corner of Asia and passes through the southern
island of New Zealand. ‘The meridian containing the smaller
diameter of the equator passes through Ceylon on the one side
of the earth and bisects North America on the other. This
position of the axis, brought out by a very lengthened calcu-
lation, certainly agrees very remarkably with the physical
features of the globe—the distribution of land and water on
its surface. On the ellipsoidal theory of the earth’s figure,
small as is the difference between the two diameters of the
equator, only 3000 feet, the Indian longitudes are better re-
presented than on the spheroidal; but there is still left at
Madras and Mangalore an attraction or disturbance of the
plumb-line seawards.
Prof. W. Siemens on Telephony. 93
As to the relative evidence for the two figures presented
in this paper, the sum of the squares of the residual cor-
rections to the astronomical observations is, of course, less
in the ellipsoid than in the spheroid ; but the difference is cer-
tainly small. The radius of curvature perpendicular to the
meridian in India, in latitude 15° say, is, on the spheroid,
20930972 feet, whereas on the ellipsoid it is 20932877; and
this last is distinctly more in harmony with the Indian Lon-
gitude Observations.
Ordnance Survey Office, Southampton,
June 15, 1878.
XII. On Telephony. By W. SteMens*.
HE surprising performances of the telephones of Bell and
Hdison rightly claim in a high degree the interest of
natural philosophers. The solution (facilitated by it) of the
problem of the conveyance of tones and the sounds of speech
to distant places promises to give mankind a new means of
intercourse and culture which will essentially affect their social
relations and also render substantial service to science ; and
hence it seems fitting that the Academy should draw these
exceedingly promising discoveries into the sphere of its contem-
plations.
The possibility of reproducing mechanically not merely
tones, but also noises and spoken sounds, at great distances is
given theoretically by Helmholtz’s path-opening investiga-
tions, which elucidated the essential nature of shades of tone
and the sounds of speech. .
If, as he has demonstrated, noises and sounds are only distin-
guished from pure tones by the fact that the latter consist of
simple, the former of a plurality of series of undulations, super-
posed to one another, of the sonorific medium, and if the noises
of speech (Sprachgerdusche) may be conceived as irregular vi-
brations with which the vocal sounds begin or end, then it is
also possible to reproduce mechanically a certain succession of
such vibrations at distant localities. Indeed practical life has
in this, as is frequently the case, outrun science. The hitherto
too little regarded so-called “ speaking telegraph,” consisting
of two membranes stretched by a strong and at the same time
extremely light thread or fine wire which is fastened to their
centres, effects a perfectly distinct transmission of speech to a
distance of several hundred metres. The threads or wires can
* Translated from the Monatsbericht der kdnighch preussischen Aka-~
demie der Wissenschaften zu Berlin, January 1878, pp. 38-53.
94 Prof. W. Siemens on Telephony.
be supported at any number of points by elastic threads of a
few inches length, and also, with similar elastic fastenings at
the angles, from any number of angles, without the apparatus
losing the capability of conveying with, perfect distinctness
and correctness completely toneless whispered speech—a. per-
formance which previously no electric telephone could accom-
plish. Although this “spedking telegraph,” or, more cor-
rectly, ‘ thread telephone,’’ possesses no practical value (since
its working is still limited to short distances and is interrupted.
by wind and rain), yet it is most deserving of notice, because
it proves that stretched membranes are fitted to take up,
almost completely, all the air-vibrations by which they are
struck, and to reproduce in another place all speech-sounds
and noises when mechanically put into similar vibrations.
Reis, as is well known, was the first to endeavour to operate
the conveyance of tones by electric currents instead of a
stretched thread. He made use of the vibrations of a mem-
brane exposed to sound-waves to produce closing contacts of
a galvanic series. The current-waves hereby generated tra-
versed, at the other end of the conduction, the coil of an
electromagnet, which, provided with a suitable resonance-
arrangement, again produced approximately the same tones
by which the membrane, struck by the sound-waves, had been
set vibrating. This could only be done very imperfectly,
since the contact-arrangements only became effective with the
greater vibrations of the membrane, and could only imperfectly
render even these.
Bell appears first to have had the happy thought to let the
vibrating membrane itself call forth the currents serving for
the transmission of its vibrations—making it of soft iron, and
placing its centre opposite and very near to the end of a steel
magnet wound round with insulated wire. By the vibrations
of the membrane the attraction between the plate and the
magnet, and therewith the magnetic potential of the wire-
enveloped end of the bar-magnet, were alternately augmented
and diminished ; by this, in the wire of the coil and in the
conduction, currents were produced which, with the minute-
ness of the vibrations of the plate, generated electrical sine
vibrations corresponding to the vibrations of the mass of air,
which were thus in a condition to call forth again membrane-
and air-vibrations in a similar apparatus at the other extremity
of the conduction. The result was unaffected by the circum-
stance that, as Du Bois-Reymond* has pointed out, in the
receiving membrane the phases and ratios of amplitude of the
partial tones are different from those in the emitting membrane.
* Arch fir Physiologie, 1877, pp. 573, 582,
Prof. W. Siemens on Telephony. 95
An essentially different path was. struck out by Edison (as
it appears, simultaneously with Bell). He uses a galvanic
series, which sends a constant current through the conduction.
At the sending end a layer of powdered graphite, which is
gently. pressed between two. metal plates insulated one from
the other, is inserted in the circuit. The upper plate is fas-
tened to the vibrating membrane, and presses the graphite
powder more or less together in correspondence with the air-
vibrations. By this the resistance of the graphite to conduc-
tion is correspondingly varied, and thereby sinusoid varia-
tions, equivalent to the air-vibrations, are produced in the
intensity of the current passing through the conducting line.
As receiving-apparatus, Edison uses no membrane, but another
and quite peculiar contrivance. It is based on the experience
that the friction between a piece of metal and a paper band
saturated with a conducting fluid and pressed against the
metal is diminished when a current passes through the paper
to the metal. I have verified this remarkable phenomenon for
the case in which the direction of the current is such that
hydrogen is separated at. the metal plate, or when the metal is
not oxidizable. Hence the lessening of the coefficient of fric-
tion by the current evidently proceeds from electrolytically
generated gases deposited on the plate of metal. Surprising,
however, remains the almost instantaneous rapidity with which
the effect takes places even with very feeble currents.
Now Hdison attaches the metal plate, pressed against the
moist, paper, to a sounding-board, and draws the moist paper,
which is carried over a roller, under the metal piece by con-
tinual rotation of the roller. If now the metal piece and the
roller (also of metal) be inserted in the galvanic circuit, the
variations produced in the current by the greater or less pres-
sure of the graphite powder effect equivalent variations of the
friction-coefficient between the metal plate attached to the
sounding-board and the paper, whereby the former is put into
corresponding vibrations, which are communicated to the
sounding-board, and through this to the air.
Hdison’s telephone is very remarkable on account of the
novelty of the expedients employed in it; but it is obviously
not yet complete for practical use; while Bell’s telephone
has, in its remarkably simple form, been widely spread in a
short time, especially in Germany; and already much mate-
rial of experience has been accumulated for judging of its
usefulness. Its principal defect consists in the feebleness of
the reproduced sounds, which, in order to be distinetly under-
stood, require the sound-aperture to be pressed to the ear,
and at the other end an immediate speaking into it. Per-
96 Prof. W. Siemens on Telephony.
fect quiet is necessary around it, in order that the ear may
not be dulled and disturbed by extraneous noises. A still
egraver obstacle to its practical employment consists in this—
that it needs complete electrical calm. As the currents are
extraordinarily feeble which are generated by the vibrating
iron membrane and put the membrane of the other instru-
ment into similar vibrations, therefore also very weak extra-
neous currents are sufficient to disturb the latter and bring to
the ear confusing noises of other origin.
In order to procure fixed points for judging the intensity
of the currents which are effective in the telephone, I placed
one of Bell’s telephones, the magnet-pole of which was wound
round with 800 turns of copper wire 0:1 millim. thick and
possessing a resistance of 110 mercury units, in a circuit con-
taining a Daniell’s cell, with a commutator, by which the di-
rection of the current was reversed 200 times in a second.
Without an inserted resistance, these current-waves pro-
duced in the telephone an extremely inharmonious noise,
audible at a long distance, and almost intolerable close to the
ear. By the insertion of a resistance, this noise was dimi-
nished, but was still very loud after the insertion of 200,000
units. If 6 Daniells were inserted, the noise was still di-
sinctly audible through ten million units of resistance. If 12
Daniells and twenty million units of resistance were inserted,
the sound was decidedly more distinct than in the last prece-
ding case. In like manner an increase in its intensity took
place when thirty and fifty millions of units were inserted
with 18 and 30 Daniells respectively. This corroborates
Beetz’s observation that electromagnetism, with equal cur-
rent-intensity, is more quickly called forth in circuits of great
resistance by correspondingly more intense electromotive
forces, than in circuits with little resistance and proportion-
ately less electromotive forces, because the countercurrents
which arise in the windings of the electromagnet count for
more in the latter case than in the former.
If in the circuit of the commutator the primary spiral of a
small voltaic induction-coil was inserted, such as is ordinarily
employed by physicians, while the telephone and resistance-
scale were in the circuit of the secondary wire, with one
Daniell element a loud-sounding noise was still obtained when
fifty million mercury units were inserted ; and this remained
distinctly audible even when the secondary spiral was pushed
back right to the end of the primary.
This sensitiveness of Bell’s telephone to feeble currents ren-
ders it very useful as a galvanoscope, especially for the de-
tection of feeble and rapidly changing currents, for which there
Prof. W. Siemens on Telephony. 9%
has hitherto been scarcely any other means of testing than
the contractions of the leg of a frog. Also, in measuring re-
sistances by the bridge method, the telephone may often be
employed with advantage instead of the galvanometer in the
branch wire of the bridge; but then it will be necessary to
employ as resistances only straight wires stretched at a greater
distance from each other, as otherwise perturbations would
- arise through induction.
This perfectly explains the extreme sensitiveness of the
telephone to electrical disturbances in the conductor, which,
indeed, almost entirely excludes its application to lines above
ground if the same posts support wires which are used for
telegraphic correspondence. Hven when two neighbouring
conducting wires on the same posts are employed to form the
- conduction-cireuit, in which case the electrodynamic as well
as the electrostatic induction proceeding from the other more
distant wires is in great part compensated, still every current
that passes through these wires is heard in the telephone as a
loud cracking noise rendering the speech of the telephone
quite unintelligible if it is frequently repeated.
Far worse still are these disturbances if the earth is used
for closing the circuit. ven when special earth-plates are
taken for the telephone-wire, or if gas- or water-pipes are
made use of for the same purpose, every current is distinctly
heard which is brought to earth through earth-plates in the
vicinity. Since, in the spreading of a current in the ground,
the electric potential diminishes with the cube of the distance
from the point at which the current enters the earth, this also
demonstrates the uncommon sensibility of the telephone to
feeble currents.
For these reasons, with overland conducting-wires tele-
phones can only be employed if special posts are appropriated
to the support of the wires. Further, the earth’s conduction
ean only be used in places where there are no telegraph-
stations, or where the earth-plates used for telegraphing are
at a good distance from those which serve for the telephone-
conductions.
Notwithstanding this sensitiveness of Bell’s telephone, it
conveys but very imperfectly the sound-waves by which its
membrane is struck to the corresponding membrane and the
ear applied toit. When aloud-ticking watch was placed close
to the sound-aperture of avery sensitive telephone constructed
after Bell’s plan, the ticking could not be heard in the other
telephone, even when the watch actually touched the telephone-
ease. On the other hand, the above-mentioned thread tele-
phone transmitted the ticking through a thread about 20
Phil. Mag. 8. 5. Vol. 6. No. 35. Aug. 1878. H
98 Prof. W. Siemens on Telephony.
metres long very distinctly ; it was still audible when the ear
was withdrawn 8 centims. from the mouth of the hearing-
tube. The ticking could be heard direct with about equal
distinctness at the distance of 130 centims.; consequently
the thread telephone conveyed about 54, of the intensity of
the sound. Since the electric telephone transmitted the softest
speech intelligibly, it must be on account of the rapid and ir-
regular vibrations which form the toneless, even if louder,
noise of the ticking, that it cannot transmit the latter.
From a like cause a proper, perfectly toneless whisper
cannot be understood through the electric telephone, while
through the thread telephone it is distinctly intelligible to a
distance of 20 metres. Just so electric telephones, which re-
produce the softest speech distinctly, do not convey at all, or
scarcely perceptibly, the loud but toneless clap of two pieces
of iron or glass struck together.
It is remarkable that the electric telephone, in spite of this
almost incapability of conveying the noises which consist of
rapid and irregular vibrations, yet so truly renders the quality
of musical tones and the sounds of speech that the voices of
the speakers can be almost as well recognized through the
telephone as direct from the speakers themselves. The voice,
however, sounds somewhat fuller, which is to be ascribed to
the circumstance that the tones are reproduced better and
more powerfully than the noises of speech. Singing, too,
sounds through the telephone, as a rule, softer and richer.
In order to gain a fixed point for the solution of the ques-
tion what fraction of the force of the sound which strikes the
membrane of the one telephone is given again by the other, I
instituted some experiments with musical boxes. The smaller
one, which gave short sharp tones, could be heard by good
ears at 125 metres distance upon an open plain, while only
isolated tones could be heard through the telephone when it
was placed more than 0:2 of a metre from the musical box.
In this instance, therefore, only about s5q55 of the sound
was actually conveyed. A somewhat larger musical box, of
not so high a pitch, and giving tones of longer duration,
could not be heard in the open air much further than the
smaller one; but the telephone at 1:2 metre distance caused
the tune played to be recognized. This gives a conveyance of
about 19395 of the sound-intensity received by the telephone.
Now, although the sounds of speech, as well as deeper and
more sustained tones, are probably conveyed better than the
melody of the musical boxes, it cannot be assumed that a
Bell telephone conveys, on the average, more than zo}o5 of
the mass of sound by which itis struck, to the other telephone.
Prof. W. Siemens on Telephony. © 99
It follows from the above that Bell’s telephone, notwith-
standing its surprising performances, effects the conveyance
of sound only in a very imperfect manner. That we can
understand the speech of the telephone excited by currents so
extraordinarily feeble, we owe to the extreme sensibility and
great range of our organ of hearing, which enable it to bear
the sound of a cannon at 5 metres distance, and yet to hear it
at a distance of 50 kilometres, consequently to have the sen-
sation of sound from air-vibrations within a range of from 1
to 100,000,000-fold intensity.
Accordingly the telephone needs, and is in a high degree
capable of, improvement. Although itis not possible entirely
to do away with loss of sound (which would be approximately
accomplished if it could be effected that the vibrations of the
second membrane should possess the same amplitude as those
of the first), since in the repeated transformations of motions
and forces there must always be a loss of vis viva by conver-
sion into heat, yet the present disproportion is much too great.
But by diminishing this loss, and thereby strengthening the
arriving sound, we should secure that the hearing would need
less exertion, and could distinctly perceive and distinguish the
transmitted sounds at a greater distance from the instrument.
Then also the perturbations produced by extraneous feeble
electric currents would be felt less disturbing, because they
would be covered by the more powerful arriving speech-
sounds.
Hereby is also given the direction which must be taken for
the improvement of Bell’s telephone. In order to produce
more intense currents, the membrane destined to receive the
sound-waves must be sufficiently large and of such a consti-
tution that the sound-waves striking its surface can impart to
it a maximum of their vis vira ; while the membrane must be
sufficiently movable for its vibrations not to be too small ; and
the work expended for the production of the electric currents
must be so much that the vis viva accumulated in the yibra-
tions of the membrane will be consumed by it—or, in other
words, so much as to make the membrane-vibrations aperiodic.
An enlargement of Bell’s iron sheet would be advantageous
only within narrow limits, since larger and correspondingly
thicker plates are apt to assume vibr ations of their own , which
diminish the distinctness of the transmitted sounds. It is also
requisite that the magnetic attraction of the iron plate in Bell’s
telephone be not raised too high, as otherwise the plate is too
much curved and stretched in one direction, which likewise
detracts from the clearness.
I have tried, with considerable success, to strengthen the
100 Prof. W. Siemens on Telephony.
attraction between the iron membrane and the wire-coiled
magnet-pole without bringing the former out of its position of
equilibrium, by bringing it between the poles of a powerful
horse-shoe magnet.
The pole which was above the iron plate had the shape of
a ring, the opening of which formed the sound-hole, while the
lower pole of the horse-shoe supported the iron pin with a wire
coil opposite to the centre of the sound-aperture. The mem-
brane itself consisted of iron only in the middle, as far as it
was opposite to the ring-shaped pole, while the other portion
was made of sheet-brass, to which the iron was soldered.
Through the action of the magnetic iron ring the middle of
the iron plate became itself strongly magnetic ; consequently
there was a very much strengthened attraction between it and
the magnetic iron pin placed opposite to it, while the iron
plate, attracted with equal force on both sides, remained, with
the whole membrane, in the position of equilibrium, and could
therefore vibrate freely towards both sides.
Another modification consisted in making both poles of the
magnet ring-shaped, and providing them with short notched
iron tubes wrapped round with spirals. There were now
exactly opposite to the iron plate two ring-shaped magnet-
poles of the same kind, while itself possessed the opposite
polarity. This is the combination I often employ with good
results in so-called polarized relays, in which the movable,
powerfully magnetized iron tongue is situated between two
oppositely magnetic poles of a magnet, at equal distance from
each, of which the ends are provided with coils.
This arrangement has also been approved for telephonic
call-signal apparatus. Ifa point in the rim of a steel bell,
attached to one pole of a horse-shoe magnet, is between two
iron pins furnished with coils, which form the other pole of
the horse-shoe, a second bell, of the same pitch and with the
same arrangement, repeats with surprising force the sound of
every stroke made upon the other, if the coils of both are in-
cluded in a conduction-circuit. The effect is the same with
tuning-forks in unison.
Instead of two bells or tuning-forks, it is sufficient to insert
only one in the telephone-circuit, if the question is only the
conveyance of the sound of the bell as an alarm-signal. Tele-
phones then give loud-sounding strokes of a bell. 7
If in this way the capabilities of the telephone can be con-
siderably heightened, yet, in retaining Bell’s iron membrane,
we are restricted within rather narrow limits, both as regards
the size of the membrane for receiving the sound and the
strength of the effective magnetism, an excess of which ren-
Prof. W. Siemens on Telephony. 101
ders the speech-sounds indistinct and accompanies them with
a stvange, unpleasant clang.
Hence, for the construction of larger telephones delivering
much more powerful currents, I do not use any vibrating plate
of iron, but I fix to the membrane that receives the sound-
waves (which is made of non-magnetic material) a light coil
of wire which waves freely ina ring-shaped strongly magnetic
field. By the vibrations of the coil, intense currents alterna-
ting in direction are induced in it, which at the other extre-
mity of the conduction set in similar vibrations either the coil
of a similar instrument or the iron membrane of a Bell tele-
phone.
As the breadth of a flat membrane cannot exceed rather
narrow limits without confusing the speech-sounds trans-
mitted, by the advice of Prof. Helmholtz I have given to the
membrane the form of the tympanum of the ear. This form
is obtained, according to Helmholtz, when a moist skin of
parchment or a bladder is stretched over the rim of a ring, and
then its centre gradually depressed to the desired depth by a
screw or otherwise. The membrane will then retain this form
after drying. If now a model be made after this form in
metal, with its aid a membrane of sheet-brass, or, better, alu-
minium can be pressed so as to have the same form as the
former. Membranes of this shape are especially suitable for
the reception of sound-waves and for the transference of their
vis viva to masses that are to be set vibrating (a purpose which
they have to fulfil in the ear also), since their flexion results
chiefly near the margin of the membrane—while in flat mem-
branes it takes place more in the vicinity of the centre, and
hence with these only those sound-waves which strike the
middle of the plate come into full action. Such a telephone
with a parchment membrane 20 centims. in diameter, a wire
coil of 25 millims. diameter, 10 millims. height, and 5 millims.
thickness, in a magnetic field of great intensity generated by
a powerful electromagnet, transmits with perfect distinctness
to a great number of smaller telephones every sound produced
in any part of a room of moderate size; and the purity and
clearness with which it transmits the sounds of speech and
musical notes are remarkable—which may arise partly from
the appropriate form of the membrane, and partly from the
coil, on moving in the cylindrical magnetic field, generating
more regular sinusoid currents than a vibrating iron plate.
An apparatus in which such a wire coil is moved rapidly up
and down by means of a winch with a long connecting-rod
could be used with advantage for the generation of sine-cur-
rents of great intensity.
102 Prof. W. Siemens on Telephony.
For giving back the sounds of speech the tympanic form
of membrane is not so well suited. It also appears generally
more to the purpose to employ larger and more powerful in-
struments for giving, and smaller instruments of more delicate
and lighter construction for receiving, at the same time bring-
ing the instrument into the most suitable position for the ear.
Too powerful receiving-apparatus have the drawback, that
the countercurrents produced by the vibrations of their mem-
brane weaken the moving currents and displace the trains of
sinusoid waves of the induced currents, by which the speech
is made indistinct and assumes strange shades of sound.
It is scarcely to be assumed generally that telephones on
Bell’s principle (in which the sound-waves themselves have to
perform the work of exciting the currents required for their
conveyance) will be successfully produced so as to utter speech
distinctly intelligible ata greater distance from the telephone;
and, as we have already insisted, it is quite impossible of at-
tainment that they should reproduce not weakened the mass
of sound by which their membrane is struck, or even re-
inforced. This possibility, however, is not excluded when a
galvanic battery is used for putting in motion the membrane
of the receiving-apparatus, which then accomplishes the work
to be expended. Reis endeavoured to effect this by means of
contacts, Edison with the aid of powdered graphite inserted
in the conduction-circuit of the battery.
Contacts will hardly operate with sufficient constancy and
certainty for the sounds of speech to be given back with purity.
But it is possible that the solution of the problem lies in the
course taken by Edison; it therein only depends on the dis-
covery of a material or an arrangement by means of which
changes in the resistance of the circuit may be produced con-
siderable in amount and proportional to the amplitude of the
vibrations of the membrane. The form and quality of gra-
phite powder are too variable to accomplish this with certainty.
Experiments which I have commenced with other arrange-
ments have not at present given any satisfactory result.
Nevertheless Edison’s procedure remains well worthy of con-
sideration, as it possibly forms the key to a future important
development of telephony.
If, however, telephonic instruments are susceptible of fur-
ther extensive improvement, the conducting-lines will always
confine the circle of their application within rather narrow
limits. Even if, as we have already shown to be indispen-
sable, special posts be appropriated to telephone-lines, carrying
no telegraph-wires, and double lines be everywhere employed
for the telephones, yet even the telephonic messages on several
Prof. W. Siemens on Telephony. 103
lines attached to the same posts would soon, with increasing
length of the lines, be disturbed one by another, not only
through imperfect insulation permitting side currents to pass
over to neighbouring wires, but also through the production
of secondary currents in them by electrodynamic and electro-
static induction, generating confusing sounds. In telegraph-
lines electrodynamic induction can, as a rule, be entirely
~ neglected, because it does not increase with the length of the
line, if the resistance of the wire coils be left out of considera-
tion, and because the duration of the electrodynamically in-
duced currents is too short to affect the telegraphic instru-
ments ; but in telephonic apparatus the brief currents generated
by voltaic induction produce very audible sounds if the con-
ducting-lines run side by side for only a short distance.
Further, secondary electrostatic induction, increasing as the
squares of the length of the conducting-line, will soon, as the
overland lines become longer, put a limit to the employment
of the telephone, even when the telephone-wires only are fixed
to the same posts.
The circumstances are much more favourable in this respect
for the telephone when underground or submarine lines are
employed. Before I had ascertained that the intensity of the
currents which yet are capable of exciting the telephone to
the production of clearly intelligible speech-sounds is so ex-
tremely slight, I doubted the practicability of employing sub-
terranean wires for great distances, on account of the great
weakening which the current-waves called forth by rapidly
alternating electromotive forces in the conducting-wires
would undergo with the length of the conduction. The expe-
riments, however, which Postmaster-General Dr. Stephan (to
whom the German Empire owes the reintroduction of the
underground wires that had for a quarter of a century almost
fallen into oblivion) caused to be made with Bell telephones,
gave the surprising result that with them people can speak
with perfect distinctness and quite intelligibly at distances of
about sixty kilometres. Hence it is very probable that, with
telephones of more powerful action, adequate intelligibility
will be attained at twice or even three times that distance.
This, at all events, may be the extreme distance at which tele-
phonic correspondence is generally practicable.
Unfortunately, even in underground conducting wires dis-
turbances by return currents from the earth, as well as by
electrodynamic and electrostatic induction, are not excluded.
The former could be pretty completely got rid of, asin lines above
ground, by the employment of entirely metallic conduction-
circuits, with the exclusion of the earth as return conductor.
104 Prof. W. Siemens on Telephony.
The same holds good in the case of disturbances produced by
induction, if the two insulated conductors forming a telephone-
circuit are united into a separate cable encased with iron wires.
If, on the contrary, as is usually done for the sake of saving
expense, a greater number of insulated conductors are com-
bined in one cable, voltaic as well as static induction makes
its appearance In augmented measure on account of the
slightness of the distance between them, and act very dis-
turbingly on the telephonic correspondence. This secondary
electrostatic induction occurs perturbingly even in long cables
for telegraphic correspondence, with which very sensitive ap-
paratus must be employed. Hence I have proposed, for
avoiding it, to provide the individual conductors which are
combined in a cable containing several wires with a conduc-
ting metallic sheath in conducting connexion with the outer
iron spinning or with the earth. Hven encasing the insulated
individual conductors with a thin layer of tin foil gets rid of
secondary electrostatic induction completely. Any one can
easily convince himself of this by experiment if he places one
upon the other two mica or thin gutta-percha plates, each
lined on both sides with tin foil. If the inner linings be in-
sulated and the charge between the outer ones be tested by
the deflection of a galvanometer by connecting the free pole
of a battery led away to earth with one of the outside sheets
of tin foil, while the second is connected through the galva-
nometer-wire with the earth, or in a similar manner by aid of
the commutator, as great a charge is obtained as if the sheets
in the middle were absent. But if the latter are connected
with the earth, no trace is obtained of a secondary charge in
the tin foil connected with the galvanometer.
We get the same negative result when the individual insu-
lated conductors of a cable consisting of several such have
been tightly wrapped round with tin foil or strips of thin plate
of any metal. The metallic conductive casing, though very
thin, completely prevents any secondary electrostatic induc-
tion or charge of one conductor by the charge of another.
On the other hand, however, the electrodynamic induction
exerted by the wires upon one another is not thereby removed,
as Foucault asserted *.
This can easily be convincingly shown by a simple experi-
ment. If two wires, insulated with gutta percha or caout-
chouc, be wound together upon aroller, powerful charge as well
* Foucault, on the 2nd of July, 1869, took out a patent in England for
encasing the individual conductors with tin foil or other conducting sub-
stances, with the expressed purpose of compensating electrodynamic in-
duction by the countercurrents arising in the tin casing.
On Salt Solutions and Attached Water. 105
as voltaic-induction currents are to be observed in one of the
wires when a galvanic series is alternately closed and opened
by the other. If the roller be now placed in a vessel, and this
be little by little filled with water, the charge-currents in the
former wire diminish, and cease altogether when the water
quite fills up the intervals between the wires, whereas the elec-
trodynamically induced currents become even more intense.
For telegraph-conductions these electrodynamically induced
currents are, as we have already remarked, of no consequence,
since they do not increase with the length of the conduction ;
but the telephone, being so extremely sensitive, is still excited
by them if the inducing currents are not extraordinarily feeble.
It will therefore be necessary to lay down special cables for
telephones, just as special posts are needed for them when the
wires are carried above ground.
As follows from the above, the telephone is still capable of
essential improvement; in a short time telephones will as-
suredly be constructed which will convey both speech and
musical tones beyond comparison more loudly, more distinctly,
and with greater purity to moderate distances than they have
been hitherto by the Bell telephone. The telephone will then
render service to intercourse in cities and between neighbour-
ing towns which will far surpass what the telegraph can per-
form for short distances. The telephone is an electrical
speaking-tube which, just like an ordinary speaking-tube, can
be managed by every one, and can be a perfect substitute for
personal conversation ; but as at very short distances it will
never supplant the speaking-tube, just as little will it be able
to take the place of the telegraph for greater distances. Yet
in the limited circle of its practicability it will soon be num-
bered among the most important pillars of modern civilization,
if external hindrances do not prevent its development and
application.
XIV. On Salt Solutions and Attached Water.
By YREDERICK GUTHRIE.
[Continued from p. 44. ]
On the Separation of Water from Crystalline Solids, inCurrents
of Dry Air.
§ 184. pa high water-worth of many of the cryohydrates
(§ 88), and the want of evidence of simple arithme-
tical relationship between the atomic numbers of the water and
salt of almost all these bodies, invited me to reexamine a few of
the most definite and stable crystalline salts containing water.
And this invitation was the more pressing because, in the
106 Frederick Guthrie on Salt Solutions
matter of the determination of water of crystallization, analysts
have for the most part allowed themselves a far greater lati-
tude in respect to agreement between the experiment made and
the conclusion drawn than they have been willing to admit in
regard to the other constituents of the salt. Prominent in
respect to agreement between experiment and the derived
constitution are the investigations of Graham, especially on
the water of crystallization of single and double sulphates.
Such accord is so rare, that in a very great many instances
the experiments actually point to a different water-worth than
that adopted by the experimenter.
That heat is sometimes liberated and sometimes absorbed
when a salt is brought into contact with water, not only ac-
cording to the nature of the anhydrous constituents, but also
to the degree of hydration, has long since shown that there is
some essential difference in the tension of the union which is
established between the water on the one hand, and the more
or less hydrated anhydride on the other. But the statements
as to the conditions. under which a salt becomes anhydrous, or
exists in combination with a definite relative number of mole-
cules of water, are neither definite nor satisfactory. The state-
ment that a salt gives up n molecules of water when heated to
the temperature H is inexact, (1) unless the hygrometric state
of the air is given, (2) unless it is known whether free circu-
lation takes place, and (8) unless the pressure on the salt is
known. The statement that a salt gives up m molecules of
water in vacuo (over a desiccator) is also ambiguous, in so far
as it ignores the temperature.
The salt which I first examined in this respect was chloride
of barium, BaCl, + 2H, O (BaCl+2 HO), it being a salt easily
got quite pure and of a stable nature. The “pure” salt of
commmerce was recrystallized, boiled with carbonate of barium,
filtered and precipitated, and washed with alcohol. It was
then twice recrystallized. It was then finely powdered, and a
part A was dried for forty-eight hours in a good vacuum at a
temperature of about 17° C.; a part B was dried between
repeatedly renewed bibulous paper in a screw-press for the
same time. Two analyses of each were made, the elements
being estimated in the usual way. |
Estimation of Barium.
Weight of
substance. :
ACD icy eis 2G 2°6912 1:57061 56°D63
118} gigi walk Io | 1°3406 0°78825 56°560
Beil vain
B (2)
Per cent. of
Sulphate. Barium. Easy
1°3942 1:3445 0°79054 56°703
0°3847 0°3480 0:49857 56°360
and Attached Water. 107
Estimation of Chlorine.
lo oride of : Per cent. of
alae meine Chlorine. chlorine.
A (1) eee OOD 49 0°7640 0°18900 23°72
A (2) aha Uno tyes) 0:9970 0°24665 28°70
B (1) meee (7804-9 1:0344 0°25590 28°92
122 ie 1°3965 1°6344 0°40433 28:91
(Ba=137, Ag=108, S=32, O=16, Cl=35°5).
Hence aie |
@aleulacd! Dried 7n vacuo. Dried between
Mean. paper. Mean.
Ba 34. .96°139 56°561 56°531
Cl, ere 29°098 28°912 28°710
2H,0. . 14°754 14:527 14°795
100-000 100-000 100-000
From these analyses, and from the direction of their diver-
gence from the theoretical composition of the salt, there can
be no doubt about the composition of the salt ; nor is there any
doubt that the water is present in simple molecular ratio.
Accordingly the hydrated chloride of barium is admirably
adapted for examination as to the conditions under which it
gives up water. ‘The only statement I can find in this respect
is that the hydrated salt gives up the whole of its water at
100° C.
§ 185. A two-ounce flask with the lip cut off was provided
with a glass cap for use alone in the balance-case: the figure
explains the rest. A given volume of air (measured by the
quantity of water leaving the gasometer) is drawn in a given
time over a thin layer of the hydrated salt, while the latter is
heated to a given temperature. The air passes first through
a long tube containing fragments of hydrate of potassium, and
then through a tube containing glass and sulphuric acid.
108
Frederick Guthrie on Salt Solutions
TARLE XLI.
Substance = 4'1605.
Volume of air
drawn through
flask at uniform
= Temperature. Loss.
rate of 3300 P
cubic centims.
in 60 minutes.
cub. cent. 3
26400 17 0:0008
3300 25 0:0000
40 0-0063
‘ o 0:0073
i: 00078
” ” 0:0075
| » ” 0:0075
: 0:0071
. i 00052
” ” 0-0078
. ti 0:0066
5 o 0-0062
” ” 0-0044
+ ” 0-0060
19800 i, 0-0412
if i 00420
if sf 00346
93 ” 0-0407
& “ 00340
9900 i, 0:0105
is cs 0:0044
7 + 0:0022
| , a 0-0020
| 19800 a 0-0029
i a 0-0059
| ‘ 0-0000
if 60 0-0063.
| 9900 70 0-0099
| 19800 70 0-0256
9900 70 0-0090
9900 50 0-0000
| 9900 50 0-0000
9900 60 00038
19800 7) 0-0210
9900 55 0-0000
9900 58 0:0000
9900 59 00000
9900 60 0:0038
19800 70 0-0187
26400 70 0-0259
39600 70 0-0411
9900 80 00239
9900 90 0-0483
9900 90 0.0358
9900 80 0-015]
4900 80) 00182
9900 60 0-0010
9900 90 0-0021
6600 100 0:0000
Loss by 3300
cubic centims.
00001
0:0000
0:0063
00073
0-0078
00075
0:0075
0:0071
0-0052 (in 45’)
0:0078
0-0066
0 0062
0-0044 (in 80’)
00060
0-0069
0:0070
0:0058
0-0068
0-0057
0 0035
0-0015
0:0007
0-0007
0-0005
0-0009
0-0000
00011
0-0033
0:0043
0-0030
0-0000
0-000
01-0013
00035
00000
0-0000
0-0000
0-0013
0-003)
0-0032
0-0034
0-0080
0-0161
0-0119
0:0050
0-0061
0-0003
0-0007
0:0000
and Attached Water. 109
As the flask had to be left for half an hour in the balance-
case every time before weighing, the above experiments occu-
pied a few weeks. At the end of this time the flask was found
to have lost 0°0017 gram.
Examining the final result as a direct determination of the
whole of the water, I found that the 4:1605 grams had lost
0°6087 gram, or 14°63 per cent., instead of the theoretical
~ amount 14°75.
The actual weight of water which a given weight of the salt
lost at a given temperature in a given time has little interest,
because it is conditioned by the attitude of the salt to the air-
current in the flask, and it is also governed by therate. But
points of very great interest are nevertheless presented when the
above numbers are compared. The first loss, at 17° C., may pro-
bably be attributable to the more complete drying of the salt,
since no further loss was experienced at 25°. Starting at 40°, a
considerable loss was experienced, which continued with very
considerable regularity until the residue approached in com-
position to the one-atom hydrate BaCl,+ H, 0; the loss then
suddenly diminished and abruptly stopped. The total loss ex-
perienced by the 4:1605 grams of salt when this point was
reached is 0°3009—that is, 7°21 per cent. As the percentage
of water in BaCl,+H,O is 7°37, there can be no question
that there is a difference in the strength of union of the two
water molecules to the salt, or, more exactly, that it requires
different physical conditions to separate «H,O from BaCl,
than are sufficient to separate 8 H, O from e« H, O, BaCly.
At what minimum temperature the 6 molecule begins to be
separated is missed in this Table: it les somewhere between
25° and 40°. But it appears that when the temperature is
such that one molecule begins to be stirred, the whole of that
molecule is removed if the current of dry air be continued.
In the case of the chloride of barium, there is a range of tem-
perature below 60° and reaching down to the above-mentioned
minimum, in which the « molecule is fixed while the 8 molecule
is removable.
The minimum temperature required to disconnect the « mo-
lecule is well marked. The salt having ceased to lose weight
at 40° C., lost weight distinctly at 60°, and still more rapidly
at 70°. On reducing the temperature to 50° no loss could be
detected ; at 60° the same as before, and at 70° the same as
before. At 55° there was no loss, nor at 58°, nor at 59°; but
at 60° the original loss was reestablished. And until the salt
is becoming anhydrous, for each temperature there is a pretty
constant loss.
The anhydrous BaCl, thus obtained, when mixed with water,
110 Frederick Guthrie on Salt Solutions
may raise the temperature from 19° to 388°. The solution is
perfectly limpid and neutral.
§ 186. In order to make a more systematic attack on the
8 molecule, a fresh quantity was taken of the salt which had
been dried in vacuo over sulphuric acid, and had then stood in
air over sulphuric acid for three weeks.
TABLE XLII.
Substance =5°6462.
Volume of air
drawn through
at uniform rate Temperature. Loss. bem by ae
of 3300 cubic cubic centims.
centims. in 15’.
— ee
9900 26 0-0005 -0002
. 29 0-0012 0004
x 32 0-002 008
in 34 0:0053 0018
03 36 0:0068 0023
i 38 0.0089 0030
40 0-01.29 0043
fs 50 0:0236 -0079
16500 58 0:1450 0290
9900 53 0:0146 0149
i 50 0-0222 -0074
. 45 0-0209 0070 (in 30’)
19800 Fie 0:0821 0137
a4 i 0:0192 0032
9900 : 0-0022 -0007
6600 g 0:0014 -0007
19800 56 0-0074 0012
9900 57 0:0029 -0010
‘ 57 0:00.22 -0007
19800 57 0-0000 -0000
It seems that the almost inappreciable loss at 26° is really
continuous with the greater losses at higher temperatures.
The loss at 25° having been shown in Table XLI. to be inap-
preciable, we may consider the loss to begin between 25° and
26°. It is observed that the rate in Table XLII. is four times
as great asin Table XLI.; and a consequence of this is that,
for given volumes at the same temperature (40°), the losses are
absolutely and relatively to the quantity less in Table XLII.
than in Table XLI., but not four times as small. |Hence,
as we might anticipate, at a given temperature and for a given
volume more water is withdrawn by a slow current than by a
quick one ; while in a given time more water is withdrawn b
a quick current than by a slow one. Withregard to the first
of these facts, itneed only be remembered that the slow current
becomes more saturated than the quick one. Although the
and Attached Water. 111
cessation of loss is for both atoms sufficiently well marked and
abrapt, the final balance of water is retained in both cases with
considerable tenacity.
In the second series of experiments the flask preserved its
weight exactly. The total loss on the 56462 grams was 0°4119
gram, showing a percentage loss of 7-277.
The whole analysis now stands as follows, allowing for the
loss of the glass in the first series, for the salt dried over sul-
phuric acid :—
Calculated.
Bates «S656 56°14
Cie » Zool 29°10
aH, O . . TA44 3
BH,O . . 7-23 (7-28 and 719) : oe
10014 100-00
On mixing the body BaCl,+ H, O with water a rise from
21° to 27° (or 6°) was obtained. The anhydrous salt with
water gave from 19° to 38° (or 19°).
§ 187. Briefly to recapitulate concerning BaCl,+2H; 0.
At the ordinary barometric pressure, and in a current of air
dried and freed from carbonic acid, one water molecule is re-
moved at all temperatures above 25° C., the other at all tempe-
ratures above 60° C. In the figure (p. 112) A shows the rates
of loss of the 8 molecule in tenths of milligrams, the ordinates
being proportional to such losses. The abscissee are the tempe-
ratures. 5B shows the losses in like manner of the « molecule.
Chromatic Value of other Media than Water.
§ 188. There are few media besides water which dissolve
metallic salts. Amongst the few glycerine stands preeminent ;
and this liquid is indeed comparable with water itself in its
solvent power. On account of this very solvent power, there
appears to be at present no evidence of the replacement of water
by glycerine in solid hydrated salts, similar to the replacement
in siliceous jellies. Some glycerates (using the term homolo-
gously with hydrates) are well-defined bodies enough ; and the
properties of some new ones will be described subsequently.
Here I shall confine myself to the description of the effect upon
the colours of a few salt solutions, according as the solvent is
water or glycerine. Being partially what is called “ colour-
blind,” I have, of course, availed myself of the services of my
friends in describing the appearances presented.
§ 189. Many are entertaining the idea of the relationship
between the vibrating periods of the light-waye and the mass
of the molecule, simple or compound, of the medium. The
Frederick Guthrie on Salt Solutions
112
e or less massive molecule, may perhaps be the most
sion “loading”? a molecule, by associating it with an-
other mor
expres
100
80 90
70
50 60
10 20 30 40
0°
and Attached Water. 1S
convenient term to apply to the cause of the increased period
of oscillation which such association entails ; but, of course,
any systematic obstruction to vibration, any drag, would have
the same effect.as the drag of inertia.
§ 190. In some experiments relating to the “ wandering of
the ions ’’ in jellies during electrolysis, which I had the honour
_ of bringing before the Physical Society on the 16th of March,
1878, I described the spreading of the acid and alkaline ions
through the unmelted jelly. These results I do not publish,
because a friend has had the great kindness to point out to me
that many of the results which were then exhibited had been
obtained several years previously by Dr. W. M. Ord. The
experiments and speculations of Dr. Ord are contained in a
very remarkable and suggestive series of papers contributed
chiefly to the St. Thomas’s Hospital Reports *. Amongst the
jellies which I then prepared but did not exhibit, was a stiff
gelatine jelly saturated with sulphate of copper. ‘This jelly
was of a bright emerald-green by transmitted light. On ex-
posure to the air of a portion which had not been subjected
to electrolysis, the water gradually evaporated and the salt
began to crystallize out. The form of the crystalline masses
was curiously modified by the jelly. Rounded masses were
formed, reminding one of my friends of the coccoliths of the
deep-sea dred gings—another, of the mineral or uric concretions
which oceur in mucous media—and yet another, of “ chlorite.”
Whether there be, as is most likely, a common cause, a colloid
medium, in all the three cases, I must not here discuss. The
ultimate crystalline element is too minute for determination; but
the elements of secondary form invariably re-
semble (1). These elements are frequently TELiay
linked two by two in one plane (2), or atright ©) a
angles to one another (3). The convex sides
are generally very deeply furrowed, so as to
give the impression of their being four second-
ray elements. These concretionscanbe picked (2) ESD
out of the jelly in which they form, like oy
almonds out of a cake. So clean is their se-' |
paration, and so feeble their blackening when
heated with oil of vitriol, that they must be (3) er)
regarded as homogeneous bodies free from aa
gelatine ; and their composition is therefore
* “Some Experiments relating to Forms assumed by Uric Acid” (St.
Thomas’s Hospital Reports, 1870); ‘‘ An account of some Experiments
relating to the Influence exercised by Colloids upon the Forms of Inorganic
Matter” (St. Thomas’s Hospital Reports, 1871) ; “Studies in the Natural
History of the Urates” (Rep. Microscopical Society, Jan 6, 1875); “On
Phil. Mag. 8. 5. Vol. 6. No. 35. Aug. 1878. I
114 On Salt Solutions and Attached Water.
of no common interest. Ten of these concretions, which
are remarkably uniform in size, weighed 0:5024 gram; the
loss on heating to 200° ©. in an air-current was 0°1452 gram,
showing 28°504 per cent. of water, This points to the formula
CuSO,+3°5 H, 0; and, as I hope to show in my next com~
munication, the subdivision of the water molecule in hydrated
sulphate of copper, or rather the multiplication of the whole
formula of that salt, does not admit of doubt. Here again we
have evidence of the continuity of composition according to
physical circumstances (compare § 142). But what a com-
plete chain of difference of diffusive potential is here indicated,
stretching from the first nucleus throughout the jelly! and
how it suggests the diffusion and accretion of the matter of a
crystalline mineral through a colloid and, perhaps, mechani-
cally rigid mineral matrix!
T'o return to the green colour of the copper jelly. Gelatine
is so complex a body, that although the formation of the blue
crystals of the sulphate shows that there has been no general
chemical change, yet there is no evidence of its entire absence.
Glycerine was therefore next employed as a medium for the
solution of various coloured salts.
§ 191. Anhydrous sulphate of copper dissolves so abun-
dantly in glycerine that the solution may be almost solid when
cold. There is no sign of crystallization; but the solution at
all strengths is a bright emerald-green.
§ 192. Crystals of permanganate of potassium, when heated
with glycerine, oxidize it with the escape of gas; but if cold
glycerine is added to a cold saturated aqueous solution of the
permanganate, a liquid is obtained, without evidence of che-
mical change, which has been pronounced to be brownish
yellow, amber, or, perhaps more accurately, “ raw-sienna.” In
view of the possible chemical change which may be incipient
here, it is perhaps better to put this result on one side.
§ 193. Chloride of cobalt, which in water gives the well-
known pink hues according to its strength, gives with glyce-
rine a beautiful carmine ; this, when heated, is greatly enriched
in its blue. When cooled ina carbonic acid cryogen, it acquires
a yellowish tint.
194. Chromium potash alum, which in water gives the pale
indigo of dilute ink, gives with glycerine an emerald-green.
Whatever be the degree of intimacy of association between
the glycerine and the salt, it appears, then, that this association
ee ee
come Points in the Natural History of Uric Acid and Urates” (St. Thomas’s
Hospital apiaea 1875); “ Urinary Crystals and Caleuli,” &c. (Medico-
Chirurgical Transactions, vol. lviii. March 9, 1875).
On the Transmission of Vocal and other Sounds by Wires. 118
does in all cases retard the light-wave period, or increases its
length. The bluing of the cobalt-glycerine solution by heat,
and its yellowing by cold also, are entirely in accord with the
before-mentioned conception. It may be noticed also that the
glycerine solution of a coloured salt is, as a rule, of a much
richer colour than the aqueous solution of the same strength,
by weight or volume.
T cannot but think that these results lend considerable sup-
port to the idea mentioned in § 189, which idea has been so
far fruitful in Abney’s hands that he has been enabled, by
associating a metallic salt with a heavy molecule, to fit the
vibrating period of a photographically sensitive film to the
light which it is desired to record.
I have to express my indebtedness to Mr. A. K. Huntington
for the patience, zeal, and skill which he has shown in helping
me in the work of the first half of this part (No. VI.) of my
research.
XV. On the Transmission of Vocal and other Sounds by
Wires. By W. J. Mituar, C.L., Sec. Inst. Engineers and
Shipbuilders in Scotland*.
L OLE CT of Paper.—The object of the present paper is
the description of a series of experiments made by the
author upon the transmission of vocal and other sounds by
wires, and the results obtained from those experiments.
2. Transmission of Sound in general.—The transmission of
sound by various media is familiarly illustrated from day to
day; and the readiness with which these media are affected
has been made the subject of many experiments.
One familiar illustration of the transmission of sound from
air to solids and thence back to the air is that which occurs in
the vertical and horizontal partitions between rooms, such as
partition walls and floor and ceiling spaces—the sounds origi-
nating in one room being thus transmitted to the adjoining
room without having recourse directly to air communication.
From a consideration of the latter, as also from other phe-
nomena, the author has for some time been convinced that
vocal sounds might be transmitted by solid bodies, such as
wires, and that to considerable distances.
After several unsuccessful atttempts, the author during the
month of January last, having occasion to use some fine
copper wire, carried a portion of it out from the house to a dis-
tance of about 20 yards, and attached a couple of pasteboard
* Communicated by the Physical Society.
[2
116 Mr. W. J. Millar on the Transntission
disks with low rims to the ends of the wire: the transmission
of vocal sounds was then found to be easily effected, conversa-
tion being readily carried on through this length Bh wire.
Since that time the author has made many experiments with
various combinations and under various circumstances. The
principle upon which they all more or less appear to depend,
so far as the rendering audible of the sounds, is that of the
tuning-fork and sounding-box, in which the sound from the
vibratory movements of a metal body is considerably intensi-
fied when the body is placed upon a sonorous substance affect-
ing the air in its vicinity.
3. Notes of some of the more important Hxperiments.
(1) No. 23 copper wire was stretched between windows out-
side of house, and attachments at right angles made to rooms
through the windows. Speaking in one room was then heard
in the other; the distance was about 20 yards. Pianoforte
music was easily transmitted by placing an ear-piece inside
the instrument and carrying the other end of the wire outside
the house.
(2) No. 40 copper wire fitted up in a building, passing
from room to room as per diagram below. Six attachments and
angles,
S
>
g
R
Passage.
of Vocal and other Sounds by Wires. 117
- Distance about 50 yards. Conversation, singing, whistling,
breathing, and the sound of a light C tuning-fork (23 inches
in fork) readily transmitted.
Various similar arrangements were also made in house from
room to room, and finally carried to a distance outside, when
all the above effects, as also the transmission of whispering,
were clearly demonstrated, the persons at either end being
quite out of hearing in the ordinary manner.
The communication was not limited to the persons at either
end of the wire ; additional connexions were occasionally made,
when three or more individuals could communicate with each
other.
(3) Carried about 7 yards of No. 23 copper wire from one
room through an adjoining one to a room beyond, the wire in
its course passing below two doors shut above it, and for the
most part in contact with the carpet, but fastened at the ends
so as to produce some tension. Made two connexions of
No. 40 copper wire at angles with the main wire; conversa-
tion was then readily carried on, and all the phenomena
already described produced. Subsequent experiments with
No. 16 copper wire arranged as above were found to yield
better results.
A somewhat similar and equally successful experiment was
made by carrying the same size of wire down stairs, passing
below two doors and partly resting on carpet and wood. A
positive advantage is gained by resting the heavy wire in
this manner, the words being clearer and more distinct, and
free from the rumbling sound occurring with a suspended wire
free to move about.
(4) Fastened No. 23 copper wire to telegraph-wire, made
another and similar attachment 75 yards further on, but within
two posts. Breathing, whistling, and tuning-fork sounds
readily transmitted.
(5) Carried the latter attachment to 150 yards, thus pass-
ing one post. Breathing, whistling, singing, and the sound of
the light C tuning-fork, formerly mentioned, readily trans-
mitted. No apparent loss though passing the support (the latter
was of the usual china-ware cup with binding-wire). The
speaking was not so distinct, although the different word-
sounds were discernible. This can be accounted for by the
fact that, as the poles were about 14 feet high, the attachment-
ends were free to swing about, which, combined with the ex-
posed situation of the main line, gave rise to a considerable
vibratory action due to other causes than the vocal sounds.
(See diagram, page 118.)
(6) About 50 yards of No. 23 copper wire was laid out so
118 Onthe Transmission oj’ Vocal and other Sounds by Wires.
as to rest partly on grass, and fastened up at the ends to pins ;
attachments were made, and vocal sounds transmitted : whis-
tling and the tuning-fork sounds very clearly heard, although
a high wind was blowing at the time.
4. The Mouth- and Ear-pieces.—The mouth- and ear-pieces
used in these experiments have been of various materials and
forms. The materials tried have been pasteboard, wood, gutta-
percha, india-rubber, parchment, iron, tin, and zinc. These
have generally been arranged as disks or drums, having a
more or less extended rim around them to confine the
sounds. ‘This rim has been of cylindrical, conical, and other
forms.
In general, greater volume of sound accompanied increased
depth of rim; but the sounds were hardly so distinct as when
the rim was kept shallower.
The wire was usually attached to centre of disk; but in
some cases good results were got where the wire was led
through a cylindrical hollow piece of wood and terminated
close_to the disk; indeed a hollow piece of wood without a
disk did very well. :
As a rule, the effects seemed: better when the wire was led
outside of the house.
High-pitched voices are more easily heard than deep strong
Voices.
In the experiments with the telegraph-wire one of the disks
used was of thin sheet-iron 34 inches in diameter. Set in a
wooden rim about 4 inch deep, the wire was fastened. into a
small piece of wood, which in turn was cemented down to
centre of disk. The tuning-fork sounds were very well heard
with this arrangement; and one peculiarity was that, on the
wooden fastening accidentally breaking away from the iron,
the sounds could again be heard by holding the disk in one
hand and pressing the wooden termination of the wire upon
the disk with the other.
5. Wéires.—The wires, as a rule, require to be more or less
tightened up; but this varies with the heaviness of the wire.
The sound is increased with a tight wire.
The volume of sound appears to be increased with a heavy
wire. Thus in the telegraph-wire about $ inch thick, pro-
bably No. 8, the sounds were stronger and fuller than in the
UN DPASS VY ING LISUTUTILETLES Ad LLVESOUTLUALOTS» iid’
thinner wires, and, probably owing to the high tension of the
former, faint sounds were more readily transmitted: thus the
accidental or intentional touching of the tuning-fork with the
rim of the mouth-piece, causing a slight clicking sound, was
distinctly heard through the ear-piece at a distance of 150
yards—and this, even although the two attachments of copper
wire were practically at right angles to the main wire, whereby
part of the sound would pass away onwards up and down the
line.
6. The great delicacy of the action may be inferred from the
fact that fine sand strewn upon the disk of the ear-piece is
unaffected by conversation through lengths of about 7 yards.
The sensitiveness also of the mouth-piece was shown by sounds
not spoken into it being readily transmitted, such as coughing,
laughing, or remarks made by persons standing beside the in-
strument. Indeed, in some cases an advantage is obtained by
keeping back from the mouth- or ear-pieces; and the author
has sometimes thought an improvement was obtained by hold-
ing the ear-piece slightly inclined to the ear.
In all cases the individual voice could easily be distinguished
though modified more or less by the structure and material of
the mouth- and ear-pieces.
The mouth- and ear-pieces were usually of the same form
and material, and were therefore used for either speaking or
hearing. Some forms, however, do better as ear-pieces, others
as mouth-pieces.
In conclusion, the author believes that many interesting
physical questions may be studied by means of these arrange-
ments, and that practical application may be made where com-
munication of this nature is required. i
XVI. On Brass Wind Instruments as Resonators.
By D. J. BLAIKLEY™.
[Plate 1.]
ie bringing before the Physical Society a few notes and
experiments on this subject, I would desire to say that
they are the result of an attempt to carry somewhat more into
detail than, as far as I am aware, has hitherto been done, some
acoustical investigations of the late Sir C. Wheatstone. A
most interesting paper on Wheatstone’s work in this field was
brought before the Musical Association by Professor W. G.
* Communicated by the Physical Society, having been read May 25,
1878.
120 Mr. D. J. Blaikley on Brass Wind
Adams in 1876; and to that paper I am in great measure in-
debted. .
A brass instrument may be defined as a resonator capable of
reinforcing a certain fundamental periodic vibration originated
by the ae and all such vibrations as have for their relative
numbers 2, 3, 4, &c. when the fundamental note is represented
by unity —these vibrational numbers being the basis of what is
known’ as the natural harmonic series of musical intervals—
and this series being the same, whatever may be the absolute
pitch of the fundamental note or the character of tone of the
instrument.
It is possible to make the lips give notes which, although
scarcely audible, are of definite pitch, without the use of an
instrument, just as a tuning-fork gives its proper note with or
without a resonator.
There are two simple forms of resonators which give the
series of notes required in wind instruments: these are the
open tube of equal section throughout, and the cone complete
to its apex, where itis of course closed. Jn the tube the wayve-
length of any note is inversely proportional to its vibr ational
number ; and the nodes or points of maximum con ee
and rarefaction, and the centres of the ventral segments,
points of maximum amplitude of vibration are equidistant: but
in the cone this is not the case. Wheatstone found experi-
mentally that the notes of a closed cone agree in pitch with
those of an open tube of the same length; and therefore the
prime or fundamental tone of such a cone is an octave higher
than the prime of a closed tube of the same length. He found
also that in conic frustra of similar lengths, but of different pro-
portions as regards the diameters of their ends, the pitch varied,
rising as the difference between the two ends increased when the
small end was closed, and becoming lower under the same condi-
tions when the large end was closed. The accompanying dia-
gram (Plate I.) shows the positions of the nodes and centres
of ventral segments in an open tube and a cone of the same
length for the notes ¢, c’, g’, ¢’, marked 1, 2, 8, 4 (¢ having
128 vib., and a wave-length of 105 in. at 60° F.). The nume-
rals grouped together and marked N show the positions of the
nodal points or surfaces, and those marked the centres
2
of the ventral segments or points of maximum vibration. The
effect that the diminishing size of the cone has upon the posi-
tion of the nodes may be easily traced. Whilst the positions
of the centres of the ventral segments remain the same as in
the open tube (the numerals for these on the cone in the dia-
gram falling exactly under those for the open tube), the nodes
Instruments as Resonators. gba
are gradually further and further apart, dividing their respec-
tive ventral segments more and more unequally, until at the
apex of the cone is a node common to all the notes. It fol-
lows from this that the centre of a ventral segment in a cone
is not the centre of the length between its nodes, and, con-
versely, that as the diameters of the two ends of the ventral
segment approach equality, so does the position of the node
become more central, until the condition of vibration existing
- in an open cylindrical tube is reached; and such a tube may
evidently be considered as a portion of a cone whose apex is at
an infinite distance. It is to be noticed that in the cone the
number of + wave-lengths, or semi- ventral segments, is not
directly proportional to the vibrational number as in the open
tube, but, with the exception of the fundamental note, is always
in excess. Thus let
N = number of + wave-lengths,
n = relative vibrational number ;
then
N =n+(n—1)=2n—1.
Instances.—Note 1 (fundamental) N=1+(1—1)=1,
Note 4 (double octave) N=4+(4—1)=7.
The velocity of the portion of wave or waves in the cone there-
fore differs with the pitch of the note, and is in no case the
same as the velocity in free space. Assuming this latter to
be 1120 feet per second, we should have in the cone the fol-
lowing velocities :—
Note. i oe aes
o Dko hae 1 it 2240
CeO) Mets. 2 a 1493°4
POOF Ooo: 3 5 1344
7 SS) Ogee 4 7 1280
and the space traversed by the waves of the different notes in
one second, measuring from the apex of the cone to, say, the
ear of an observer:—
PRO Iss hese cc cadads LID? 187 5teet.
5. DARTS RE a eae P09 aaa,
OAS csnteseSides cans DAO 292 ie
GAD AIG ern ae 1120°5468
>]
The method I used to find the positions of the nodal points
in the cone, and which is applicable to wind instruments or
tubes of any varying section, may be illustrated by a conic
frustum open at both ends. Holding a vibrating fork over
one end (in this case ¢ 512), gradually sink the tube in water :
122 Mr. D. J. Blaikley on Brass Wind
the water-level when the tube is giving its maximum reso-
nance shows the position of the node.
Brass instruments are generally considered to be cones, or
cones combined with cylindrical tubing, neither of which de-
scriptions properly applies; and this | will endeavour to make
clear by experiment. We may, in the first place, consider
whether the resonance of cones and tubing is influenced ap-
preciably by the action of the lips; and it will be found that,
whether the lips or a tuning-fork be used to excite the vibra-
tion, the pitch is the same. ‘Two illustrations may be given—
the first a common hunting-horn, pitch ¢ 512 when it is
blown, and giving an excellent resonance to the ¢ 512 fork
when the mouthpiece is closed; if, however, we slightly alter
its length either way, the resonance to the fork is no longer at
its maximum. Jor the second illustration, I take a cylindrical
tube which becomes closed on being placed against the lips:
blowing it as a wind instrument, we find its proper tones are
c 128, 9’ 384, e” 640, bb 896, be, the same as it would give
as a resonator , and that the pitch of these tones is so definite
that it is very difficult to alter any of them by the lips more
than two or three vibrations, except the lowest. We may here
note that the power of a resonator to reinforce the different
notes of a series of tones, with the prime or fundamental one
of which it is not truly in unison, is much greater for the fun-
damental than for the higher notes; and this gives the reason
for the ease with which the fundamental note of a wind instru-
ment may be varied within pretty wide limits, say half a tone
sharper or flatter than its proper pitch. ‘Taking, for illustra-
tion, a closed tube 21 inches long, it will be found to give ap-
preciable resonance to a fork of 128 vibrations with quarter
wave-length of 264 inches, but scarcely any to a fork of 584
vibrations (g/ the twelfth from ¢ 128) with quarter wave-length
of 83 inches: when the ¢ fork is sounding, the length of the
resonance-chamber is to the quarter wave-length as 21 to 262;
but when the g fork is used, the corresponding proportion is
practically as 34 to 82; for in this case there is a second node
at a half wave-length, or 174 inches from the closed end.
For musical purposes a cylindrical tube blown by the lips
is evidently unsuited, by reason of its poor tone, as well as by
its giving only the odd intervals. The cone gives the required
intervals ; but it cannot be used by the lips in its complete
form; it would be necessary to cut off a considerable portion
to get sufficient width for the action of the lips. Assuming
the cone shown on diagram to be cut at the second node of
note 4 (counting the node at the apex as the first) and there
closed by the lips, that note of the original cone can still be
Instruments as Resonators. 123
sounded, but no other; the other notes that can be produced
may be regarded as the notes 3 and 2 made flatter by their
nodes being drawn back, as it were, to the position of node 4,
where the cone is cut and the lips are placed; the original
notes 2, 3,4, or c’, 9’, ¢’, becoming thus the Ist, 2nd, and
ord notes of a new inharmonic series, with pitches approxi-
mately cZ, ep’, c’’—thus approaching the notes of a cylindrical
stopped tube. I have here two other tubes tapering in differ-
ent degrees—the first two proper tones on the one being ¢ and
c#’’, and on the other c’ and e” (a major tenth). From these
experiments it may be seen that, by using portions of cones
of different proportions with their small ends closed, it is pos-
sible to get different series of intervals varying between those
of an open and those of a closed cylindrical tube—that is, the
first interval varying between an octave and a twelfth.
One of the examples just shown (the tube with notes c/ and
c#’’) appears to give intervals not very far removed from those
required: it may be made use of to illustrate the effect of the
combination of a cone with cylindrical tubing, such tubing
being of necessity used in practice in connexion with valves
or slides to complete the scale. Flattening this cone a fourth,
from c’ to g, by adding tube, it gives the intervals g, e’, d’’ in
place of the g, g’, d’ required, or the ratios 1, 12, 3 in place
of 1, 2, 3, the second interval being actually greater than the
first.
These illustrations prove that neither a conic frustum, nor
a conic frustum combined with cylindrical tubing, can truly
be resonators to notes in the natural harmonic series; but
‘seeing that a bugle or other wind instrument, although it has
a considerable diameter at the mouthpiece, may nevertheless
be in tune, it appears that its nodal points cannot be in the
same positions as those in the cone. On the diagram is re-
presented a bugle of the same pitch as the open tube and cone,
with the positions of its nodes and semi- ventral segments as
determined by experiment with tuning-forks. Comparing on
the diagram the positions of the nodes of any given note in
both the bugle and the cone, it will be noticed that there are
great differences. The nodes of note 2 show this clearly.
Compare lengths from both ends: from mouthpiece to node
the length is more nearly equal to that between similar nodes
on cylindrical tubing than to that between similar nodes on
the cone; but from node to open end it is greater than on the
cone, the bugle opening more rapidly.
Thus, then, by altering the proportions of the different semi-
ventral segments of which such an instrument may be con-
ceived to be built up, the positions of the nodes may be so
124 Mr. D. J. Blaikley on Brass Wind
arranged that there shall be a node for every note of the har-
monic series at the mouthpiece as required ; and according as
that is more or less perfec tly effected will the instrument be
more or less perfectly in tune. This bugle is divided into its
seven semi- ventral segments for its 4th note, ¢ 512, according
to the diagram ; and it will be found that by blowing at any
one of the nodal points, with any length of the bugle contain-
ing an odd number of semi- ventral segments, the note c” can
be produced. The total number of pieces and combinations
that can give this note is eighteen.
Having given these few illustrations of the conditions upon
which correct intonation, or the relative pitch of the different
notes that can be sounded on a brass instrument, depends, I
will now endeavour to show the connexion there is between
this point and the question of quality of tone, understanding
by quality of tone that characteristic of sound which enables
us to recognize a difference between tones of the same pitch.
Helmholtz has fully demonstrated that it is only in exceptional
cases that we hear a simple musical tone—the vast majority of
musical tones being in reality compound tones, in which the
fundamental or prime tone has blended with it many upper
partial tones of the natural harmonic series,—and that the
variety of quality of tone depends mainly upon the number
and intensity of these upper partial tones. Blowing the note
c 256 on three resonators of different forms we get three di-
stinctly different qualities of tone: the resonators now used
are a common paraffin-lamp chimney, the conic frustum
already shown (having for its first two proper tones ¢’ and ¢’’Z),
and the bugle. Analyzing these three tones by tuning-forks
or resonators, we find that the lamp-chimney of irregular form
gives no upper partials; the tone is pure or simple. The cone
has the second and third partials sounding, but not strongly,
as it is not strictly in tune for them, or, in other words, there
is a difference of phase between the prime tone and the par-
tials. And the bugle has all the partials up to the seventh,
gradually diminishing in power, but all tolerably strong up to
the fifth inclusive. Slghtly altering the form of the cone by
adding tubing to the narrow end, and maintaining the original
pitch of the prime tone (¢ 256), by cutting a portion off the wide
end the pitch of the second tone may be altered until it is
c 512, an exact octave from the prime; and we find that the
quality of tone of the prime or fundamental note is altered,
owing to the more perfect resonance which the cone now gives
to its second partial. In its original form, with proper tones
c'—cz", the cone could give but an imperfect resonance to ¢”
the second partial to its prime c’.
Instruments as Resonators. $25
In the trombone and the euphonion we have two instru-
ments of yery different and characteristic qualities of tones—
the trombone being brilliant and piercing, and the euphonion
mellow. We may take the Bb of about 120 vibrations (army
pitch) on each of these and endeavour to give a visible proof
of the existence of high upper partial tones. Tor this purpose
I use small tubular resonators covered at one end with a tightly
strained diaphragm or tympanum of goldbeater’s skin, against
the centre of which is hung a very small bead, or drop of
sealing-wax, by means of a single thread of cocoon-silk. The
two resonators now used are tuned respectively to the fourth
and ninth partials of B?, or b) of 480 vibrations and ¢” of
1024. When the proper tone of such a resonator is sounded
in its neighbourhood, either as a simple tone or as a partial in
a compound tone, the agitation of the membrane puts the bead
in violent motion, which can easily be seen in the image thrown
on the screen by the electric lamp. It will be noticed that
when Bp is sounded, either on the euphonion or on the trom-
bone, both resonators are agitated—but that the excursions of
the bead due to the partial tone of 1024 vibrations are much
greater with the latter than with the former instrument,
although both are played with but moderate force, thus
proving that, though partials as high as the ninth exist in the
quality of tone produced by both these instruments, yet in the
trombone the upper partials have much greater strength than
in the euphonion. With a resonator more suitable for private
experiment than these, I have distinctly heard the sixteenth
partial tone in the Bp of the trombone. <A tapering tube open
at both ends, or a common wine-boitle with the bottom knocked
out, is very convenient for analyzing tones. Sinking such a
tube in water and holding the ear close against the small end,
the various partials existing in a given compound tone may be
readily discerned, as the length of the tube changes according
to the depth it is immersed in the water.
Although one wind instrument may be made to approach
another in quality of tone by means of different methods of
blowing, and it is therefore not so easy to analyze the tones of
these as it is those of keyed instruments with fixed tones, yet
I have endeavoured to establish some general data ; and these I
will lay before you. The instruments the tones of which I
have analyzed are the Bp tenor trombone, the Bp euphonion,
the F French horn, the Bp cornet, and the bugle. The par-
tial tones named in the Table are those heard when the instru-
ments are gently blown; with loud blowing higher tones can
be discerned. ‘he ordinary marks of musical expression, pp,
p, mf, f, are added in cases where I found it possible to make
a comparison.
126 Mr. D. J. Blaikley on Brass Wind
| Instrument. | Note. | N eee Partial tones heard.
| | Py
( B,b 60 1, 2,3, 4,-5, 6, ee: toe:
P
BD aeet anetys Bb | 120 1,2,3, 45,6, &e, to 12,
ioe 180 | 1, 2, 3, 4, 5, 6,7.
\ p [than 12 weak.
Bb 60 | 1, 2, 3, 4, 5, 6, &. to 12; higher
P
Bb Euphonion ... < | ae sc eae ae re .
| f 180 | 1,2,3,4,5.
p
| c 135 1, 2, 3, 4, 5, 6, 7, 8.
| mf p pp
| F French horn Hd f a“ | t, 2,8 nee
| 2
el i i | 360 | i 2, o; 4, 5 6.
| N | P Pp
Bb; Cormet j..--2:-..2| 6D 2405 i) 12, Bes OO Beis:
Pp
WLS ere si55 aos anna se ee 256 Lo: 4. Ge
| S if p pp
While submitting that the different qualities of tone are ac-
counted for by the difference in the number and force of the
upper partials in any given compound tone, I must at the
same time acknowledge that I can do no more than throw out
a few suggestions with respect to the causes that influence the
production of such upper partials in this remarkable manner.
The partials being in the natural harmonic series, it is evident
that if the various proper tones of a vibrating column of air
such as is enclosed in a wind instrument are not in exact
agreement with this series, the resonance to the partials can-
not be at its best. Take for illustration two instruments no-
minally the same (say two bugles), but with somewhat differ-
ent qualities of tone. Suppose that a certain compound tone
on both should have its first and second partials of equal in-
tensity, but that one instrument has that one of its proper
tones that is nearest in pitch to the required second partial a
semitone sharper than that partial; the supposed compound
tone sounded on that instrument will be deficient in the quality
the second partial should give.
As regards instruments of different characters, the chief
points influencing the tone are the general form of the instru-
ment (understanding by this the proportions of the column of
air, and not the shape into which the instrument may be bent
up for the convenience of the player), the extent of the flan-
ging of the bell, and the form of the mouthpiece. As an
Instruments as Resonators. nee
illustration of the first of these conditions the trombone may
be compared with the euphonion; the tubing of the trombone
is cylindrical for about two thirds of its length from the mouth-
piece, but the euphonion opens with gradually increasing cur-
vature from the mouthpiece to the rim of the bell. The high
upper partials being more powerful on the former than on the
latter instrument, it would appear that the cylindrical tubing
has the power of maintaining the intensity of the short waves
to a greater extent than the tapering tubing has, The bell-
flange may be increased in size to a considerable degree with-
out altering the pitch of an instrument; but such increase has
a marked effect on the quality of tone, greatly subduing the
force of the upper partials. I find by experiment that the pitch
is not altered by the extension of the flange curvature beyond
a point at which its tangent would make an angle of about 40°
with the axis of the instrument, although the quality of tone
is decidedly altered by such extension. ‘This may be illustrated
by changing the bell-end of a bugle for a bell with much wider
flange, more like that of a French horn: comparing the two,
it will be noticed that the change in quality of tone is very
marked.
The form of the cup of the mouthpiece varies for different
instruments, from that of a long deep conical funnel to that of
a comparatively shallow well-rounded cup—the first form
representing the French-horn mouthpiece, and the second the
mouthpiece for instruments of brilliant tone, as the trumpet
and trombone; those for cornets, bugles, and saxhorns are of
an intermediate character. Although it is manifest that a
shallow cupped mouthpiece favours the production of high
upper partials, | have not as yet succeeded in arranging any
experiments which would illustrate the cause of this. One
fact, however, noticed by many observers, appears to me to be
suggestive, and worth bearing in mind in connexion with this
subject. It is this:—Ifa vibrating tuning-fork be placed on
a sounding-board, the quality of tone it gives varies with the
pressure applied: touching the board very lightly with the
fork the prime tone is well heard; but on pressing the fork
down to the board the tone appears to jump up an octave ; at
least the second partial (octave of the prime) is heard with
great distinctness. This experiment appears to prove that if
an elastic resonant body (in this case the resonant board) is in
a state of initial pressure at the point of origin of vibrations,
a vibration that would otherwise be simply pendular becomes
a vibration compounded of two or more simple pendular vi-
brations. Applying this consideration to wind instruments,
and bearing in mind the initial pressure caused by the escape
128 Prof. P. E. Chase on Radiation and Rotation.
of air from the lips, it would appear probable that mouth-
pieces of different forms so modify this initial pressure as to
cause a variety in the number and intensity of the upper partial
tones.
XVII. On the Nebular Hypothesis —1X. Radiation and Ro-
tation. By Pursy Harte Cuase, LL.D., S.P.AS., Pro-
fessor of Philosophy in Haverford College*.
(Continued from vol. v. p. 367. |
MONG the most interesting of the unsolved astronomical
problems are the questions as to the origin of solar ra-
diation and of cosmical rotation. These two problems, as I
have already shown, are intimately connected, at the centre of
our system, by the ultimate equality which exists between the
velocity of light, the limiting centrifugal velocity of solar ro-
tation, and the velocity of complete solar dissociation.
It has been commonly assumed that physical forces tend to
ultimate equilibrium and consequent complete stagnation. The
imperfections of any plan which looks to such a final result
have led some writers to suppose that there may be some com-
pensating provisions, hitherto undiscovered, for a renewal of
activity. In the search for such provisions, the equality of
action and reaction, and the possibility that the compensation
is continually furnished by Him who is ever “ upholding all
things by the word of his power,’ seem to have been wholly
overlooked.
If we assume the existence of a luminiferous ether, whether
as a reality, or as a convenient representative of coordinated
central forces, its undulations, when obstructed by inert centres,
would necessarily lead to such phenomena as those of grayi-
tation, light, heat, electricity, magnetism, &e. Confining our-
selves for the present to the action of gravitation, it is well
known that the limiting velocity of possible gravitating action
and consequent centrifugal reaction at any given point is uf 2qr,
the velocity varying as we = If, according to the hypothesis
-
of Mossotti, each particle is provided with a definite zthereal
atmosphere, the density of that atmosphere in a condensing
nucleus should vary as 3. But, according to Graham’s law,
T
* Communicated by the Author, having been read before the American
Philosophical Society, June 21, 1878.
Prof. P. EH. Chase on Radiation and Rotation. 129
va va : Therefore, in order to satisfy the conditions of
gravity, the ethereal elasticity, within any nucleus which is
either wholly or almost wholly gaseous, « ae
Since such is the supposed character of the solar nucleus, it
_ seems not unlikely that, the centrifugal radiations of any hea-
venly body being at all times equivalent to the centripetal
radiations which it intercepts, solar and stellar light and heat
are only the reactionary consequences of such perpetual in-
ternal oscillations as the ether has first transmitted to the
luminous orbs and then resumed. ‘The fact that the reaction
which is shown in the centrifugal force of solar rotation, and
the action which is shown in parabolic orbital velocities, find
a common limit in the velocity of light, may perhaps be re-
garded as a crucial test of this hypothesis, which is further
strengthened by the following considerations.
In the huge comet-like nebulosity which is indicated by the
solar-stellar paraboloid, the interesting relation which has been
pointed out by Stockwell* between the perihelia of Jupiter
and Uranus, and the many indications of normal “subsidence ”’
which I have shown in previous papers, suggest the probability
of an early ellipsoidal nucleus with subordinate nucleoli—the
_ major axis of the nucleus being bounded by 2; (60°939) and
25; (41°358), and the Sun being in the focus. The vis viva
of condensation would give velocities of incipient orbital sepa-
ration at Y, (30:470) and 6; (20°679); and 4, would then be
in the centre of the entire system (30°470 —20°679 —2 =4:°885 ;
44=4°886), even as ©; is nearly in the centre of the secondary
system (6,+ 9,+2=1-017).
If we apply Gummere’s criterion (n=11°656854), we find
that three prominent centres of “subsidence”’ were deter-
mined by this early ellipsoidal nucleus. For 2¥;~n=5:228,
43 being 5°203; 26;—n=3:548, which is near the outer limit
of the asteroidal belt, (107); being 3560; (Y1— 61) +n=1-022,
the centre of the secondary system being, as above stated, 1:017.
The Harth is still in the centre of a “ subsidence ”’ ellipsoid, of
which the Sun is in one focus, while the outer asteroidal region -
(3°2028) and 43 (5°2028) are at opposite apsidal extremities
of the major axis. Moreover 3°2035 is the extremity of an
atmospherical radius which would move with the velocity of
light, provided the sun’s surface were moving with orbital ve-
locity, or the velocity of incipient dissociation (4/97).
* Smithsonian Contributions, xlv. p. 232,
Phil. Mag. 8. 5. Vol. 6. No. 35. Aug. 1878. K
130 Prof. P. E. Chase on Radiation and Rotation.
It seems probable that, in consequence of subsidence, Ju-
piter, which, as we have already seen, was the centre of nucleal
volume, may have also been the centre of nucleal mass at the
time of its complete orbital separation, and that it was there-
fore the primitive Sun of the extra-asteroidal planets before it
became our Sun’s “companion star.” Jor with the present
mass of the system, and with a mean radius vector = Yy+ 41
(34°4845), the orbital period of Neptune would be 73,966 days.
Two successive subsidences (34°4845-—-n”) would bring the
solar nucleal surface to about 2 of §3, or 54°53 solar radii.
The angular acceleration of rotation, due to subsequent nucleal
1
contraction, would a 2 Therefore, when the Sun had con-
tracted to its present limits, its rotation-period would be
73966 +54°53’ = 24°88 days*.
If this were the only coincidence of its kind, we might per-
haps have some good grounds for looking upon it as merely
curious and accidental; but the bond of connexion which we
have already found between rotation and revolution, in the
limiting formative undulations which are propagated with the
velocity of light, may prepare us for accepting evidences of a
similar bond in the phenomena of nebular subsidence.
There are three other known systems of cosmical rotation
which may help us to judge as to the rightfulness of such an
acceptance, viz. :—that of the extra-asteroidal planets, with an
estimated average period of about 10 hours; that of the intra-
asteroidal planets, with an estimated period of about 24 hours;
and that of the moon, with a synodic period of 29:5306 days.
If these periods are dependent upon the same subsidence which
led to the early belt-formations, we may reasonably look for
evidence of that dependence of a character similar to that
which we have found in the case of the sun.
We have seen that the first subsidences from 2Y and 3y
account for the orbital ruptures of Jupiter and Harth; second-
ary subsidences from points within the orbital belts account
* These relations may have an important bearing on Croll’s hypothesis
of the origin of solar radiation. In the stellar-solar paraboloid, of which
traces still exist between Sun and # Centauri, there must have been fre-
quent collisions. Some of Croll’s critics have shown strange misappre-
hensions as to the possible velocity of collision. The limit of possible
relative velocity, from the simple gravitation of two equal meeting masses,
is 2V2gr. This would be equivalent, taking the values of g and 7 at Sun’s
apparent surface, to ‘017747, or more than 750 miles per second. If pro-
jection were added to gravitation, or if the two masses had small solid
nuclei of great density, while the greater part of their volume was gaseous,
or if there were a large number of equal masses, the limit of possible velo-
city might be largely increased.
Prof. P. E. Chase on Radiation and Rotation. 131
for these three rotation-periods. For 4;+n = 101°73 solar
radii, and Jupiter’s orbital revolution (4832-585 d.)—-101-73”
=10°05 h.; e,+n=19°66 solar radii, and Harth’s orbital re-
volution (366°256 d.)+19°66?=24:205 h.; d4+n=5°442
Karth’s radii, and Harth’s rotation x 5-442?=29°619 d. In
these accordances we have additional evidence of the equality
of action and reaction.
The normal character of rotation is still further traceable,
even after the formation of the subordinate planets in the two
principal planetary belts. If we seek the point of incipient
condensation which would lead to such rotation-periods as
have been generally assigned by astronomers to the different
planets, we readily find that Gummere’s criterions, Newton’s
third law, and the law of equal areas lead to the formula
er er,
n(>)'= ae in which n = Gummere’s criterion, > = num-
ber of planetary rotations in one orbital revolution, R=radius
of nebular contraction, p = Sun’s present radius. Taking
Herschel’s values for T and ¢, we have
(2)? Ry, B (9).
t 0 p
& 1104 U;. 1024 — do, 1111
@ 1776 Q5 166-4 43, 1766
® 223-1 1 2222
3 301°8 g, 301-5 =
4454 | (3) 4271 to 7194 | 20, 444-4
Y 11925 5 1185-9
h 1829-5 hy 1876-7
6 3245°7 SW, 3258-9
It thus appears that—
1. Allthe points of incipient condensation, 5 (), are within
Kirkwood’s “ spheres of attraction.”
2. In the pair of extra-asteroidal planets which are nearest
the asteroidal belt, the incipient points are near the secular
aphelion of the inner, and the secular perihelion of the outer
planet.
3. In the pair of intra-asteroidal planets which are nearest the
asteroidal belt, the incipient points are near the mean aphe-
lion of the inner and the mean perihelion of the outer planet.
4. The sum of the radii of nebular contraction for the two
principal planets of the solar system (1192°5 + 1829-5 =3022)
is almost precisely equivalent to the sum of the mean perihe-
lion radii of the same Senge 1069°6 + kh, 1950°4=3020).
, 2
132 Prof. W. E. Ayrton on the Electrical
. . . . . R
5. The secondary points of incipient condensation, Pe
are all referable, through the simple accumulation of vis viva,
to primary mean aphelia.
6. The significance of the fourth accordance is increased by
Stockwell’s discovery* that ‘the mean motion of Jupiter’s
node on the invariable plane is exactly equal to that of Saturn,
and the mean longitudes of these nodes differ by exactly 180°.”
7. Gummere’s criterion confirms the theory of Democritus,
that the evolution of worlds was due to a-vortical movement,
which was generated by the descent of the heavier atoms
through the lighter.
XVIII. The Electrical Properties of Bees’-wax and Lead Chlo-
ride. By W.H. Ayrton, Professor in the Imperial College
of Engineering, Tokio, Japant. :
| Plate IL. ]
on the two papers by Prof. Perry and myself on Ice as an
Electrolyte, recently read before the Physical Society,
we showed that both the conductivity and specific inductive
capacity of { ane increases regularly, without discon-
tinuity, in passing from several degrees below the freezing
point to several degrees above it. We drew attention to the
fact that, in consequence of the absorbed charge in water
being immeasurably greater than the surface-charge, we
could not hope, by any method of experimenting, to properly
compare the true specific inductive capacity with the index
of refraction for light of infinitely long waves; so that, in
fact, the only support that Prof. C. Maxwell’s electromagnetic
theory of light could hope to derive from these experiments ©
must be based simply on the fact that in { De } both the
water
specific inductive capacity and the index of refraction increase
as the temperature rises. At the meeting of the Society on
November 3rd, at which the second of our two papers was read,
Prof. G. Foster mentioned that he had recently been collecting
all the results he could find connecting specific inductive
capacity with index of refraction. I therefore beg to forward,
as a contribution to this collection, the following results of
some further experiments which I have been making on this
subject.
* Loc. ct.
+ Communicated by the Physical Society.
Properties of Bees’-waxz and Lead Chloride. 133 ©
For the last two years my attention has been turned to wax
as a good material for electrically testing, especially in regard
to the connexion which, in our paper on the Viscosity of
Dielectrics, communicated to the Royal Society, we pointed
out existed between high specific inductive capacity and low
specific resistance. I therefore had constructed a large con-
denser, consisting of many sheets of letter-paper soaked
in melted bees’-wax, with alternate sheets of tin-foil. After
the condenser was built up in the usual way, melted bees’-wax
was poured in, the plates squeezed together, and the whole
shut up in a fairly good water-tight wooden box. The con-
denser was buried several feet under ground, to ensure uni-
formity of temperature, connexion being made with the insu-
lated coating by a piece of Atlantic-cable core, and with the
other coating by a piece of bare copper wire.
After this condenser had been buried for a short time
underground, it showed the apparently abnormal condition
of diminution of resistance by electrification. This pheno-
menon then formed the subject for special investigation
with this condenser, an account of the results obtained being
given at the end of this short paper.
As bees’-wax is one of the few substances in which the
index of refraction for light increases in passing from the
liquid to the solid state, it seemed important, in connexion
with the electromagnetic theory of light, to carefully mea-
sure the specific inductive capacity of a wax condenser as
it was gradually cooled through the solidifying point. A
small, shallow, clean copper box, 19 centims. long by 17
centims. wide, was therefore lined with a sheet of letter-paper,
0-036 centim. "thick, previously well soaked in melted bees’-
wax. A clean copper disk, 12°8 centims. in diameter, was
placed on the top, weighted down, and the dish filled
up with melted wax. This condenser, AB (fig. 1), was
heated in an oil-bath, CD. E and F are holes for the
insertion of thermometers, of which the bulbs were just
above the wax condenser; G is an opening through
which the insulated electrode H of the condenser may pro-
trude without touching the oil-bath. A wooden stand, W W,
supports the condenser in the middle of the bath; and a glass
vessel V holds strong sulphuric acid to keep the inside space
artificially dry. The bath is closed by a double door, which
is made to fit well by a strip of leather inserted between it
and the bath.
The condenser having been inserted, the bath was heated to
about 90° C., and kept at that temperature for some time ; the
lamps were then removed, when the temperature fell very
134 Prof. W. E. Ayrton on the Electrical
slowly. The capacity was then measured (several observations
being made at each temperature) by charging the condenser
with 75 Daniell’s cells joined in series, and discharging it
through an exceedingly delicate Thomson’s reflecting galva-
nometer. The curves ABCD, HFG, HIK (fig. 2) repre-
sent the results obtained on three different days, distances
measured parallel to O X representing temperature, the points
O and X corresponding respectively with 0° C. and 100° C.,
and distances measured parallel to O Y representing capacity,
the zero-line for capacity for the curves ABCD, EFG,
HIK being below OX by a distance equal to # of OY.
For the curve G HI the zero-line is OX. It will be seen at
once that these curves, obtained on different days, do not give
the same capacity for the same temperature (the numbers,
therefore, that have been calculated for the specific inductive
capacity are not given) ; but considering, first, the very small
capacities that had to be measured, and, secondly, the difficulty
of accurately determining the temperature of a non-heat-
conductor like wax, even when enclosed in the oil-bath, the
discrepancies in the curves are not to be wondered at. One
fact, however, is very striking in all the three curves ; and that
is the rise in capacity as the temperature very slowly falls
from about 80° to 60° C., and the subsequent diminution in
the capacity on a still further diminution of the temperature.
Probably, had experiments on capacity been made when cooling
from a much higher temperature, there would have been
observed, first,a gradual diminution in capacity due to cooling
down to about 80° C. (traces of this first diminution are seen
in the portion A B of the curve ABCD); then we have the
rise of capacity as the wax solidifies at about 60° C.; and,
lastly, we see the subsequent rapid decrease on further cooling.
Now this is precisely in agreement with the changes known
to occur in the index of refraction for light; and hence the
interest of these experiments.
As there was always a small electromotive force in the wax
condenser, and as the vibrations of the galvanometer-needle
were, as usual, damped by the air-vane, | used for calculating
the capacity the formula developed by Prof. Perry and
myself for employment in such cases*, which is
H P ou tan-12 TT 2 Loe
poet ee SE 42 np 2 pa of oe See eS 2 a —— ae
Q eas { Pe evan! +e
* A Test for determining the Position of a partial Discontinuity,
pathous Earth-fault,’ by Professors W. E. Ayrton and John Perry,
a
Properties of Bees’-wax and Lead Chloride. 135
where Q is the quantity of electricity discharged through the
galvanometer, H the horizontal intensity of the galvanometer-
field, 7 the half length of the needle, G the galvanometer-
constant, P the periodic time of vibration, L the logarithmic
decrement, x, the first sudden swing on discharge, 2, the
deflection that would be produced by the small constant
current, and which is equal to
a+ Daz
1+D’
where # is the second swing and D the decrement. :
It might, of course, be at once objected that the rise in
capacity as the wax cools from about 80° to 60° C. is perhaps
not due to any change in the specific inductive capacity, but
merely indicates that the distance between the copper plate of
the condenser was slightly diminished by the wax shrinking
on solidifying. ‘This solution, however, is improbable, since,
although a sudden expansion of the wax on solidifying (if
such an expansion existed) might have separated the plates,
it is unlikely that the contraction which really occurred
could have brought them nearer together than the thickness
of the paper by which they were separated when the wax
was liquid. Nevertheless, partly to obtain additional evi-
dence on this point, and partly to measure the specific
resistance (or resistance per cubic centimetre) of bees’-wax
at different temperatures, I made ten distinct sets of expe-
riments, occupying many days, on the conductivity of wax.
In these experiments the wax condenser was heated up to
about 130° C., and_a current sent through it with the 75
Daniell’s cells in series. The temperature was kept constant
at about 130° C. until the galvanometer-deflection had reached
its maximum, when it was considered that the wax had ac-
quired the temperature indicated by the thermometer. The
temperature was then allowed to fall very slowly, and fre-
quent readings of the galvanometer and thermometer were
taken. The results obtained are shown on fig. 3, temperature
being measured parallel to O X, the points O and X corre-
sponding with 30° and 130°C.; distances measured parallel
to OY represent conductivity on such a scale that for the
curve LM, representing the conductivity between 115° and
65° C., OS corresponds with a resistance of 67,735 megohms
per cubic centimetre ; and for the curves N P, QR (which
are drawn on a larger scale) the distance OT represents a
resistance of 186,000 megohms,—the zero-line for conductivity
for all three curves being OX. The point P, corresponding
to a resistance of 37,000,000 megohms per cubic centimetre,
136 Prof. W. E. Ayrton on the Electrical
represents the lowest conductivity I was able to measure with
certainty directly with the galvanometer. It may here be
mentioned that such high resistances could be measured with
the galvanometer, since one Daniell’s cell, through a resistance
of 600 megchms, gave 130 scale-divisions deflection on a scale
about 14 metre distant. The various curves obtained for con-
ductivity between 115° and 65° C. agree so closely that they
may all be represented by the one curve LM. The curves for
the conductivity between 80° and 40° C. are all quite regular,
but not all of exactly the same slope, the difference depending
on the highest temperature to which the wax was heated before
cooling on the particular day of experimenting, this being
sometimes about 130°C. and at other timesabout 90°C. All
the curves, however, agree so closely that they are all contained
between the two limiting curves N Pand Q R shown in fig. 3.
In no curve was there the slightest appearance of a rise of con-
ductivity at the melting-point, which would probably have
been obtained had the copper plates approached one another
an appreciable distance on the wax solidifying.
We may therefore conclude that in the previous experiments
the rise in the capacity at melting indicates a true increase in
the specific inductive capacity coincident with an increase in
the index of refraction for light.
As regards apparent increase of resistance by electrification,
which, as mentioned, I observed during repeated experiments,
extending over some months, with the wax condenser buried
underground, the general conclusions arrived at were that
not only did the conductivity usually increase by electrification,
but that it steadily increased day by day—a result indicating
that the wax was deteriorating, probably from damp penetrating
through the joints of the wooden box in spite of leather having
been inserted between the different parts of the wood before
they were screwed together. This conclusion appeared to ke
correct, since, on digging up the condenser and keeping it
near a fire for many days, it regained its original high
resistance. The damp must therefore not only have entered
through the joints in the wood, but through some small cracks
that were observed in the mass of wax when the condenser
was opened ; and it was probably due to this damp that the
peculiar effects of polarization were observed similar to those
noticed by the Comte du Moncel when testing stones, and by
Mr. T. Warren in certain insulating oils.
I now made a number of experiments with lead chloride as
a dielectric—a substance to which my attention was especially
drawn by some remarks of M. Buff in Ann. Chem. Pharm. ex.
p. 258 (1859), in which he says that this substance conducts
Properties of Bees’-wax and Lead Cloride. 137
electricity like a metal (that is, without decomposition)—a
conclusion, however, which at first sight would appear to be
negatived by certain experiments of M. Wiedemann published
in Pogg. Ann. cliv. 818-320, from which he found that the
resistance of lead chloride diminished by increase of tempe-
rature. .
I first had made a small carbon box containing a carbon
plate, but prevented from touching it by three small pieces of
clean glass. The carbon plate had a carbon electrode attached
to it, the whole being cut out of a solid piece of carbon so as
to have the shape of aninverted T. Into the box lead chloride
was poured in a fused state until it covered up the plate, but
leaving the carbon electrode of the plate protruding for con-
nexion with the battery. The whole was then allowed to cool
very slowly. The outer part of the carbon box and the end
of the carbon electrode were now electrotyped, and copper
wires soldered on, the junctions of the carbon and copper being
quite clear of the lead chloride.
With this condenser the results given on the next page were
observed.
In addition to the resistance of the condenser being mea-
sured while the battery was connected, time-readings were
also taken with the galvanometer of the discharge from the
condenser after the removal of the battery, as well as time-
readings with an electrometer of the electromotive force in
the condenser producing the discharge. As, however, the
diminution in the discharge-deflection was in each case quite
regular, the curves are not given.
It is interesting to observe in the Table (p. 138) that in
every case there isa diminution of resistance by electrification,
although in some cases there was an increase during the first
minute. Looking at the first group of tests, taken between
November 13th and 15th, we see a gradual increase in the
resistance day by day. Looking also at the second group
made between November 21st and December Ist, we likewise
see a steady daily increase in the resistance ; but in the interval
between November 15th and 21st, when no tests were made,
there appears to be a decided diminution in resistance. Con-
sidering, however, that the tests taken on November 13th, at
the beginning, and on December Ist, at the end of the inves-
’ tigation, give almost identical results, it cannot be concluded
with certainty that there was any decided deterioration taking
place in the lead chloride. But on breaking up the condenser,
the lead chloride was found to contain many small holes ; so
that it is possible that damp may have collected in these.
This solution, however, would at first sight appear to be rather
ao
Prof. W. I. Ayrton on the Electrical
WMOdf OOUVYSTSAL UT MOTYNULUUTp Apvaqg
‘OINUTUL JSATE OY} JO O[pprut ony
ULOAf ODULISISEL UT UOTJNUTUITP Apeayg }
‘OINULUT PUODIS OY} JO SuruUTSeq oy} =}
MOA BDURASISAI UT UOTNUTUITp Aproyg i
‘INULUL PUOVES oY} JO Suruurseg oy}
WLOA} BOULISISAL UL UOTJNULUATp Apreyg |
‘QINUIUM JsAy OY} JO oTpprur ory
WIOIF OULISISAL TL WOTNULUUTp Apeeyg }
‘OINUTUL PUODES OT[} JO SUIMUIHEq OT} \
WlOAf VOULISISEI UL UOTYNULUATp Apreyg
‘ONUTUL PUODES OT[} FO OTPprur 174
MOL} BOULISISOI UL UOTJNUTUUTpP Apreqg }
“‘SULUUTSOq OT} \
WOAf GOULISISAL UL UOTyNUTUITp Apee}g
‘OINUIM JSF OT} JO pus 944
WLOA} COULISISEL UL UOTJNUTUAIP aoe
"UOTJVATOSQO 4SATZ OT}
WLOL COURYSISOL UL MOTYNUTUITp Apre}g
‘QINULUL PTY OT} JO PU oT}
WOU, dOULISISEL UT WOTNUTUIpP Aproqzg \
‘OINUIUL ISA OY} JO 9TPprat oy \
WII} GOUBISISAL UT UOT;NUTUATp Aproyg
“SY IVULOY
"81894 0} AtOAO LOB JoY PodLVTPOSIp [T0a4 LOSUepPTO(
C6G-1, “UrtE G
E9L-9 “Ura OT
OFP.g “urtd 9
6OF-g “Uru 9
SOL-p “UIT G
0Z8.¢ “urut g
COG-p “UU ZT
166-6 “Ure FT
109-2, “Urea g
Z89-8 “ULUt G
96.9 “UTU FT
PLL-Q “Ula FT
IJV
661-8
G18-L
OLE-9
PLO
116-4
LOL-9
“CLU T
Joye
667-8
OOT-8
PLLO
981-9
LOT-9
OLLG
SE1-G
STT-6
CL-O1
SF8-4
L108
"028 Q
Ioqye
169-8
C18-L
eee eee
ee eens
L6-L
‘098 CT
LO}
‘SUIOSOUL UT ‘TOSMOPTOD XVAA OY} JO dOULISISEIT
seers XOG MOGAVD OF
r ood
)
saddoo s}joa Qe
J “* 9yvyd tog.ard 04
{ .
| ejod
i ejod aaddoo s}[0A Qe
“= "**XOQ TOL 04
taddoo sjfoa OE
5" xOq WOGIvd 04
toddoo s}joa Te
£0 YCT
a ihe SE ————
SSE Oki cad!
a. wibes ye ae
20h ears
be eee ee
Se re)
YI9G “AON | *L
4IVG “AON | 9
1G “AON |G
O G-o8T {IGT “AON | “Pb
‘D 6-o06T TPT “AON |
O8o8l | WET AON |G
O 8-o8T Ss TST “AON | 'T
‘dxo
‘diay, ‘aque jo
‘ON
OO ee
Ce re
Properties of Bees’-wax and Lead Chloride. 139
improbable ; since the condenser, both when being tested and
when not tested, was kept in an atmosphere kept partially dry
with sulphuric acid.
Some fresh lead chloride was prepared in the same way as
before—that is, by precipitating from a solution of lead acetate
with a solution of common salt, and carefully washing the
precipitate several times with distilled water. But the new
condenser, made with the carbon box and plate, was found to
have a resistance of only two megohms at 16° C.; and, unlike
_ what was experienced in the former case, the resistance in all
the experiments was now found to increase by electrifications.
This, however, is probably explained by the fact that, whereas
in the previous case thirty volts electromotive force was used,
now only one volt was employed; so that decomposition
(whether of the lead chloride itself, or of the damp which after
decomposition may act on the chloride) was probably not pro-
duced. Some preliminary temperature-tests were now made;
and, in accordance with Wiedemann’s results, 1 found that
the resistance diminished with elevation of temperature.
The condenser was now left in an atmosphere dried with
sulphuric acid from December 21st to January 7th, when it
was found that the resistance had increased to about 15°6
megohms at 70°C. A large number of measurements of the
conductivity at different temperatures, using the same oil-bath
for raising the temperature as is shown in fig. 1, were now
made. The different experiments gave results so nearly
agreeing that they may all be represented by the curve STV
~ (fig. 4), in which distances parallel to OX represent tempe-
rature, the points O and X corresponding to the tempera-
tures 0° and 100° C. respectively ; and distances parallel to
OY represent conductivity on such a scale that the point T,
corresponding to a temperature of 70° C., represents a re-
sistance of about 15°6 megohms. ‘The curve is approximately
logarithmic; that is, the ratio of the difference of the
logarithms of the conductivities to the difference of tempera-
tures is approximately constant.
Thinking that possibly the method previously employed for
making the lead chloride, by precipitating it from a solution of
lead acetate with a solution of common salt, may have intro-
duced traces of some salt of lead other than the chloride, the
following method was now employed for making another
supply of the chloride. From a clear solution of lead nitrate
a precipitate was formed with colourless hydrochloric acid,
and the precipitate well washed with distilled water. A third
condenser was now constructed, three small pieces of glass
0:225 centimetre thick being used to separate the carbon
140 Prof. W. E. Ayrton on the Electrical
plate from the box. The connexions with the box and plate
were made as before, by first electrotyping the carbon with
copper and then soldering on copper wires, the junctions of
the carbon and copper not being in contact with the lead
chloride. A condenser was also made with a copper box and
a copper plate, the two being well coated with graphite to
protect them from the action of the lead chloride, and separated
from one another by three small pieces of glass 0°135 centi-
metre in thickness.
Tests of conductivity were now made at different tempera- ~
tures with both condensers, 0:075 volt being employed with
the carbon and 7°35 volts with the copper condenser, or some-
times 2°2 volts with the latter. With the carbon condenser
and with the smaller electromotive force the resistance was
found to increase with electrification, whereas with the copper
condenser and with the electromotive force 2°2 volts the re-
sistance diminished with electrification, and with 7:5 volts this
diminution became much more rapid, these results being
observed at both high and low temperatures. In the earlier
experiments with this copper condenser the diminution was
regular, whereas later on it proceeded irregularly ; but on the
whole it may be said that when an electromotive force not
exceeding 12 volt was employed there was an increase in
resistance by electrification, such as is usually experienced with
gutta-percha and with ordinary dielectrics, while when the
electromotive force exceeded this limit there was either a
regular or an irregular diminution of resistance by electrifi-
cation—the results apparently not depending much on whether
carbon or copper coated with graphite was used for the plates
of the condenser.
As this limiting electromotive force appears to be about the
same as that necessary to decompose water, I think we may
fairly conclude that the diminution in resistance is due to a
decomposition of the damp (which appears to be contained in
the lead chloride even when careful means are taken to dry
it), and to the products of the decomposition acting on the
chloride. Fig. 5 shows four electrification-curves, A A A,
BBB,CCC, DDD, obtained from four successive experiments
with the carbon box, and corresponding with the temperatures
15° C., 57° C., 14° C., 61° C. respectively. Time is measured
parallel to O X, the points O and X corresponding to the
moment of applying the battery, and to 50 minutes after-
wards; conductivity is measured parallel to O Y from the line
O X of zero conductivity. The curves BBB and CCQ, for
57° C. and 61° C., are drawn on a vertical scale five times
smaller than that employed for A A A and C C C—the scale for
Properties of Bees’-wax and Lead Chloride. 141
time, however, remaining the same. All the tests from which
these curves are drawn were made with 0:075 volt electro-
motive force. The curves aaa, bbb, ccc, fig. 6, are the dis-
charge-curves obtained in the three above experiments for
15° C., 57° C., and 14° C., observations of the discharge in the
experiment for 61° C. not having been taken. The scale both
_ for conductivity and for time is the same exactly as that
employed in the curves AA A, CCC, fig. 5. All the curves
show a regular increase of resistance with electrification, the
increase being far more rapid at a high than at a low tempe-
rature. As was seen from the curve 8 T U, fig. 4, so also from
fig. 6 we learn that the conductivity is much greater at a high
than at a low temperature ; and we also see from the curves
AAA, BBB, CCC, D DD, that the general effect of testing
day by day appears to lower the conductivity.
Hlectrification-curves HEE, FE F,GGG, HH HG, fig. 7,
were obtained from four successive tests with the copper-box
condenser, and correspond with the temperatures 15°C., 60°C.,
13° C., 61° C. respectively. Time is measured parallel to O X,
the points O and X corresponding to the moment of apply-
ing the battery; and 50 minutes afterwards conductivity is
measured parallel to O Y from a zero as far below O X as the
point Y is above. Curve FFF is on a scale for vertical
distances one twentieth of that employed for the curves H EH
GGG, and HHH on a scale one fifth of that used with
HHE,GGG: that is tosay, if the same scale were employed
for vertical distances for all four curves, the two for the higher
temperatures would be far above those for the lower tempera-
tures—in fact, would be off the paper altogether. For hori-
zontal distances (that is, for time) the same scale is employed
for all the curves, An electromotive force of 7:5 volts was
employed with all the experiments from which these four
curves were drawn. Although the curves are irregular, still,
on the whole, there is an increase of conductivity or diminution
of resistance with electrification ; and that this is probably due
to the chemical action of the current referred to above is shown
from the irregularity of the discharge-curve ggg obtained
after removing the battery in the test at 15°C. Curve hhh,
however, which is the discharge-curve for the test at 61°C.,
does not show any such irregularity ; but then it must be
noticed that H H H, the charge-curve for this temperature,
indicates on the whole rather an increase than a diminution
of resistance by electrification.
April Ist, 1878.
[ 142 ]
XIX. Theory of Voltaic Action. By J. Brown, Esq.*
a production of a difference of electric potential by vol-
taic action is attributed by some primarily to the differ-
ence of chemical attraction between the two elements of a
voltaic couple for one of the components (ions) of some com-
pound body (electrolyte) in contact with both, that element
which has the greater affinity being the positive one. It is
said by others to be due to the simple ‘‘ contact’ of the two
elements without the intervention of any third substance or
combination, and has been attributed, in the case of two metals
such as copper and zine, to their mutual chemical attraction.
Faraday could not, however, discover any current during the
combination of two metals (tin and platinum), through great
heat was evolyed{; and he considered that though the source
of energy in a voltaic pair was the combination of the active
ion with the positive plate, decomposition was necessary to its
development in the form of electricity. Numerous old expe-
riments may be cited which show how in*various ways altera-
tions in the electric relations of metals in voltaic pairs may be
produced without altering their contact. |
The following experiments seem to go far towards establish-
ing the truth of the first-mentioned (chemical) theory.
If a potential series (A) be formed by immersing couples of
various metals &c. in an oxidizing electrolyte and testing for
the current generated, and another (B) by the use of condenser-
plates in the usual way adopted by contact theorists, the two
series will be found curiously similar. The simplest conclusion
appears to be that the so-called “ contact”’ excitement is due
to the presence of a gaseous film § containing water, carbon
dioxide, or other oxygen compounds between the plates, which
film may be considered as having all the properties of an oxi-
dizing electrolyte except its conductivity.
If in forming series A we use an electrolyte containing
some other active ion such as sulphur, we obtain a totally dif-
ferent series, which, as Professor Fleeming Jenkin remarks],
is “ quite anomalous and inconsistent with the simple poten-
tial theory.” But if the chemical theory be true, then in
forming series B, if we substitute for the ordinary atmosphere,
containing watery vapour and other oxygen compounds, an
* Communicated by the Author.
+ Sir William Thomson, ‘ Electrostatics and Magnetism,’ § 400; Tait,
‘Recent Advances,’ p. 805 et seq.
t Phil. Trans. 1834, p. 486.
§ Wiedemann, Galvanismus, p. 12.
|| Electricity and Magnetism, p. 217.
Mr. J. Brown on the Theory of Voltaic Action. 143
atmosphere containing a suitable sulphur compound, the ano-
maly should disappear, and we should obtain effects with the
condenser which would place the metals in the same potential
order as when immersed in sulphur electrolytes. In order to
verify this the following experiment was made. Starting with
the fact that iron is positive to copper in an oxidizing electrolyte
(as water), while copper is positive to iron in a solution contain-
ing potassium sulphide or other similar sulphur compound, I
made a condenser with disks 44 inches in diameter, one of
copper, the other iron, well ground together. The irondisk was
screwed on the lower end of an iron rod sliding in a brass tube
fixed with shellac in a wooden cover fastened on the neck of a
gas-jar. The jar stood on a wooden stand, through the middle
of which rose a similar insulated rod carrying the copper disk.
Means were provided for adjusting the disks parallel to one
another, and also for filling the jar which enclosed both disks
with any required gas.
To measure the charge excited by the “contact”’ of the
plates a quadrant-electrometer was employed, which gave a
deflection of 5 millims. for the potential of a bichromate cell.
When the condenser-plates were placed together (in ordinary
atmosphere) connected with opposite pairs of quadrants and
then separated, the index light moved over 1 centim., the iron
being positive, as was to be expected. Hydrogen sulphide
was then allowed to flow into the gas-jar; and on repeating
the connexion and separation of the plates the iron proved to
be negative, the light-spot moving over about 3 centims. in
the direction opposite to its first motion. This was repeated
several times ; and on examining the plates after the experi-
‘ment, the copper was found to be of a deep blue colour, while the
iron was scarcely altered. It will be observed here that the
only alteration in the circumstances of the experiment was the
change in the atmosphere surrounding the plates. The con-
tacts all remained the same; and when the atmosphere con-
tained a sulphur compound, the plates assumed the same elec-
tric relation as they would in an electrolyte containing a
sulphur compound. LEven the proportionate degree of tension
between the plates in air and in hydrogen sulphide is similar
to the ratio of their electromotive force in water and in potas-
sium sulphide solution.
The next experiment appears to confirm in a marked way
the view that the difference of potential between two metals
in contact is due principally, if not altogether, to the difference
of their affinities for one of the elements of some compound
gas in the atmosphere surrounding them. The experiment is
a modification of one devised by Sir William Thomson, and
144 Mr. J. Brown on the Theory of Voltaic Action.
described in his ‘Papers on Electrostatics and Magnetism,’
p- 317 :—“ A metal bar insulated so as to be movable about
an axis perpendicular to the plane of a metal ring made up
half of copper and half of zine, the two halves being soldered
together, turns from the zinc towards the copper when vi-
treously electrified, and from the copper towards the zine when
resinously electrified.’’ Instead of a copper and zinc ring Lused
a copper and iron one, OC I, 3:1 inches
diameter outside, with a 1 inch hole in
centre. It was supported on a tripod
inside a case with plate-glass sides, and
which could be connected by rubber
tubing with an apparatus for genera-
ting hydrogen sulphide. A piece of
lead-paper was placed inside the. case
to detect the first entrance of the gas.
From the tep of the case rose a ver-
tical glass tube with a torsion head,
from which depended a platinum wire
°0025 in. in diameter and about 19 in.
long, carrying the needle or bar, n, of
thin sheet aluminium, 13 in. long by
32s In. wide, a mirror M of about 4 ft.
focus, and a glass weight, W, which
dipped in a vessel of water to steady
it. The tripod carrying the ring
rested on the points of three screws
passing up through the bottom of the
case, by means of which the plane of
the ring could be adjusted so as to get
equal deflections on each side of the
zero-line. The needle hung at a distance of 1 or 2 millims.
above the ring, as nearly as possible over the junction of the
metals, and having. its suspension-wire in the centre of the
ring. It was electrified by connecting it with the positive
or negative conductor of a Winter’s plate machine.
In a preliminary experiment with a copper-zine ring, de-
flections of 5 centims. on each side of zero on the scale were
readily obtained. With the copper-iron ring, however, the
deflections were only 4 to 1 centim., the iron being as zinc to
the copper. As the potential of the needle could not be main-
tained constant by the means employed, the deflection was
continually varying in amount; but when the machine was
carefully worked these variations were slight, and did not in-
terfere with the result. What follows is from my notes of the
third time of going over the experiment. The needle being
= :
ee ee ee >
Notices respecting New Books. 145
negatively electrified and deflection about $ centim. towards
iron, the case was connected with the hydrogen-sulphide bottle,
and sulphuric acid poured in to generate the gas. At 2}
minutes afterwards the lead-paper began to darken at edge;
and in half a minute more the needle crossed the zero-line and
turned towards the copper half of ring—defiection about 4
-centim. The needle was then connected with positive con-
ductor and immediately turned towards iron; connected again
to negative it turned towards copper ; and so on, till in about
10 minutes after admitting the gas the deflections became un-
decided, the copper having become covered with sulphide,
which has no affinity for sulphur.
Edenderry House, Belfast,
January 1878.
XX. Notices respecting New Books.
Astronomical Observations made at the Royal Observatory, Edinburgh,
Vol. XIV., for 1870-1877. By Prazzt Smytu, FLASH. ge.
Published by order of Her Majesty's Government. HKdinburgh:
Neill and Co., 1877.
= this volume Professor Smyth has given his attention to a most
important feature of Sidereal Astronomy, viz. “Stellar Proper
Motions.” At present we know but little either of the distribution
of the stars in space or of the directions in which they are moving.
Proctor has shown that groups of stars separated, as seen by the
unassisted eye, many degrees from each other, possess a community
of motion, the logical inference being that they are in some way
connected. The spectroscope reveals to us the fact that many stars
are receding from us in the line of sight, and that others are ap-
proaching us in the same line. Proctor’s deduction of “Star
Drift” is based, if we mistake not, on the Proper Motions as given
in yarious catalogues which he found necessary to study in con-
structing his star-maps; but neither the present recorded Proper
Motions nor the recorded motions in the line of sight give us any
information as yet as to the distribution of the stars in space; and
if Professor Smyth’s suggestion be carried out, of fillimg up the
lacune purposely left in his catalogue for the reception of obser-
vations of R.A. and N.P.D. from other sources to which he has not
had access, it is extremely probable that many corrections may be
made to the numerical values of Proper Motions now on record.
Whether the Astronomer Royal for Scotland has succeeded in truly
correcting the values on record or not, he has at all events drawn
the attention of astronomers to the subject, and that in a way which
cannot fail of contributing to its advancement.
It is considered, by astronomers competent to give expression to
Phil. Mag. 8. 5. Vol. 6. No. 385. Aug. 1878. L
146 Geological Society:—
a sound judgment, that the best determination of Proper Motions
which we possess are by Mr. Stone; they are contained in yol, xxxiii.
of the Memoirs of the Royal Astronomical Society, and are derived
from a comparison of Bradley’s observations with the Greenwich
seven-year Catalogue for 1860, giving an interval of 105 years, on
which the determinations rest.
It is greatly to be desired that the Proper Motions of the Stars,
as now recorded in various catalogues, should be most scrupulously
examined, Stone’s determination being taken as the basis. Among
the stars we have a remarkable class, viz. those having large Proper
Motions. Professor Newcomb, in his ‘ Popular Astronomy,’ refers
to the star 1830 Groombridge as the most remarkable of them, its
Proper Motion being more than seven seconds of are per annum,
which, combined with its parallax, gives a real motion of two hundred
miles in a second of time. There are two stars said to have a
greater Proper Motion than this star, viz. 2151 Navis, whose
Proper Motion is 79 per annum, and e Indi, 77. By giving
close and unremitting attention to these stars, light may be thrown
on the question as to whether they are members of a group passing
through our siderea] system with immense velocity. If Professor
Smyth’s Catalogue contributes in any degree to elucidate our know-
ledge of stellar Proper Motions on a great scale in our sidereal
system, he has not done his work in vain. We greatly approve of
the plan he has adopted of leaving spaces for the insertion of ob-
servations from other sources, also of devoting a page to each star;
and we shall look with great interest for the appearance of the next
four hours of the Catalogue.
XXI. Proceedings of Learned Societies.
GEOLOGICAL SOCIETY.
(Continued from p. 73. ]
May 8, 1878.—Henry Clifton Sorby, Esq., F.R.S., President,
in the Chair,
a following communications were read :—
1. “On the Glacial Phenomena of the Long Island, or Outer
Hebrides.” 2nd paper. By James Geikie, Esq., LL.D., F.R.S., F.G.S.
In this paper the author gave some additional notes on the
glaciation of Lewis, and a detailed account of the glacial
phenomena of Harris and the other islands that form the
southern portion of the Outer Hebrides. Additional evidence was
adduced to show that Lewis has been glaciated from S.E. to N.W.:
and the shelly boulder-clays and interglacial shell-beds of that part
of the Long Island were described in detail. Harris, North Vist,
Benhecula, South Uist, Barra, and the other islands that go to form
the chain of the “ Long Island ” were successively described under the
headings of Physical features, Geological structure, Glaciation, Till or
Glacial Phenomena of the Long Island or Outer Hebrides. 147
Boulder-clay, Erratics and perched blocks, Morainic débris and Mo-
raines, Freshwater lakes and Sea-lochs. Numerous bearings of strie,
which abound, were given; and these were held to provethat the whole
Outer Hebrides have been glaciated by ice that flowed outwards from
the mainland of Scotland. The position of abundant roches moutonnées
points to the same conclusion; and this is still further supported by
the “travel” of the Till. That deposit is generally absent or very
sparingly present on the rock-faces that look towards the mainland;
but it is heaped up in their rear, and spreads over the lower tracts
that slope gently towards the Atlantic. On the west side of the
islands not a few boulders occur in the Till which have been derived
from the east; and the same is true of certain erratics lying loose
at the surface of the ground. The islands are well glaciated up to
a height of 1600 feet above the sea; and the line of demarcation
between the glaciated and non-glaciated areas is extremely pro-
nounced. Above 1600 feet the hills show rugged, splintered, jagged,
and sometimes serrate tops. The author regarded the Till or boulder-
clay as the morainic material that gathered underneath the ice; and
proof of this is given. Hrratics and perched blocks are very numerous ;
and most of these, as well as much of the morainic débris, are believed
to have been dropped where we now find them during the final melting
of the ice-sheet. It was shown, however, that certain erratics and
perched blocks and some well-marked moraines are due to local
glaciers, as are also some of the striations in a few of the mountain-
valleys. ‘The origin of the rock-basins which are now lakes was dis-
cussed, and attributed to the erosive action of ice. ‘To the same
cause were assigned the rock-basins which occur in certain of the
sea-lochs.
In concluding, the author pointed out that we may now arrive at
a true estimate of the thickness attained by the ice-sheet in the
north-west of Scotland. Ifa line be drawn from the upper limits
of the glaciations in Rosshire (3000 feet) to a height of 1600 feet in
the Long Island, we have an incline of only 1 in 210 for the upper
surface of the ice-sheet; and of course we are able to say what
thickness the ice reached inthe Minch. Between the mainland and
the Outer Hebrides it was as much as 3800 feet. No boulders de-
rived from Skye or the mainland occur in the Till of the Outer
Hebrides; and this was explained by the deflection of the lower portion
of the ice-sheet against the steep wall of rock that faces the Minch.
The underpart of the ice that flowed across the Minch would be
deflected to right and left against the inner margin of the Long
Island; and the deep rock-basins that exist all along that margin
are believed to have been scooped out by the grinding action of the
deflected ice. ‘Towards the north of Lewis, where the land shelves
off gently into the sea, the under strata of the ice-sheet were enabled
to creep up and over the district of Ness, and thus gave rise to the
lower shelly boulder-clay of that neighbourhood, which contains
boulders derived from the mainland. ‘he presence of the overlying
interglacial shell-beds proves a subsequent melting of the ice-sheet,
148 Geological Society :—
and a depression of the land for at least 200 feet. The overlying
shelly boulder-clay shows that the ice-sheet returned and overflowed
Lewis, scooping out the older drift-beds and commingling them with
its bottom moraine. The absence of kames was commented upon,
and shown to be inexplicable on the assumption that such deposits are
of marine origin, whilst if they be of torrential origin their absence
is only what might be expected from the physical features of the
islands. The only traces of Postglacial submergence are met with
at merely a few feet above present high-water mark.
2. “ Cataclysmic Theories of Geological Climate.” By James
Croll, Esq., LL.D., F.R.S. Communicated by Prof. Ramsay, LL.D.,
F.R.S., F.G.S.
The author commenced by calling attention to the great diversity
of the hypotheses which have been brought forward for the explana-
tion of those changes in the climate of the same regions of the earth’s
surface which are revealed by geological investigations—such as alte-
rations of the relative distribution of sea and land, of the ecliptic,
and of the position of the earth’s axis of rotation—all of which, he
maintained, have proved insufficient or untenable. Sir William
Thomson has lately maintained that an increase in the amount of
heat conveyed by ocean-currents, combined with the effects of clouds,
winds, and aqueous vapour, is sufficient to account for the former
prevalence of temperate climates in the Arctic regions; and this view,
the author stated, he had himself been contending for for more than
twelve years. He thinks, however, that alterations in the eccen-
tricity of the earth’s orbit is the primary motive cause, whilst Sir
William Thomson believes this to be the submergence of circum-
polar lands, which, however, in Miocene times, appear to have been
more extensive than at present. He pointed out that a preponderance
of equatorial land, as assumed by Sir Charles Lyell to account for
the milder climate of Arctic regions in Miocene times, would rather
tend to loss of heat by rapid radiation into space, whilst water is re-
markably powerful as a transporter of heat; so that, in this case,
equatorial water rather than equatorial land is needed.
In speaking of the glacial climate, the author maintained that
local causes are insufficient to explain so extensive a phenomenon.
He indicated that we are only too prone to seek for great or cata-
clysmic causes ; and although this tendency has disappeared from many
fields of geological research, this is not the casein all. His explana-
tion of the causes of a mild climate in high northern latitudes is as
follows :—Great eccentricity of the earth’s orbit, winter in perihelion,
the blowing of the south-east trades across the equator perhaps as far
as the tropic of Cancer, and impulsion of all the great equatorial
currents into northern latitudes; on the other hand, when, with
great eccentricity, the winter is in aphelion, the whole condition of
things is reversed: the north-east trades blow over into the southern
hemisphere, carrying with them the great equatorial currents, and
glacial conditions prevail in the northern hemisphere. Thus those
warm and cold periods which have prevailed during past geological
On Serpentine and associated Igneous Rocks of Ayrshire. 149
ages are regarded by the author as great secular summers and
winters.
3. ‘On the Distribution of Ice during the Glacial Period.” By
T. F. Jamieson, Esq., F.G.S.
The author believes that a study of the distribution of ice during
the Glacial period proves that the greatest accumulations of snow
took place in precisely those districts which are now characterized
_ by a very heavy rainfall; and he pointed out how exactly this is in
accordance with the views of Prof. Tyndall as to the conditions most
favourable to the development of glaciers. In support of this con-
clusion he reviewed the phenomena presented by the most highly
glaciated districts of the British Islands, of Scandinavia, and Europe
generally, and of Asia and North America, and contended that in
every case his opinion is borne out, the districts which are now re-
markable for an excessive rainfall having been formerly centres of
dispersion for great systems of glaciers. The notion of a polar ice-
cap he held to be opposed to many well-known facts; and he dis-
cussed the distribution of various forms of life during and since the
Glacial epoch, with the object of determining whether the drainage
of ice from the great polar basin was effected by means of the de-
_ pression of Davis’s Straits or of Behring’s Straits. The evidence
appeared to him to be in favour of the former channel.
May 22.—Henry Clifton Sorby, Esq., F.R.S., President, in the
Chair.
The following communications were read :—
1. “On the Serpentine and associated Igneous Rocks of the
Ayrshire Coast.”” By Prof. T. G. Bonney, M.A., F.G.8., Professor
of Geology at University College, London, and Fellow of St. John’s
College, Cambridge.
In a paper published Q. J. G. 8. xxii. p. 513, Mr. J. Geikie states
that the rocks of this district are of sedimentary origin, a felspar-
porphyry being the “maximum stage of metamorphosis exhibited by
the felspathic rocks,” and the diorite, hypersthenite, and serpentine
beingall the result of metamorphism of bedded rocks. This view is also
asserted in the catalogue of the rocks collected by the Geological
Survey of Scotland. ‘The author had seen specimens of rocks from
this district which so closely resembled some from the Lizard, that
he visited the Ayrshire coast in the summer of 1877. The conclu-
sions formed in the field have since been tested by microscopic exam-
ination. He finds that several, at least, of the group of “ dioritic”
rocks are of igneous origin, and are dolerite and basalt, since they
contain augite, not hornblende. The serpentine is undoubtedly an
intrusive rock, the evidence being abundant and remarkably clear.
One specimen can hardly be distinguished at sight from the black
serpentine of Cadwith (Lizard); the resemblance also is most stri-
king when the rock is examined chemically and microscopically.
Examination of different varieties shows the serpentine to be, like
that of Cornwall, an altered olivine-enstatite rock. The rock called
150 Geological Soctety:—
hypersthenite is also intrusive. The author found no hypersthene.
There are two varieties :—one a remarkable rock, consisting mainly
of large crystals of diallage, a gabbro extremely rich in this mineral
and almost free from felspar; and a gabbro of later date, much re-
sembling the ordinary gabbro of the Lizard, the felspar being con-
verted into a kind of saussurite, and some of the diallage into horn-
blende. The “ felspar-porphyries ” appeared to the author in the
field to present all the characters of true igneous rock, to be asso-
ciated with tuffs, and to be unconformable with the above-described
group of rocks. Microscopic examination placed their igneous cha-
racter beyond doubt. There are also some basalt dykes of later date
than the above. The author is accordingly of opinion that the prin-
cipal conclusions of the paper referred to above are not warranted
by either stratigraphical or lithological evidence. He considers it
probable that the “felspar-porphyry,” like so much of that in
Scotland, is of Old~-Red-Sandstone age, and that the serpentine is of
later date, but Paleozoic.
2. “*On the Metamorphic and overlying Rocks in the neighbour-
hood of Loch Maree, Ross-shire.” By Henry Hicks, M.D., F.G.S.
The rocks in the neighbourhood of Loch Maree have been described
by various authors, but chiefly and most recently in papers commu-
nicated to the Geological Society by Prof. Nicol, of Aberdeen, and
by Sir R. Murchison and Prof. Geikie, of Edinburgh. The views
held by these authors in regard to the order of superposition of the
rocks are well known to be greatly at variance, not only as regards
some of the minor subdivisions, but in relation to the actual age of
nearly the whole of the rocks to the east, or those forming the Cen-
tral Highlands. The older geologists and; more-recently, Prof.
Nicol hold the view that the Central Highlands consist almost en-
tirely of the old fundamental (pre-Cambrian) gneiss, or rocks of that
age; whilst others, represented by the late Sir R. Murchison and by
Prof. Geikie, say that the rocks forming the whole of the Central
Highlands are of much later date, and for the most part of Silurian
age. In the present communication the author endeavours to show,
from results obtained by him recently by a careful examination of
a section extending from Loch Maree to Ben Fyn, near Auchnasheen,
that the interpretations previously given are in some important
points incorrect, and that this has been to a great extent the cause
of such very diverse opinions.
The section described by him runs for some miles along the north
shores of Loch Maree, is then continued in a 8.E. direction along the
heights opposite Kilrochewe and across Glyn Laggan, and then in an
easterly direction through the heights on the north of Glyn Docherty
to Ben Fyn and the range of mountains to the north of Auchna-
sheen.
On the western and for some distance along the north shores of
Loch Maree the Lewisian rocks (fundamental-gneiss series) are seen
to consist chiefly of reddish or greyish gneiss and hornblende- and
mica-schists, The strike in these beds is more or less continuous
On the Metamorphic and overlying Rocks of Loch Maree. 151
from N.W. to 8.E., varying occasionally to N. and 8.; and they dip
generally at a high angle and are much contorted. Resting uncon-
formably upon this gneiss series, and forming here the upper part of
the mountain Shoch (about 4000 feet high), are the Cambrian con-
glomerates and sandstones, made up chiefly of masses of the rocks
below cemented together by a comparatively unaltered matrix. In
this, however, he found masses of other rocks, very similar to those
- found in the Cambrians of Wales, and which he thinks must have
come from beds of an intermediate age (like the Pebidian series in
Wales), which have either been completely denuded off here, or
must be present in some other area not far distant. These
beds are, for the most part, nearly horizontal; but on the east side
they dip slightly to the 8.E., where they are succeeded unconformably
by the quartzites of Crag Roy. (These quartz rocks are also beau-
tiiully exhibited on Ben Eay, to the south of Loch Maree, and rest-
ing unconformably on the Cambrian rocks of the magnificent Torridon
Mountains.) Alternating with these rocks are some of the so-called
fucoidal bands, the beds all dipping with a considerable inclination
to the S.E. Upon the quartzites are seen the Limestone bands,
occupying chiefly the sloping ground on the westside of Glyn Laggan.
These are penetrated by a great mass of granitic rock, which produces
here considerable contact-alteration, the limestone, however, at
some distance from the mass being in a comparatively unaltered
state. In all sections across Glyn Laggan hitherto described the
mass oi intrusive rock is made to penetrate along the bedding, and
is supposed to separate the Limestone entirely from the upper series
of rocks, the so-called Upper Gneiss, &e. The author, however, found
another series of sandstones, calcareous grits, and blue flags beyond the
main intrusive mass, and occupyimga considerable portion of the gra-
dually descending ground between the river and the heights on each side.
These were also penetrated by another arm of the granite, but, as in
the case of the limestone, with the sole result of altering them near
the junction. Prof. Nicol places a fault at this poimt, and says that
the fundamental gneiss is here brought up to give an appearance of
overlying conformably the unaltered series. The author, however,
holds, with Sir R. Murchison and Mr. Geikie, that the next is a
younger series, and that it truly overlies the unaltered beds; but he
entirely demurs to the view held by them that these should in any
way be called gneiss rocks, or associated in any way with beds
which have undergone the metamorphic change so characteristic of
the pre-Cambrian rocks as known in this country, and which could
only be induced, he believes, by great depression combined with
heat, moisture, and pressure. On examination he found these upper
beds everywhere unaltered, except near dykes; and the change there
induced in them was that now well known as contact-alteration,
and which is so entirely distinct from true metamorphism. These
beds all dip to the 8.E., and attain a thickness of several thousand
feet. They are flag-like in character, are made up chiefly of
fragmentary materials, and are occasionally even slightly calcareous,
152 Geological Society :—
They are much like some of the Lower Silurian flags in Wales, and
are in no degree more highly altered than the majority of those
rocks, especiaily in the more disturbed districts. About three miles to
the east of Glyn Laggan these beds die out, or at least are lost, and
the Lewisian rocks, fundamental gneiss, hornblende-schists, and
mica-schists, such as those described on the east of Loch Maree,
again come to the surface ; and the whole of the remainder of the
section consists of these last rocks, the great mountains Ben Fyn,
Mulart, and others being entirely made up of these rocks without a
vestige of the unaltered beds reappearing there. Of the gneiss,
hornblende-schists, and mica-schists which compose these moun-
tains, it need only be said that, on comparison with others from
Loch Maree, Gaerloch, &c., it is impossible to recognize any dif-
ference in them, the metamorphism being in each case identical in
character, and garnets and other crystals occur in them in equal
abundance. ‘The strike of the beds at Ben Fyn he found also to be
almost identical with that of those on the west coast, the dip being
either to the N.E. or E., and seldom if ever south of that pomt. He
also found these rocks, and with a similar strike, in the low ground
in Glyn Docherty, near the road to Auchnasheen ; and there the
Silurian beds are seen resting unconformably upon them. From
this the author believes that the Cambrian and Silurian beds are
contained in a basin or depression formed of the older rocks, being,
however, now altered in their dip and position by slight faults and
some folding which has taken place since they were deposited.
3. “On the Triassic Rocks of Normandy and their Environments.”
By W. A. E. Ussher, Esq., F.G.S.
The author stated that his investigations were eonenea to the
provinces of Calvados and La Manche, more especially the latter.
Haying briefly alluded to the physical areas of the Bocage and
Cotentin, he proceeded to show that whilst the Secondary rocks were
confined to the Cotentin, the presence of several Paleozoic inliers
proved that they were of no great thickness. He then briefly
described several sections illustrative of observations made by him
in walking over the Triassic districts of Valognes, Montebourg, and
Carentan, and of Bayeux in Calvados. The result arrived at (as
far as possible, despite the presence of drift concealing the Trias
almost everywhere) was that the Norman Trias is composed of
gravels, sands and sandstones, and marls. The gravels replace and
give place to sand and sandstone ; but the position of the marls could
‘only be distinctly ascertained near Carentan, where they underlie
sandstones. The gravels and sands either directly underlie the
Infra-lias, or are separated from it by a thin bed of marl. The
Norman Trias can scarcely exceed 200 feet in thickness.
The author then briefly enumerated the Paleeozoic rocks of the
Bocage, and summed up the results of his investigations in the
following conclusions :—
First, that the Triassic rocks of Normandy are the south-easterly
prolongation of the Triassic area of Somerset and Devon.
On Foyaite. 153
Secondly, that Upper Keuper deposits are alone represented in
Normandy.
Thirdly, that fragments of the Paleozoic rocks of what is now
Normandy were neyer incorporated in the Triassic rocks of Devon.
Fourthiy, that the constitution of the coasts of Normandy, Devon,
and Cornwall is such as to justify a belief that varieties of
Cambrian, Silurian, Devonian, and Granitic rocks formed the bed of
the Triassic waters in the area now occupied by the English
Channel, and that to these sources fragments foreign to the Devon-
shire soil found in the Triassic beds on the South-Devon coast are
to be attributed.
4, “On Foyaite, an Eleolitic Syenite occurring in Portugal.”
By C. P. Sheibner, Esq., Ph.D., F.G.S. Communicated by Prof. T.
M‘Kenny Hughes, M.A., F.G.S.
The name foyaite is derived from Mount Foya, in the south of
Portugal. This rock occurs intrusive in Devonian grauwacke in
the ancient province of Algarve, where it forms two dome-shaped
hills, the Foya and the Picota, rising respectively to 2968 feet and
2410 feet. The texture of the rock varies from fine- to coarse-
grained, and is sometimes porphyritic. An almost compact variety
occurs cutting the coarser rock in dykes and veins. The coarser rock
occurs mainly on the southern slopes, where, however, the adjoining
erauwacke is less altered than elsewhere. The masszf is also cut by
intrusive veins of phonolite and basalt of Tertiary age. Much rock
has probably been removed from the district by denudation.
Macroscopically foyaite consists of orthoclase, eleolite, and
greenish hornblende. Orthoclase with imbedded eleolite occurs
porphyritically. A lens shows titanite, biotite, magnetite, and
pyrite to be accessories. Microscopically examined, the above con-
stituents are seen to be present, and exhibit considerable variety in
their mode of occurrence, together with nosean and sodalite as
characteristic accessories, and occasional plagioclase (recognized as
oligoclase), muscovite, hematite, and apatite. The elexolite is irre-
gular in outline; nosean and sodalite are often associated with and
imbedded init. The latter minerals are associated and intergrown.
Their mode of occurrence and the tests for their presence are
described in detail. Hornblende and augite occur in foyaite in
about equal quantities, associated and intergrown. ‘These also are
fully described, as well as the characteristics of the other accessories.
Analyses of the eleolite and the foyaite are given. The author
concludes by pointing out the close resemblance of the rock to
ditroite, miascite, and certain syenites of Brevig and Cape Verd,
stating that on this account there is no need of a special group of
foyaites.
pga
XXII. Intelligence and Miscellaneous Articles.
PHOTOGRAPHY AT THE LEAST-REFRANGIBLE END OF THE.SOLAR
SPECTRUM. BY CAPT. ABNEY, ht.H., F-R.S.
eee two years ago I had the honour of reading a preliminary
note on photographing the least-refrangible end of the spec-
trum ; and it seems that the time has come when I ought to redeem
the promise implied by a “ preliminary note” and enter further
into the subject. Last year, owmg to a change in residence, J was
unable to pursue the subject with any degree of activity; but
during this last winter and the present spring I have made fair
progress in my researches, the results of which I lay before the
meeting. These results are principally photographs themselves ;
and the first to which I shall call attention is one taken through
three prisms of dense flint glass, each of which had a vertical
angle of 62°. They were placed at the angle of minimum devia-
tion of B, and kept so. The focal lengths of the collimator and
camera were 18 inches and 2 feet respectively ; and a condensing
lens of 6 feet focus was employed to collect the light, the middle
of the collimating lens alone being filled with solar rays. In front
of the slit was placed a plate of orange glass, in order to cut off
the suffused blue rays, which experience had previously taught me
were inimical to the production of good negatives, owing to the
light dispersed in the prisms themselves. It will be noticed to
what an enormous distance below A the impressions of the bands
in the ultra red are to found. If the wave-lengths be used as~°
abscissze and the measured distances of the known lines be used
as ordinates, it will be found, if the waves be completed by hand,
that a wave-length of not less than 10,400 tenth metres is im-
pressed. Roughly speaking, A is 7600 tenth metres, and D
5900 tenth metres—by which it will be seen that I was within the
mark when I announced that I had obtaied photographs as much
below A as D was above it. Now this negative, though interesting
as a feat in photography, has no practical scientific value, as the
ultra red is so tremendously compressed that the absolute wave-
leneths could not be obtained from it.
About the time I read my last paper, Captain Tupman kindly
lent me a speculum-metal grating, by Ruthertord, having about
8600 lines to the inch; but it was only lately, after removing its
glass covering, that I was fully able to appreciate its value. In
all gratings the red, or rather the ultra red, of the first order is.
overlapped by the ultra violet and violet of the second order, and
the higher the order the more overlap there is. ‘To remedy this,
which was a defect for the purpose for which I required it, I
placed before the slit of the collimator red glass, which completely
cut off the yellow and only allowed a little of the green to pass.
The prisms were replaced by the grating, and a photograph of the
Intelligence and Miscellaneous Articles. 155
second order of the spectrum was taken by it. Theoretically
speaking, the time necessary for taking a photograph of the first
order is 1 that for taking one of the second, and 5. for that of the
third. Practically this is not quite true, for reasons which it is
unnecessary to enter into here. This induced me to think that
if I could get a grating with double the number of lines to the
inch, its first order would give me the same dispersion as the
-second order of the grating I was using, and at the same time the
exposure ought to be more than halved. Mr. Lockyer kindly lent
me such a grating; and the third photograph was taken by it.
You will see that it gives the lines from C to A almost perfectly.
A positive copy of this photograph I sent to Professor Piazzi
Smyth, as he drew the map of this region of the spectrum, which
he published in the last volume of the ‘Edinburgh Astronomical
Observations ; and I cannot do better than quote his words re-
garding the accuracy of the photograph :—“ As the size of the
glasses approximated closely to my standard-camera size, 2°25 inches
x 4:25 inches, I was able at once to view them with any magnify-
ing power in a compound microscope long since arranged for such
things ; and the effect was astounding. J almost thought I was
back again in Lisbon, viewing the Sun’s spectrum itself as I used
to see it.”
This acknowledgment of the value of the photograph was
particularly gratifying, as it came from an astronomer who
had paid special attention to this particular part of the
spectrum.
The next plate shows the region of the ultra red as taken with
the same grating. The most conspicuous group has a wave-length
of about 8400 tenth metres; and the extreme line visible has a
wave-length of about 9200 tenth metres. At this point the
closer-ruled grating seemed to fail me, and I could not get beyond
this point. It then struck me that the glass on which the lines
were ruled might absorb the rays beyond (for I must explain
that this grating was ruled on glass and silvered at the
back), or that the red glass might absorb them. I then
reverted to the first grating and adopted a different method of
proceeding.
This was Fraunhofer’s method, to which I was practically new—
though I believe I have been credited (though inaccurately) with
using it for other experiments; and after various attempts the
following is an outline of the arrangement adopted. ‘The slit
was placed horizontally ; a prism of 60° occupied a position at the
end of the collimator next the lens; the reflection-grating then
received the rays and reflected them into the camera-lens, the
camera being tilted at an angle to make them fall on the sensitive
plate. To show what sort of effect cam be got, I exhibit a pho-
tograph in which from the first to the fourth order of spectra
were impressed on the same plate in a small camera. When this
156 Intelligence and Miscellaneous Articles.
method was applied to the larger apparatus I got further into
the ultra red than I had done before; and such a plate you see
before you: the wave-length of the last line of my group of lines
visible on the plate is about 10 ,300 tenth metres. From indica-
tions on other plates I am inclined to think that we may get as
far as 12,000 tenth metres, which it will be admitted is a tolerable
distance to travel along the invisible spectrum. In these ultra
regions the lines are faint, but perfectly measurable under a
moderate magnifying-power; and I have therefore proposed to
myself to make a map of the ultra red. For the purpose I pro-
pose to use the overlapping of the higher order of the spectrum
over that used. By cutting off the red in one case and using half
the length of the slit for one exposure, and then by cutting off
the blue and using the remaining half of the slit for the other,
we shall have one spectrum over the other. The wave-lengths
of the most-refrangible rays are known; and since the dis-
persion of the higher order is double that of the one below it, the
wave-lengths of the latter can be accurately ascertained. When
once a scale is obtained, the greatest difficulty will have
vanished.
Now as to the process. My object has been to weight the
molecules of silver bromide that they may absorb the red rays.
With ordinary silver bromide the film allows these very rays
to pass through, whilst a blue absorption takes place. In other
words, my endeavour has been to find a heavier molecule of a
sensitive salt, which shall answer to the swing of the waves of
the red and ultra-red rays. This I first accomplished (as I stated
at the time) by adding resins to the silver salt and forming what
I may call a bromo-resinate of silver. But I am happy to say
that I have secured the same end by, I believe, doubling the
molecule of the silver bromide. Now this doubling the molecule
is a matter of manipulation more than of chemical knowldge ;
and I might describe the process in detail, as I have already done
in papers I have published, and yet the double molecule would
not be obtained unless careful manipulation were attended to—
manipulation easy to follow when seen, but difficult to follow
from any description. I should therefore prefer to teach prac-
tically any one who is acquainted with silver-bromide-emulsion-
making, rather than allow him to be misled by what must be
imperfect directions.
L exhibit two films, both prepared with sensitive emulsion
which is composed of exactly similar ingredients, viz. pure silver
bromide. You will at once note the difference in colour of the
light transmitted. The one which is sensitive to the red and ultra
red is of blue tint; the other is orange. You will see that the
blue tint would appear to be due to a physical arrangement of the
molecules; for if a part of the film be rubbed you will see that it
changes to a ruddy tint, passing through an emerald-green stage.
Intelligence and Miscellaneous Articles. 157
We have it so on the screen. Whether it be right or wrong in
regard to other matter, 1 am convinced that in silver bromide
we have the possible existence of two sizes of molecules. In the
blue film we have the presence of both; when only the larger
size 1s present we shall have a compound which is very much
more sensitive to the lower end of the spectrum than it is to the
upper. Allow me to say that these views are not original, except
in so far as they are applied to this subject. Whether they are
correct or not, they have formed a good working hypothesis which
has led me to the results obtained.
Before closing I must refer to the comparative lengths of ex-
posure required for these photographs. My impression is that at
A the exposure required is about 25 times that required for G, in
a fairly bright sun at midday; for the ultra red, as far as I have
gone, I should say about 35 times. These are only approximations,
but still will enable you to form some idea of the sensitiveness. I
show you a photograph taken about 4P.M.on March 18. The
exposure was about 50 seconds. You will see that the red end is
as strong as the blue, with the yellow much lacking in density. In
other words, the yellow rays are nearly inactive.
The photograph which I showed you of the four orders of the
spectrum was taken on April 3, at 2.30. It had an exposure of
one minute and a half. The photograph in which the furthest
band of lines was seen had an exposure of 12 minutes, on the
8th, at 2.30. The slit was in this case closed as nearly as pos-
sible.
In conclusion, I have to remark that in a short time I hope to
reduce the exposures considerably. In the course of some investi-
gations, the results of which have just been communicated to the
Royal Society, I found that the red rays could oxidize a photo-
graphic image as well as form it, and that in an oxidized state it
was unable to be developed. If the tendency of the sensitive
compound to become oxidized exceeded its tendency to become
reduced, no image could be developed. By exposing i vacuo, or in
a nitrogen atmosphere, I hope to eliminate altogether this oxidizing
effect, and so get firmer images.—Monthly Notices of the Royal
Astronomical Society, April 1878.
ON THE FRICTION OF VAPOURS. BY DR. J. PULUJ.
Friction-experiments with vibrating disks confirm for vapours
also the law that the friction is independent of the pressure up to
the limit of saturation, and the law of its proportionality to the
absolute temperature, which latter law has been experimentally
proved by A. v. Obermeyer and the author for more easily com-
pressible gases.
For ether-vapour the calculation gave, within the temperature-
158 Intelligence and Miscellaneous Articles.
interval 72-36°5 degrees Centigrade,
n=0:0000689 .(1+0:00415752)0'94,
The experiments were made on seven vapours, for which the mean
lengths of path were calculated and compared with the exponents
of refraction determined by Dulong.
The remarkable relation pointed out by Director Stefan, starting
from the view that molecules are surrounded by an envelope of
ether, has been confirmed in the case of vapours also. He showed
in gases that higher exponents of refraction correspond to shorter
lengths of path. Unfortunately, the refraction-exponents for only
two vapours (the highest hitherto observed) were determined expe-
rimentally by Dulong.
The author obtained for
aD by? (222) 0 eee Ra oe 1,=0-0000151 n=1-:000158
ARP ihe a iils aLgeslimie 0:0000082 1:000294
Bisulphide of carbon. . 0:0000029 1:001500
Hither .25. 3s... yesrenrn ti: 00000022 1:001530
Director Stefan calculated from the coefficients of diffusion that the
mean length of path of ether-vapour is 0:0000023, and of bisul-
phide of carbon 0:0000032, with which values the above are in very
good accordance.
Finally, for the vapours examined the proportional numbers of
the molecular volumes were calculated from the friction-constant,
according to the formula deduced by Lothar Meyer,
See Vad
v, mM, Oe
in which m,, m, are molecular weights, and n,, », the friction-con-
stants of two gaseous bodies. Ifthe molecular volume of hydrogen
v, be taken as unity, we obtain for the molecular volume of the va-
pours examined the numbers in the third column of the Table.
v VU}.
Vapours. Composition.| 240 |——————
%3 From friction.| After Kopp.
NVALED Ie Corea tescreeiee EO 4°9 22°9 18:8
Bisulphide of carbon.., CS, 14:0 65°5 62°3
Chiprotorm: (jrscseincs. 5: CHCl, 18°6 87-1 84-9
We 70) 116) NEAR Ree: Cro 11:3 52:9 62°8
MCEHONS. Waetcereneoneenn: Cae 16-4 768 78:2
Benzol . 2.365 sce... seater C, H, 21:2 99-2 99-0
Bieber cu seen oe ever eee oe @, Hy)0 21:6 101-1 1058
By means of the molecular volumes v,, calculated after Kopp
from the densities, the molecular volume of hydrogen was de-
Intelligence and Miscellaneous Articles. 159
termined, according to the above formula, from the friction-constant,
to be 4°7.
By multiplying the proportional numbers - by 4:7, the values of
2
v in the penultimate column are obtained, which agree with the
numbers in the last column, calculated by Kopp, as well as can in
general be expected in experiments of this sort.
_ The molecular volume of free hydrogen, 4:7, is less by more than
half than 11-0, the value calculated from its liquid compounds.
The author endeavours to account for this in the following manner.
If molecules are spheres surrounded with envelopes of wether of
variable density, two such molecules, on central impact taking
place, will probably act on each other as soon as they arrive at a
distance from one another equal to the sum of the radii of the actual
sphere of action. The action lasts until the vis viva is reduced to
zero and reversed. Molecules with greater velocities, in the gaseous
state, will approach nearer to one another, and reciprocally pene-
trate with their ether envelopes more deeply than molecules with
lower velocities, in the liquid state. Hence in the former case the
radius of the apparent sphere of action, consequently the molecular
volume, must be smaller than in the latter.
Jo the same assumption of a variable sphere of action we are
conducted, as first remarked by Director Stefan, by the fact that
the friction-constant is proportional not to the square root of the
absolute temperature, but to another power of the same, which, ac-
cording to the experiments of A. vy. Obermeyer and the author, is
greater than } and at the highest is =1,
A second basis of explanation may, according to the view of
Lothar Meyer, lie in the circumstance that, in determining the mo-
lecular volume from the density of the liquid compounds, with them
the empty space is measured which is open to the atoms for their
motions, while, from the magnitude of the obstruction which one
particle coustitutes for another, only the volume of the gas particles
themselves is determined.
Experiments with air under very low pressures led to this result
—that while the pressure diminished from 754 to 0°03 millim. the
friction-constant became less by only about one half of its initial
value, from which it may be seen how proportionally great must be
the quantity of gas which remains in a very good vacuum, since it
can conyey quantities of motion so considerable. This is in excel-
lent accordance with the kinetic theory of gases, according to which,
in a cubic centimetre of air of one millionth of an atmosphere pres-
sure, nineteen billion molecules are still present.—Aaiserliche Aka-
demie der Wissenschaften in Wien, math.-naturw. Classe, July 1, 1878.
ON THE DEPOLARIZATION OF THE ELECTRODES BY THE SOLU-
TIONS. BY M. LIPPMANN.
It has long been known that certain salts possess a depolarizing
property. The first pile with a constant current, constructed in
160 Intelligence and Miscellaneous Articles.
1829 by M. Becquerel, owes its constancy to the employment of
sulphate of copper; the sulphates of zine and cadmium have been
made use of by MM. du Bois- Reymond and J. Regnault for the
construction of impolarizable electrodes and constant elements.
Notwithstanding the importance of its applications, this property
appears to have been but little studied. The experiments I am
about to describe have made evident an essential condition of the
phenomenon.
It is the following: in order that the electrode may be depo-
larized, it must be formed of the same metal as is contained in the
solution. Thus copper is the only metal which becomes depolarized
in sulphate of copper, while gold, silver, and platinum are polarized
in that solution. Inversely, copper polarizes in sulphate of zine,
cobalt, &c. <A salt depolarizes only its own metal. To make the
experiment, operating for example on sulphate of copper and plati-
num, two strips of platinum are to be immersed in the liquid, and
put into communication with the poles of a capillary electrometer.
The mercury column is then at zero. A feeble current is then
~- caused to pass into the liquid so as to employ one of the strips as ne-
eative or exit electrode. The electrometer shows a deflection, which
remains even after the interruption of the current, thus proving
that polarization is produced in the sulphate of copper, as it might
have been produced in pure or acidulated water. For the same
reason, a couple formed of strips of copper and platinum dipping
in sulphate of copper furnishes only a current of brief duration,
the platinum receiving, owing to its polarization, an electromotive
force equal and opposite to that of the copper. One may even go
further and communicate to the platinum, by means of an exterior
pile, an electromotive force superior to that of the copper, so that
then the platinum will behave like a more negative, more oxidizable
metal than copper.
Similar experiments have been made with strips aun solutions of
silver, mercury, lead, cobalt, and zinc.
An application readily presents itself. Since ie property of
depolarizing a metal belongs exclusively to its salts, it permits us
to detect the presence of that metal in a solution. Taking copper
as an example, if we dip into the liquid to be tested a copper wire
which we use for the negative electrode of a feeble current, it will
be polarized if there is ae dissolved copper, it will not be polarized
if the solution containszy\y5 of sulphate of copper. It is possible,
therefore, thus to detect the presence of copper in a mixture of
metallic salts. With a silver wire we can in the same way test
for silver. The delicacy of this electric process appears to be
still greater for silver than for copper; but it has not yet been
measured.— Comptes Rendus de V Académie des Sciences, June 24, 1878,
tome Ixxxvi. pp. 1540, 1541.
THE
LONDON, EDINBURGH, axp DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE. |
[FIFTH SERIES. ]
SHPTEMBER 1878.
XXIII. Recent Researches in Solar Chemistry.
By J. N. Lockyer, P.R.S.*
HE work which is now being done in the various new
fields opened up in connexion with solar studies may be
conyeniently divided into three perfectly distinct branches.
We have, first, that extremely important branch which has for
its result the complete determination of the position of every
thing which happens on the Sun. ‘This, of course, includes a
complete cataloguing of the spots on the sun which have been
observed time out of mind, and also of those solar promi-
nences the means of observing which have not been so long
within our reach. It is of the highest importance that these
data should be accumulated, more especially because it has
been determined that both in the case of spots and promi-
nences there are distinct cycles, which may in the future be
very much fuller of meaning to us than they seem to be at
present.
This brings me to refer to the second branch of the work ;
and it is this :—These various cycles of the spots and promi-
nences have long occupied the attention both of meteorologists
and magneticians ; and one of the most interesting fields of
modern inquiry, a field in which very considerable activity has
been displayed in the last few years,is one which seeks to connect
these various indications of changes in the sun with changes in
our own atmosphere. The sun, of course, is the only variable that
* Communicated by the Physical Society, May 11, 1878.
Phil. Mag. 8. 5. Vol. 6. No. 36. Sept. 1878. M
162 Mr. J. N. Lockyer on Recent
we have. Taking the old view of the elements, we have fire re-
presented by our sun, variable if our sun is variable. Earth, air,
and water, in this planet of ours we must recognize as constants.
From this point of view, therefore, it is not at all to be won-
dered at that both magneticians and meteorologists should
have already traced home to solar changes a great many of
the changes with which we are more familiar. This second
branch of work depends obviously upon the work done in the
first, which has to do with the number (the increasing or de-
creasing number) of the spots and prominences, and the vari-
ations of the positions which these phenomena occupy on the
surface of the sun. As a result of this work, then, we shall
have a complete cataloguing of every thing on the sun, and a
complete comparison of every thing on the sun with every me-
teorological phenomenon which is changeable in our planet.
When we come to the third branch of the work, the newest
branch, things are not in such a good condition. The workers
are too few ; and one of the objects of any one who is inter-
ested in this kind of knowledge at the present moment must
be to see if he cannot induce other workers to come into the
field. The attempt to investigate the chemistry of the sun, even
independently of the physical problems which are, and indeed
must be, connected with chemical questions, is an attempt
almost to do the impossible unless a very considerable amount
of time and a very considerable number of. men be engaged
upon the work. If we can get as many workers taking up
various questions dealing with the chemistry of the sun as
we find already in other branches, I think we may be certain
that the future advance of our knowledge of the sun will be
associated with a future advance of very many problems which
at the present moment seem absolutely disconnected from it.
I have today to limit myself to this chemical branch of the
inquiry ; and first let me begin by referring to the characteris-
tics of the more recent work with which I have to deal. Here,
as in other branches of physical and chemical inquiry, advance
depends largely upon the improved methods which all branches
of the science are now placing at the disposal of all others.
Our knowledge of the chemical nature of the sun is now being
as much advanced by photography, for instance, as that de-
scriptive work of which I spoke in the first instance (which
deals with the chronicling and location of the various phe-
nomena) has, in its turn, been advanced by the aid of photo-
graphy. I do not know whether the magnificent results
recently obtained by Dr. Janssen have been brought before
this Society ; but the increase in photographic power recently
secured by Dr. Janssen is one which was absolutely undreamt
Researches in Solar Chenustry. 168
of only a few years ago. It is now possible to record every
change which goes on on the sun down to a region so small
that one hardly likes to challenge belief by mentioning it.
Changes over regions embracing under one second of angular
magnitude in the centre of the sun’s disk can now be faith-
fully recorded and watched from hour to hour.
_ One of the advantages which has come from the intr ae:
tion of the new apparatus has been the possibility of making
maps, on a very large scale, of the solar lines and of the me-
tallic lines which have to be compared with them. Thanks to
the great generosity of Mr. Rutherfurd, who is making the most
magnificent refraction-gratings which have ever been seen,
and who is spreading them broadcast among all workers in
science, one has now easy means of obtaining with inexpen-
sive apparatus a spectrum of the sun, and of mapping it on
such a scale that the full magnification of the fine line of
light which is allowed to come through the slit will form a
spectrum the half of a furlong long: an entire spectrum on
this scale, when complete (as I hope it some day will be,
though certainly not in our time) from the ultra-violet, already
mapped by Mascart and Cornu, to the ultra-red, which has
quite recently for the first time been brought under our ken
by Captain Abney, will be 315 feet long. ‘This is a consider-
able scale to apply to the investigation of these problems; but
recent work has shown that, gigantic as the scale is, it is really
not beyond what is required for honest patient work. I have
already had an opportunity of bringing before the Physical
Society several of the methods in use for comparing the spectra
of the various elementary bodies with that of the sun. It is not,
therefore, necessary now to refertothem. There are, however,
others of recent application which are of very considerable
importance.
When, instead of inquiring into the coincidence of the me-
tallic lines, we wish to determine the coincidence of the lines
due to various gases, the method hitherto employed has been
to enclose the gases in Geissler tubes, to reduce their pressure,
and in that way to fine down the lines. The importance of
this apparently small matter can be very well demonstrated by
an experiment easily arranged in an electric lamp, which sodium
enables us to perform without any great difficulty. The point
of this experiment is that, if we vary the density of any vapour,
we vary sometimes to avery considerable extent the thickness
and intensity of the lines. 1am about to throw the spectrum
on a small screen which I have behind the lamp ; and I hope
I shall succeed in rendering the phenomena visible. I want
_ you to observe the vain tion in the thickness of the reversed
M 2
164 Mr. J. N. Lockyer on Recent
line of sodium. Every turn of the screw which raises or
lowers the upper pole, enables me to vary to a very consider-
able extent indeed the thickness of that absorption-line.
Now the way in which that has been managed is very simple.
The only arrangement required is one which shall enable me
at will to vary the density of the sodium-vapour. "When I
make the sodium-vapour as dense as possible, then the line is
very thick. When I make it much less dense, the line becomes
thinner. If the spectrum on the screen had been a gas-spec-
trum (supposing it were possible to exhibit a gas-spectrum to
an audience), the exact equivalent of that experiment would
have been, that the gaseous spectrum at atmosphere pressure
would have given us most of the lines as thick as the sodium-
line was at its thickest; while if by any possibility we could
have rendered the phenomena visible while the pressure was
being reduced, as the pressure of the gas was reduced the
line would thin. Now there are very great objections to the
using of Geissler tubes. One very valid objection is that the
gas becomes much less luminous as its pressure is reduced.
Here is a method which is excellent in this way, that it en-
ables all the work connected with gaseous spectra to be done
at atmospheric pressure, and we get the line down as thin as we
choose, not by reducing the pressure, but by reducing the quantity
of gas ina miature. Ifwe take, for instance, a spark in ordi-
nary atmospheric air and observe its spectrum, we find the lines
of the constituents of atmospheric air considerably thick ; but
if I wish to reduce the lines, say of oxygen, down to a consi-
derable fineness so that I can photograph its lines (these should
be fine,in order to enable me to determine their absolute posi-
tion ; to accomplish this) the spark is made to pass in a glass
vessel with two adits and one exit tube. If I wish to observe
the oxygen-lines fine, I flood the vessel with nitrogen so that,
say, there is only 1 per cent. of oxygen present, and observe the
current between the enclosed electrodes. If I wish to observe
nitrogen-lines fine, I flood it with oxygen, so that there is
only 1 per cent. of nitrogen present. In this way, by merely
making an admixture in which the gas to be observed is quan-
titatively reduced, so that the lines which we wish to investi-
gate are just visible in their thinnest state, we have a perfect
means of doing this without any apparatus depending on the
use of low pressures ; and those who have worked most with
Geissler tubes will appreciate the very great simplicity of work
which is thus introduced.
Another important application of spectroscopic theory re-
cently applied to the investigation of the chemistry of the sun
is this :—Assume that the spectrum of any substance is not a
Researches in Solar Chemistry. 165
pure spectrum of that substance, but of that substance as it
generally exists in an impure state.
The spectrum will be found rich in lines; and when very
considerable care is employed, one may go away with the idea
that in iron, for instance, all the lines which are observed in
the spectrum of iron coincident with Fraunhofer lines repre-
sent coincidences in the case of each line with iron in the sun
and iron in our laboratory. But the more the work is carried
on, the more one finds that the complex spectra which are ob-
served are really. much more simple when all the impurities
are taken into account. |
In the region of the solar spectrum, for instance, recorded
on the map exhibited we have a great many iron-lines ; but
before the method of determining impurities was utilized, the
spectrum was very much richer than itisat present ; possibly
one fourth of the lines have been withdrawn. In every specimen
of iron which has been used in this work the lines of calcium,
aluminium, and some of the lines of manganese and cobalt have
been represented ; and no chemist will wonder at this result.
But there is a very curious thing which chemists, I think, will
wonder at. In this part of the spectrum there were two lines
which, by their thickness both in the solar and iron spectra,
seemed undoubtedly to belong to iron ; but further inquiry led
to this extraordinary result—that one of these lines in all proba-
bility has its origin in the vibration of molecules of tungsten,
the other being probably a line of molybdenum. Glucinum
is another metal which may be referred to in this connexion ;
and it would appear that it is almost impossible to get a spe-
cimen of iron which does not contain, not only calcium and
aluminium, but others which we consider rare metals on the
earth, such as tungsten, molybdenum, and glucinum.
, A few years ago, taking the work of Kirchhoff, Bunsen,
Angstrom, and Thalén into consideration, and connecting it,
so far as one could connect it, with those ideas of which recent
eclipses have been so fruitful, our chemical view of the sun’s
atmosphere was one something like this :—We had, let us say,
first of all an enormous shell of some gas, probably lighter
than hydrogen, about which we know absolutely nothing,
because at present none of it has been found here ; inside this
we have another shell, of hydrogen ; inside this we have another
shell, of calcium, another of magnesium, another of sodium,
and then a complex shell the section of which has been called
the reversing layer, in which we get all the metals of the
iron group plus such other metals as cadmium, manganese,
titanium, barium, and soon. The solar atmosphere, then, from
top to bottom, consisted, it was imagined, of a series of shells,
166 Mr. J. N. Lockyer on Recent
the shells being due not to the outside substance existing only
outside, but to the outside substance extending to the bottom
of the sun’s atmosphere, and finding in it at a certain height
another shell, which again formed another shell inside it, and so
on; so that the composition of the solar atmosphere as one
went down into it, got more and more complex: nothing was
left behind ; but a great many things were added.
The recent work, so far as | am acquainted with it, has not
in any way upset that notion; but what it has done has been
to add a considerable number of new elements to this reversing
layer. Instead of consisting of 14 elements, as it was then
found to do, it may be, I think, pretty definitely accepted now
to consist of about thirty.
The metals considered to be solar as the result of the
labours of Kirchhoff, Angstrom, and Thalen together with
the considerations brought forward regarding the length of the
lines, were as follows:—
Na Fe Ca Mg Ni
Ba Cu it Cr Co
H Mn i Al
Those more recently added, with the evidence by which
their existence in the solar atmosphere is rendered probable,
are as follows (in the Tables, pp. 167-169).
It is important to bear in mind that the lines recorded in
these Tables are in most cases the very longest visible
in the photographic region of the respective spectra ; in some
cases they are limited to the region 39-40, which I have more
especially studied ; so that the fact-of their being reversed
in the solar spectrum must be considered the strongest evi-
dence obtainable in favour of the existence in the sun of the
metals to which they belong, pending the complete investiga-
tion of their spectra.
Where, however, there is only one line, as with Li, Rb, &e.,
the presence of these metals in the sun’s reversing layer can, -
for the present, only be said to be probable. Neither must it
be forgotten that, in addition to the long lines which a spec-
trum may contain in the red, yellow, or orange, long lines
may exist in the hitherto unexplored ultra-violet region ; so
that the necessity for waiting for further evidence before de-
ciding finally upon the presence or absence of such metals in
the sun will be rendered obvious.
It will be thought remarkable that, if the long lines of such
metals as lithium and rubidium are found in the photographic
region of the spectrum, the long lines Li W.L. 6705, Rb-
W.L,. 6205 and 6296 should have escaped detection.
167
Researches in Solar Chemistry.
“OuT] MONT ee ececreoce Cree toeneerseres jeuliou eajoods TL} quosq
‘QUIT MONT [titerecettereetetesteeteeeeteeeeseeen ees - UIT TY 0} 28019
‘oury MON ft Risforstcleisibisisieipivie'wigie jeuttou exyeds woz yuosqy
OUT], MONT | | rstecUetertseetereeonestes Tem Tou aajoods WOIT JUOSqW
‘OUT MONT [ttereeestteeeeeee es verre Teurtou oaqoods UOdT quesqy
"OULT MONT [TT treeettteeteeeeereeeees TeUTTOU atjoods WOAS Juesq YT
POU UO Reso nen tense ence remot eajoods WOAT OSG
Sy SS Boye a eee ae “-ommoauyy | [eee estes eerste eee teres on jemi0u
L 0-664 PO { siecle | erjoods Ul 6.961 “TAA J@ UIT pousisseun uy
ee “ONyOAyy | | cecceeeeteeteteeetteteee stent eeeeseetenaee sees yeuisou
8-9L9% PO { Ewen ud [eu } eajoods Ul G.O/OF “T'AA 3B OUIT pousisseun uy
p G.zoop | ay eRe usyey, UseGsasash seers aesnsne) MTUTOM OI0eds TONE quesq'y
s Gene joo Gale Cops wie eer ee ee cess yeuriou orjoods ur (GZ-LGOP
‘T’M) Uorztsod poamber avou curl pousissvun uy
“OUNT MONT [rtteceteeeeete te erees cents yeuttou aajoods WOA] yWOSGY
‘ 7 an ee ee \ “oo ugTeaT, | BO 07 pousisse yeusou o.qoods ur ¢.FQOF Ye OUT V
: tae ae io } eas ugeyL | OF-SIZh "I'M ‘80 0} pousisse [eutou oayoods uy
: meige re te } “-ugTVyg, |" "BO 0} pousisse teutou oaqoods Ul B.910F 98 OUT V
OUT] MONT |*** OUI] UT Su] «vou ‘yeutaou oajoods woayz yuosqy
| qsoqqstaq= | “y4sue] :
“AVISUOJUT -OAB AA Me
‘poddeu ATsnora
-oid. wloy a kg “‘BUOTIVALOSG QC)
"So[quy, SU9[VyT, Woay sxepnorysteg
‘pouliyuoo st ung oy} ul Yorya Jo sousseid oy} sTRyoTy
86-9F0P
00-66LF
G6-190P
08-990F
86-610P
09:-L09F
00-C16P
LL-9LOF
09-6607
‘umnaqoods
IVOS OY}
UT PasaoAod
soury JO "TAA
dy
OJVULIXOL
GL-GhOF
00-LL9F
see eee
untae.)
‘> TUNED
uINnIssejog
TaNImMpey
‘[eJoUI JO ome Ny
Mr. J. N. Lockyer on Recent
G Zoser | IN
g Roger EN “eugeyy, je teeett INT 07 WIQayssuY Aq pousisse avou curt | 4 0.628h
+ G.6Z8F teseee Om °
5 O-818b eee tes On mene) 120 FF SOP e eer ts see eh oes sesves deur smonssay WOds qyuesq Vy 60-818P
57 G.OELF eooree OW ee eeros mC) At TPO oee eee wes ooveesresreroes OT 07 maga POULy, Aq pousissy 0-08LF * umuepq Top]
3 “hw ion oa ores OTEU Core eevoevereeserraneooesrs oO 04 wonsduy kq pousissy 0:90L4
‘ouT] MONT Seer eres esoenss oases seeserers TruIgEe ay ka } poyeooyye 4ONT 0-91¢F
SEyyqpNe) ap | Iposuout RN ehete niaccipiete tie «vaiaieveleteiniciais wisiWateiese °oury aq cvou £104 0-206
¢ 0-FL8F seeeee Pd sveceeee ugTeq, eee e nee ren eeereeesene Cee eee ereeerasreeoene Oe eeeee . oO 04 \
mga seuy Aq pousisse uorqtsod poamboes cvou uty W 0-FL8F
e 0: LISP : i: . . Pd weteeees udTeuy, seccessee Ovonsoecrverveccones T1O.A4S86 oy) &q poyeooTye JON 0-L18F
a eis 2S ne See ugpeqy, [ee 4 oF Of woxssuy fq pouSissy ies “' UMIpeleg
OUT ASN 0-8966
SOT oN, 0-E68¢
i GLOPP "BA } Sth enon ugTey, fc cette oat asteats ed 0} woajsSuy Lq poudiss C.10)
g OLOFF |" «680 ; e) V So DeMeTRRY: G¢-LOVY
G 0-688 |" ast Speen eee NUTT & 1 can uuuieectiars sgretaaetgeces
; p6aep [tt ep ugTey, BQ 04 moagasuy Aq pousissy 0-68EF
T 0-F8Eh sees 7 ae reas (0) (CTE pele gee go oe CODE OE EE GLa demu 8 WoIssUY ULOAF qJuesq O.FS8P
J ye pee oe seer acomerayiy, | scecssnsctcescnetestscese 1 0} moysiuy fq pouswsy | Q.GLep | br mmmpean
SUL BaN: 6-666
ee SAN G-2668
“OUIT MONT G9-6866
SOOT AON, 6-6068
tie ee e-106e | /
‘ysoyqsuq= [| ‘yysueT ‘umnajoads
ce as 7 -OAR AA PPW addenn BOS OY
at a "P [snota “SUOTIVALOSYO) UI posdoaat | ‘PRJoM JO oULAT
ms -oid woym Sg sour, JO “TM j
ISL S.U9leqgy arosy sxenonseg ayeurxoaddy |
“ung ou] ur quosoad Ayquqoad syeqyoTT
169
Researches in Solar Chemistry.
‘qsoqqsnq=T[} ‘WydU0T
Pe aa nO ee ec ed I ae el 9 ee
a
I @.eogp [oct uy
I O.10Ip | OT
*AVISUOJUT OAR MA THN
‘SO[QBT, SU9TVILT, Worf sav~NoyAeT
ee | ee
‘OUT MONT eeatnreces teeretrene OG OC IOOOLOUD * eUrou eaqoods ul JON, S-1868 oe UINIgAnT
‘OUTT MONT eeebbececewens Risjaeralaes eveisieetrelecbieraviecaie jeuriou aaqoods ul JON 9-668 10 man 49 K
Palins Pale ae “OuT] MONT PO TOC SOUIOUMOUOHOUCT ORICUTEO Sliveubie anise [euou eajoods ul JON G)-F06E eoerecces uNUTONTY)
ee: ie “ ‘OUT MONT niayeia:ece OL OO ROVE SCLC) Dibiereiejsie eie;areié vee jeu4ou eajoods ul JON $0:G66E |
‘OUI, MONT 7” OE ae Seeger oye ue VOC Ce aayoods UL JON 08868 ic UINUeYyyUe'T
‘Oul] MON eo ee ee cine lit deh taker ad (12 200 (1 (00 earjoods ul JON G:8h6S
t biacp lems agen en eee a ir ee (seeks) LAMONB ST B.BSGP
qe OUI, Iq suLmMoqysrou we ‘TeuLLou eajoods Ut JON 0: FSF aks og ee mee! Hh
I 0-COLP S elele(b eiaie ° ica OOOO OU u9|eyL, esece ttovce peeecence oes . ‘dvut § TLOLSSUY TWHOTT quosqy Wadh a wecweesseves qynUstey
Ko ‘OuTT MO N averse SC OORODIIE ODO LACIDT deut 8,00 Isduy Lue Cones quoesq Vy 0-C69P
‘SUT ONT 2 heehee Caen cee e ee eateeranseeseserssecssoes ee °uomsod sity] sss oS5 TEN TGCL)
UL UITeAT, Ul ouly ou fag 07 woayssuy Aq pousissy | —G.PaCF
G 0:Z0GF eae eees b> ayy eeerene UgTeyy, se oeenee econ oul] OrT quoorlpe ou} SuLduLm OpevUul puv
0-LOGh 38 pooed st deu swoyssuy ur out] omy, OcOGr |S wantpiqnyy
seen enves ug eyT, seer emer w see ereernn nee pousisse yejour ou pure L-1O9F
‘TM 7 poovd st deut smoysduy ul cull oyy, OeOGre |S wNIyWT
winefee wires Moylan) pessoa: Vukte vans ease deut gs Wossuy toy FUOSqY 0:G0GF
seoeeugreyp [te ieceeensersneagtersssscseconerooeces Oeoeeee CNG Hee oMpUy
-oods xefos UI OUT OT YIM yuoproutoo ATyuoreddy 0-1O1F
‘tanaqoods
: IBIOS OT}
ee eae *SUOT}VAIOBGGO UI postoAod | ‘[BJOUT Jo oMEN
: Mee tfol sour, JO TTA
oreurrxorddy
‘(panuajuoo) ung oy} ur yuosead ATqeqoad speyop
170 Mr. J. N. Lockyer on Recent
To this it may be replied that, although these red lines may
be apparently the brightest to the eye, it by no means follows
they are the longest, since they are situated in a part of the
spectrum which affects the visual organ more strongly than the
photographic region does, It is possible also that the reason-
ing I have lately used in a paper communicated to the Royal
Society, on the spectrum of calcium, may be applied in these
cases.
Since a sensitized film is affected by some rays more strongly
than by others, in determining the lengths of lines from a pho-
tograph it is not fair to compare together portions of the
spectrum separated by too great an interval.
Furthermore, the fact of these red lines having been over-
looked in the solar spectrum is not conclusive proof of their
absence, inasmuch as this portion of the spectrum is both
brighter and less refrangible, and a greater degree of disper-
sion would be necessary when prisms are employed to render
visible faint dark lines which are easily detected in the photo-
graphic region. |
At present, then, out of the fifty-one metals with which
we are acquainted here, more than thirty are known to exist
in the sun with more or less certitude. Now it was a very
remarkable thing that although such metalloids as carbon and
sulphur, iodine, bromine, and the like, had been very dili-
gently searched for, no trace whatever had been found of
them, giving any evidence that they existed together with the
metals in these zones (these shells) to which I have referred.
Some years ago evidence was brought forward of the pos-
sible existence of the metalloids as a group outside the metals ;
and the evidence for this suggestion was of the following
nature:—Independently of any questions connected with solar
physics, I think all students of science now agree that the
vapours of the various elementary bodies exist in different
molecular states ; if these different molecular states are studied
by means of the spectroscope, perfectly different spectroscopic
phenomena present themselves. If we use a large coil, we
can drive every chemical substance with which we are
acquainted, including carbon and silicon, into a molecular
grouping competent to give us what is called a line spectrum,
the spectrum with which we are most familiar when we use
metals or salts of metals in the electric are.
If, however, other conditions are fulfilled; if these bodies
are not so roughly handled—if, in other words, we employ a
lower degree of heat, or if we use electricity so that we get
quantity instead of tension, then these line spectra die away
altogether, and we have a spectrum, so called, of channelled
Researches in Solar Chemistry. 171
spaces or flutings. Perhaps it will be convenient that I should
throw one of these spectra on the screen, and point out exactly
the difference to which I refer. I will first call attention toa
line spectrum. Those lines are due to the vibrations of mole-
cules of calcium and aluminium. The flutings which I now
throw on the screen are perfectly different in appearance ;
in this case they have been produced by the vibrations of
carbon at exactly the same temperature at which we get the
line spectrum from aluminium and calcium.
Now, while we got these thirty-three metals to give us line
spectra coincident with Fraunhofer lines, the only evidence
(very doubtful evidence) of the existence of the metalloids in
the sun at all, depended on the fact that, in the case of iodine
and chlorine, some of the channelled spaces observed in their
spectra at a very low temperature were imagined to be traced
among the Fraunhofer lines in the spectrum of the sun. It
is four years ago since evidence was gathered of a more con-
clusive kind in the case of carbon. The kind of evidence will
be sufficiently indicated by throwing a comparison of the solar
and carbon spectra on the screen. Below we have the bright
flutings due to carbon-vapour ; and above the solar spectrum
this photograph includes a part in the ultra violet. When this
negative is placed under a magnifying-glass, we find that
most of the very delicate lines constituting the fluting in the
bright portion have their exact equivalents among the F'raun-
hofer lines. This is the best-established piece of evidence, so
far as | know, which seems to indicate that we have truly some
of the metalloids present in the atmosphere of the sun by
the coincidence of their spectra with the Fraunhofer lines.
Further, carbon at all events exists under such conditions that
its molecular structure is very much more complex than that
of the metals in the reversing layer; and therefore it is pro-
bably withdrawn from the excessive heat of the lower region oc-
eupied by the reversing layer, which is competent, as we know
from from other considerations, to drive even carbon and silicon
into the line-stage, supposing carbon and silicon to be there.
This branch of the work to which I have just referred, a
branch which enables us to say that such a temperature must
exist in such and such a region of the solar atmosphere, de-
pends, in the main, upon questions raised by the differences
between the spectra of certain bodies in the sun and in our
laboratories. If, for instance, one wishes to observe the coin-
cidence between, let us say, iron and the sun, iron is placed
in the electric lamp ; its spectrum is photographed : side by
side with it we have the spectrum of the sun also photo-
graphed ; and, as a rule (I say as a rule ; but this is not abso-
172 Mr. J. N. Lockyer on Recent
lute in the case of such metals as iron), the intensity of
the iron-lines which we get in our laboratories is equivalented
by the intensity of the so-called iron-lines which we assume to
exist in the spectrum of the sun. That is the great argument,
in fact, for the existence of iron in the sun. But when we
leave the iron group of metals, we find others in which this
coincidence, this great similarity of intensity from one end of
the spectrum to the other, is very considerably changed. We
get in the case of calcium very thick lines of calcium corre-
sponding with very thin lines in the sun, and we get thin lines:
of calcium corresponding with very thick limes in the sun. In
fact, the two thickest lines which have already been mapped
in the spectrum of the sun are lines due to calcium. If we
photographed the spectrum of calcium with a very weak are in
that electric lamp, they would scarcely be visible at all. If,
however, we pass from the tension of the are to the tension
which is obtainable with the use of a very large coil, then we can
make the spectrum which we get artificially correspond exactly
with the spectrum with which the sun presents us naturally ;
and the more we increase the tension (the larger the coil and
the larger the jar we employ), the more can we make our ter-
restrial calcium vibrate in harmony, so to speak, with the cal-
cium which occupies a very definite region in the atmosphere
of the sun. Now this gives us this very precious teaching :—
We know that the vapour of calcium occupies such and such a po-
sition in thesun; we know that to get the two things in harmony,
as I said before, we must employ a very large induction-coil ;
and we know, again, that if we do employ a large induction-
coil, all these beautiful flutings in the carbon-spectrum which
have been thrown on the screen disappear utterly. That kind
of carbon is no longer present in the reaction ; but instead of
it we have a new kind of carbon which is only competent to
give us bright lines. We know, fourthly, that those bright lines
do not exist reversed in the spectrum of the sun. Therefore
the carbon must exist higher than the calcium, in a region of
lower temperature.
In what I have said up to the present moment (and I have
just touched very slightly on the physical side of the work,
because I believe that in the future it will be most rich in
teachings of the kind I have indicated), I must remind you
that I have dealt solely with the Fraunhofer lines. Now it is
knowledge ten years old, that if we observe the solar spectrum
with that considerable dispersion which is now, I think, impe-
rative if we are to do much good with it, there are bright lines
in the ordinary solar spectrum side by side with the dark ones.
Researches in Solar Chemistry. 173
In a paper communicated to the Royal Society in 1868 I
find these words :—“‘Attention has recently been drawn to cer-
tain bright regions in the ordinary spectrum.”’ The position
of these bright lines in the ordinary spectrum was then stated,
and attention was called, among others, to one between b and
I, I call especial attention to that line now because the re-
- quisite amount of dispersion is now so common that any one,
whenever the sun shines, may turn to 4 and see that bright
line for himself. It will be found just as much outside the
fourth line of } as the third line is on the other side of it.
This bright line, lying in the most visible part of the spectrum,
is exactly similar to many others, some of them in the yellow
and some of them in the red. A careful list of these lines
was made some years ago; and, [ am sorry to say, the list
was unfortunately lost by one of my assistants in a Metropo-
litan Railway-carriage ; at all events, enough was said in this
and other countries about these bright lines in the years 1869
and 1870 to have given rise, at all events, to the hope that
uny.one interested in solar physics would be perfectly familiar
with them. Among other matters which called attention to
their existence was a correspondence which took place in the
Comptes Rendus of the Academy of Sciences in Paris between
Father Secchi and another observer in connexion with solar
spots. Ihave remarked that a large dispersion is requisite to
see these bright lines, because with a small dispersion bright
regions of another kind in the solar spectrum are very obvious.
When this small dispersion, however, is changed for a large
one, one sees that these bright regions in the solar spectrum
are due to the absence of fine lines; and, indeed, if one ob-
serves the solar spectrum with considerable dispersion through
_ a cloud which prevents the fine lines from being seen, then
there is a very considerable relative diminution in the intensity
of some parts of the spectrum, and a very considerable rela-
tive increase in others, where these very fine lines are present
and absent relatively, so as to give rise to the appearance of a
very considerable change indeed in the background of the
spectrum.
When, however, a very considerable dispersion is employed
and photography is brought into play, if precautions be
taken to give sufficient exposure, these bright regions, as op-
posed to the bright lines, entirely disappear. Ihave here, by
the kindness of two friends, Mr. Rutherfurd and Captain
Abney, the means of showing you exactly what I mean. A
Rutherfurd grating containing 17,000 lines to the inch has
been used as a means of obtaining the spectrum ; and the film
employed was kindly put on the plate for me by Captain
174 Mr. J. N. Lockyer on Recent
Abney himself. We find, now, that Mr. Rutherfurd has
given us an engine of such enormous power that the fine-
ness of the collodion film is entirely distanced ; that is to say,
we can get from these perfect gratings spectra so extremely
fine and so full of detail, that they can be enlarged until the
structure of the ordinary collodion comes in and prevents a
fine picture. But if instead of the ordinary collodion process,
those which are being worked out with such success by Cap-
tain Abney be employed, then it appears that the film is as
perfect a thing in its way as the grating is in its way, and
one can go on obtaining any magnification one wants.
This is a photograph of the H lines obtained by the grating
and film to which | have referred. Between the H and K lines,
where the eye sees faintly three lines, there are now nearly
a hundred; and that will speak more than any words of
mine as to the extreme importance of the introduction of pho-
tography in such a research as this. Now here there are no
bright lines ; but, very conveniently, this next photograph con-
tains one of the bright lines discovered and carefully recorded
by Cornu, who has recorded bright lines in the ordinary
solar spectrum as well as Hennessy. In exactly the middle
of the field now is the bright line recorded as a bright line by
Cornu in his map of the blue end of the solar spectrum; but
excepting that.one bright line, which is much more intense than
any other part of the spectrum, bright lines are non-existent.
During the course of last year Dr. Draper, of New York,
published the first results of a research which he has undertaken,
going over very much the same ground with regard to the
metalloids as had been gone over in this country with regard
to the metals. Dr. Draper, who has long been known as a
most earnest student of science, approached this subject with
a wealth of instrumental means almost beyond precedent; and
his well-known skill and assiduity, in the course of the two or
three years during which his work was carried on, enabled him
to accumulate facts of the very greatest importance. Iam
most anxious to make these preliminary remarks, and to state
my very highest respect for Dr. Draper, because in referring
to his work I shall have to point out that some of his results
are, in my opinion, not yet completely established. Dr. Draper,
in the first instance, claims the discovery of the bright lines
already referred to, and bases a new theory upon them. It is by
no meansas a stickler for priority that I regard this as a very
great pity, but because I think that, if the very considerable
literature touching these bright lines (papers by Young, Cornu,
Hennessy, Secchi, and others) had been before Dr. Draper
when his paper was written, the necessity for the establish-
ment of a new theory of the solar spectrum, which doubtless
Researches in Solar Chemistry. 175
cost him very considerable thought, would probably have been
less obvious. :
Dr. Draper was so kind as to send me some little time ago
a photograph of the solar spectrum confronted with the lines
of oxygen ; and the result which this photograph is claimed
to show is, that a considerable number of the oxygen-lines are
coincident with bright lines in the solar spectrum. I will
throw this photograph of Dr. Draper’s on the screen, in order
that we may have common ground of thought. The lower
part of the photograph gives the lines of oxygen ; the middle
part gives Dr. Draper’s photograph of the sun, and the upper
part a photograph of the sun taken in England, which I have
put side by side with Dr. Draper’s in order that the definition
of the two photographs may be contrasted.
On examining the upper photograph with a very consider-
able magnifying-power, the detail comes out marvellously, and
the spectrum between the more marked lines is found to be
occupied with extremely fine lines in those regions where Dr.
Draper’s photograph gives ribbed structure, which, I fear,
may not be due to the solar spectrum atall. In the silver-on-
glass gratings, one of which Mr. Rutherfurd was so kind as
to give me, I find that, in consequence of the grating being
ruled on the back surface of the glass and the double trans-
mission of the light through the plate, there is a considerable
formation of Talbot bands, and the solar spectrum is in some
regions entirely hidden and absolutely transformed. Lines
are made to disappear ; lines are apparently produced ; so that
if one compares a part of the spectrum taken with one of
these silver-on-glass gratings with an ordinary refraction-
spectrum, the greatest precaution is requisite. Indeed I
think 1 am not going beyond the mark when I say that the
positions of all lines below the third or fourth order of inten-
sity must be received with very great caution indeed when
these gratings are employed. So well is this known to Mr.
Rutherfurd himself, who prepared these gratings for another
purpose, that he is now, with equal generosity, distributing
gratings containing the same number of lines to the inch
(17,500, or something like that) engraved on speculum-metal
in order that these defects may be obviated.
With regard to this work of Dr. Draper’s, then, I wish to
point out that the photograph in which these comparisons with
the oxygen-lines have been made is not one which is compe-
tent to settle such an extremely important question. Secondly,
upon examining these oxygen-lines, I do not find the coinci-
dences to which he refers with bright solar lines and oxygen-
lines in that part of the spectrum with which I am most fami-
liar, for the reason that there are no bright lines whateyer in
176 Mr. J. N. Lockyer ‘on Solar Chemistry.
this portion of the spectrum. I have here enlargements of
negatives going nearly the whole length from G to H, one of
the regions which are included in this photograph of Dr. Dra-
per’s. I have carefully gone over these regions line for line;
and in no case do J see any bright line in the sun whatever
coincident with any line of oxygen whatever. I cannot pro-
fess to have gone over the ground in the ultra violet ; but it
will appear to me very surprising indeed if, when we go fur-
ther, when we include the H and K lines which have already
been thrown on the screen, that Dr. Draper will find any
possible coincidences with bright lines of the sun even there,
because, when perfect instrumental conditions are brought into
play, no bright line whatever exists in the part of the solar
spectrum which is included in this map.
The bright line discovered by Cornu exists outside K ;
but between the region included in this map and the G lines I
find no obvious bright line.
There is an experiment which any member of the Physical
Society who possesses a spectroscope with three or four prisms
can make for himself. Take the spark in air in an apparatus
of the kind to which I have referred, use a comparison prism,
flood the air with nitrogen, and in the field of view which
includes b (and therefore one of the most marked bright lines
in the solar spectrum itself) you will find three or four un-
doubted lines of oxygen. Ihave made that experiment, which
is quite a simple one ; and I find no coincidences in this part
of the spectrum between any of these oxygen-lines and the
undoubted bright lines. I have not tried it yet for the lower
parts of the spectrum in the red and yellow, because I hope
that Dr. Draper will try for himself.
I do not say that Dr. Draper’s alleged discovery is no dis-
covery at all; I say (and I think it is my duty to say it, as I
have been occupied in closely allied work for some considerable
time) that I do not hold it to be established.
I have no doubt that Dr. Draper will carefully go over his
work himself; and I am quite certain that he will be the very
first to hail what I have said today with satisfaction, because
his desire, I am sure, is the desire of every true man of science,
that the truth should prevail. In any case Dr. Draper has
begun work in a branch of the chemical inquiry into solar
matters which, up to the present time, has been sadly neg-
lected ; and we should all be grateful to him on that ground.
I have no doubt that he on his side, as I on mine, hopes,
as I said before, that the Physical Society of London and the
Physical Societies of America will come forward and supply
more workers for a branch of science which I am certain in the
future will be regarded as one of very considerable importance.
a iy
XXIV. On the Resistance of Telegraphic Hlectromagnets.
By OviverR Heavisive*.
is | hgamee appears to be some uncertainty regarding the
proper resistance which electromagnets for signalling-
purposes should have—whether a receiving instrument should
_ have a resistance equal to that of the remainder of the circuit,
or a half, ora fifth, or some other fixed fraction thereof. Prac-
tical experience, especially with high-speed instruments, has
shown that the resistances in general use are too high—and
that advantage is gained by reducing the resistance of an elec-
tromagnetic receiving instrument, employing fewer windings
of a thicker wire in place of more windings of a thinner,
thereby reducing the self-induction as well. Ohm, as long
ago as 1826, showed that the resistance of a galvanometer
should equal that of the rest of the circuit in which it is placed,
to obtain the maximum magnetic force. When the correction
needed on account of the thickness of the insulating covering
of the wire is also reckoned, then the thickness of the wire of
the galvanometer should be such that the external resistance
is to the resistance of the galvanometer-coil as the diameter of
the covered wire is to the diameter of the wire itself (Maxwell,
vol. ii. p. 321).
Now if, in telegraphic signalling, sufficient time were
allowed during every signal (positive, negative, or no cur-
rent) for the full effect to be produced in the circuit by the
electromotive force, or for the current to entirely die away,
the above result would hold good also. But such is not the
case; for by reason of electrostatic and electromagnetic induc-
tion, the current has not time to reach its full strength during
every signal. On a land-line, unless it is very long, electro-
magnetic induction is the principal retarding cause ; and it is
this case which is here considered.
2. Let there be a simple harmonic variation of electromotive
force
i sin mt,
where E and m are constants, and ¢ is the time, in a circuit of
resistance RK and electromagnetic capacity L. The equation
of the current is
E sin me=(R+L 7 Jy, ‘da uh Guana
where y is the current at time t. The solution of (1) is
= eee (me— tan7! )
ar J R2 + L?m? Rays
* Communicated by the Author.
Phil. Mag. 8. 5. Vol. 6. No. 36, Sept, 1878. N
178 Mr. O. Heaviside on the Resistance
neglecting a vanishing term. The amplitude of the current-
waves is thus reduced from
a
R
(what it would be were there no retardation) to
E
r= So —— ° Fy . e e ° s
J R?+ LP?’ ou
where I signifies the maximum current. Or the current is
the same as if the resistance were increased in the ratio of
1 ava (=z):
1+ R
If Lm is large compared with R, then I’ is small compared
with = or the diminution of current-strength is large.
Let T be the time of a complete reversal. Then
peed
ial
With the Morse code, when T=, second, or m=80z, an
automatic transmitter produces 100 words per minute, or a
little more. Let = be between +}, and +, second, then Lamm
R R
is between ee and 87, or (say) between 2°5 and 25; therefore
the current wiil be reduced from 2°5 to 25 times. °
On telephonic circuits, owing to the great rapidity of the
reversals, the reduction in current-strength is great, and is
nearly inversely proportional to the pitch of the tone, thus
rendering it impossible to reproduce at the receiving end the
same quality of sound as is emitted at the sending end, irre-
spective of mechanical or acoustical difficulties. The second
partial tone of any continuous sound will be weakened twice
as much as the first, the third thrice as much as the first,
and so on, thus producing a general deadness or want of
brilliancy.
It also appears from (2) that the resistance of the circuit
becomes quite subordinate when at large; and it may then
be greatly increased without much weakening the current.
This is remarkably evident on telephonic circuits. On auto-
matic circuits it has sometimes been found beneficial to intro-
duce resistance-coils at the receiving end. The irregular
effects of leakage from neighbouring wires, which mutilate
of Telegraphic Electromagnets. £9
the propes signals, are reduced in a greater proportion than
the proper signals themselves.
3d. Now let R and L belong to the electromagnet alone, and
R, and L, be the resistance and electromagnetic capacity of
the remainder of the circuit. Then (2) becomes
iD ?
P= Gt eee LD
In solenoidal electromagnets, if x is the number of wind-
ings of the wire in unit of length, and the number of layers in
unit of thickness, R varies as n*. L also varies as n*, while
the magnetizing force due to the unit current varies as 7’.
Applying this to equation (3), if F is the magnetizing force,
F is a maximum, n being variable, when
R24 Lm?=R?2+L2m?, . 2 . . . (4)
R, and L, bemg considered constant, as belonging to the line.
We may write (4) thus,
i 2
14m? f=)
oe COSA UI Can AM Sanat eed
R .
oV TG)
I, . :
Now =" is constant for the same line-wire, whatever its
length, since both L, and R, are proportional to the length of
the line. Alsoz is constant for the same coil, if only the dia-
meter of the wire is variable, since both L and R vary as n’*.
But the time interval 2 for the electromagnet is in general
R
much greater than the time interval — for the line-wire ;
whence it follows, by inspection of (5), that R must be much
less than R, to produce the maximum magnetizing force ; and
the higher the speed, which is proportional to m, the less
should R be.
The calculation of Ly
Ry
straight, and parallel to the earth; but the calculation of =
is not so easy, owing to the variety of shapes assumed by elec-
tromagnets used for telegraphic purposes, with their cores,
polepieces, and armatures, which all influence the electromag-
netic capacity, though they do not influence the resistance.
It is therefore impossible to enunciate a general law, that the
N2
is easy, since the line-wire is long,
180 Mr. O. Heaviside on the Resistance
resistance of an electromagnet should be such or sueh a frac-
tion of the external resistance ; for the result will be different,
not only for every speed, but for every different construction
of the electromagnet.
4, Approximate results are, however, easily obtainable in
the case of a solenoidal electromagnet. Let its length be J,
external radius w, internal radius y, with an iron core of radius <.
Its electromagnetic capacity is
L=27'ln*(@—y)(a? + 2ey + 8y? + 24rK2?) . . (6)
(‘ Maxwell,’ vol. ii. p. 283), where « is the coefficient of mag-
netization of the core. Its resistance is
R= apin*(2’—y"), . « «see
where p is the resistance of unit of length of wire of unit dia-
meter. Therefore
L g nee
p= lb Barene . 2 2
approximately, by leaving out x? + 2xy+3y’ in (6) as small in
comparison with 247rx«z?, which is a large number, unless the
core is very small. Let «=382; also, if the specific resistance
of copper be taken at 1:7 microhm = 1700 c. g.s., then
A
p=1700~x =e and
L
Rae seconds. . . «enema
5. To determine oi for the line wire, Maxwell (vol. ii.
R,
p- 282) gives the coefficient of self-induction of a straight
wire, the circuit being completed by a parallel wire. ‘The
same method of calculation is applicable to any number of
parallel straight wires, by finding the integral
T=3\\{ Hw dx dy dz,
where T is the kinetic energy of the system, and H, w are
the vector-potential and the current at a point, both parallel
to the axes of the wires. Thus, for n parallel straight eylin-
drical wires of length /, conveying currents Q,, Cy,..., of
radil ay, dg,..., Specific magnetic capacities 4, Me,..., repre-
senting the distance between the centre of two wires m and n
by ban we shall have
2T
ca =$(fyC? + woO2 +...)
—2u,(C? log a, + C2loga,+...) (10)
—4p)(C,C, log b a+ C,C; log by 3+ CC; log bys te aie ),
of Telegraphic Electromagnets. 181
with the sole condition
C,+C,+C3+. oe == (),
Let there be only four wires, 1 and 3 for one circuit, 2 and 4
for another; then C;= —C,, and C,=—C,. Substituting in
(10),
== 01 (MEH + 2u log 4 _ O13 “2 )
ie
+ C3 (He Ht + 24,10 og —*
Agty
b, 4b
+ 20,0, x 2fy log as rch ket oy peeve el)
The coefficient of C} in (11) is the coefficient of self-induction
per unit of length of the circuit conveying the current Cj.
Similarly for C2; and the coefficient of 2C,C, is the coefficient
of mutual induction per unit of length of the two circuits.
From (10) we may find the coefficients of induction of sus-
pended wires, the circuit being completed through the earth.
Let M be the coefficient of mutual induction, and L,, L, the
coefficients of self-induction of two wires of radii ay, a2, heights
above ground /,, hz, horizontal distance apart d, and specific
magnetic capacities (44, Md, ; then
a Sea,
L 2/ ¢
=F +2log ae cheese 4 na)
M Ze a? + (hy they?
noe °8 P+ (hy — hg)”
where “y is made equal to unity.
As a practical case, let
hi=h,=8 metres,
a,=a,='002 metre, my=pyp=1+4re=315, if e=25, and
d=" metre. Then
f=L5=173,
M=
approximately, Also, if the resistance is aor ohms per mile,
the resistance per centimetre is 80778 ¢. g. s. ; therefore
LoS ELI.
m, © S07TS ©
6. This time interval being in general very small compared
= "(0204 second.) yee Cle)
182 Mr. O. Heaviside on the Resistance
with = for the electromagnet, we may neglect it; and then (5)
becomes
nts 1
R. = ey Sasa
, /1 +m" Fs
or R,=Lm approximately. The resistance of the electro-
magnet for high speeds varies inversely as the speed to obtain
the maximum strength of signals.
Using the value of z given in (9), we have
Abu os eee ates
Bag pee
“ry
Qa
where T= —-
m
At 100 words per minute Morse code, T=about gy second;
therefore at this speed
By 595-624 2
R aty
Suppose «=2, y=z=1 centimetre; then —
Ry 2.
Ral rye
or the resistance of the electromagnet is 7},th part of the ex-
ternal resistance to obtain the maximum magnetizing foree—
a very low result. If = is taken into account, this becomes
Al
rath.
7. Having made the magnetizing force a maximum for a
given speed and size of electromagnet, by varying the thick-
ness of the wire, we may next find the ratio between the outer
and inner radius of the coil to make the attractive force be-
tween the core and a soft-iron armature a maximum. We
have
Sree SAV
J (R+ R,)? + L?m?
(neglecting L,), where
L=27'ln*(e—y) (a? + 2ay + 8y? + 240K2’),
R=mpln‘(a’?—y’), |
of Telegraphic Electromagnets. 183
Also
F=1TG,
where F is the magnetizing force, and
G=4rn(«2—y).
To make F a maximum, n being variable, we found
R?+ L?m? = Ri.
Therefore
ree HG. =
a /2(1+ 7)
1. 2(1+ R,
Substituting
4 a max—y)R
alte a) for G,
we have
82r(a—y) KH?
F2 pl(z+y) 5
R
R,(1+ z).
Now
ty \/ ieme? Tim :
= 1+ Tor ae approximately,
aman 2—y 5 Ss 5
= aa, pues (a? + 2vy + 3y? + 24arK2’).
Therefore
12K?
Pe Ry
lm( a? + Qay + 8y? + 24aK2”) + —— =
Now the magnetization of the core is proportional to the mag-
netizing force ; and the attractive force between the core and
a soft-iron armature placed close to it is proportional to the
square of the magnetization and to the cross section of the
core. Therefore, if A is the attractive force,
5?
ES iy es Spl > ——, , (14)
Im( a? + Qay + 8y? + 24erK2” eo
184 On the Resistance of Telegraphic Electromagnets.
grap
This increases with 2; therefore let z=y, the inner radius of
the coil ; let « be constant and y variable ; then A is a maxi-
mum when
Fo Be dp «vty
2
yy Dary’m w—y
is a minimum; and that is when
2mm 4 v
ae
The least value of 2 is
a 2
Using the former value of p, viz. 1700 x = also m= 807 and
“=2 centimetres, then
a ~
J: 1 nearly.
x
Yi + .
= increases very slowly as « and m increase.
In this determination of “ , the outer radius has been sup-
posed to be constant, and the inner variable, and with it the
iron core. If, on the other hand, the inner radius is fixed and
the outer variable, a different ratio is obtained, viz.
J
2m : x
—
—
z i Ney)
oe
which gives lower values to 2 than before.
It also appears from (14) that the attractive force varies
inversely as the length of the coil. Though the formule are
only true for long coils, yet it points in the direction of short,
flat coils; for the attractive force is also increased by increasing
the transverse dimensions of the coil.
8. In paragraph 5 we found L,=173 and M=5 approxi-
mately for iron wires of a certain size, distance apart, and
Liffect of Pressure on Disruptive Discharge. - 189
height above ground. ‘The ratio
Ly
Mn 34
expresses the ratio of the strength of the sinal wave currents
in the wire containing the electromotive force E sin mt to the
corresponding induced currents in the parallel wire, or, rather,
the minimum value of that ratio for rapid reversals. For if
wy L, belong to the primary circuit, R,, L, to the secondary,
then
ee Ev R?2 + 12m’ + Lim
J/ {R,R,—m?( LL, — M’)}? + m?(R, Ly + Rl,
and
Ze Mm
VRE 12m?
As m increases, this approximates to
r, _M
re oes
equal to about 3 if there are no electromagnets in the second-
ary circuit, otherwise much less. It is here assumed that
x=25 for the iron wire.
XXV. On the Effect of Variation of Pressure on the Length of
Disruptive Discharge in Air. By J. EK. H. Gorvon, B.A.,
Assistant General Secretary of the British Association*.
[Plate IIL]
Mistory.
ie 1834 Mr. Snow Harris stated{ that, other things being
equal, the length of the spark which an electric machine
or Leyden jar will give in air varies in the simple inverse
ratio of the pressure. He, however, gives no tables or figures
in support of his law.
Sir William Thomsont{ has determined, by means of an ab-
solute electrometer, the difference of potentials corresponding
* Communicated by the Author, having been read before Section A of
the British Association, Dublin, 1878.
+ Philosophical Transactions,
t Proc. Roy. Soc. 1860, Papers on Electrostatics, p. 247.
186) Mr. J. E. H. Gordon on the Effect of Variation of
to the lengths of sparks between flat plates. The extreme
length of spark used in his experiments was 1°52 millim.
In the experiments made by M. Masson, the spark passed
either between two balls in the air, or between two similar
balls inside a globe in which a more or less complete vacuum
could be produced. The distances between the balls could be
varied, as well as the pressures. Within the limits of his ex-
periments, he found that the length of spark was inversely
proportional to the pressure. The greatest length of spark
which he used was 1171 millims.
In 1843 M. Knochenhauert worked witha constant length
of spark of about ?incht, and measured the electric density re-
quired to produce a spark in air at various pressures. Within
the limits of his experiments he found that the ratio of the elec-
tric density required to produce a spark, to the pressure of the
air, increases sensibly as the pressure diminishes. Now itis a
simple deduction from Harris’s law that the length of spark
is proportional to the electric density; and therefore Knochen-
hauer’s results show that the law given by Harris and Masson
does not hold for all distances and pressures.
Wiedemann and Ruhemann§ found a purely empirical for-
mula for variations in the lengths of sparks where the longest
spark was 9°95 millims.
In the experiments described in this paper, an attempt has
been made to determine the ratio of the spark-length to the
pressure for distances ranging from 6 inches to 30 inches by
means of one and the same apparatus. The experiments also
differ from any former experiments with which the author is
acquainted, in the fact that an induction-coil was used as the
source of electricity instead of an electric machine.
Description of the Apparatus|} used.
The Coil.—This was a particularly fine instrument, giving
a spark of 17 inches (42°5 centims.) in air at the ordinary
pressure. It was worked by 10 quart cells of Grove’s battery
arranged in series. It was provided with a vibrator and with
a clock contact-breaker, either of which could be used.
The Air-pump was of the ordinary Tait’s construction, but
* Annales de Chimie, 3° série, t. xxx.; or Mascart, Electricité Statique,
t. ii. p. 94.
7 Bape. Ann, lviii. p. 219; or Mascart, t. ii. p. 95.
t He does not state the length of spark he used, but gives the height
of his whole apparatus, and a drawing which, if it is to scale, shows that
the discharging balls were about ? inch apart.
§ Mascart, t. 11. p. 97.
|| The whole of the apparatus was made by Mr. Apps.
Pressure on the Length of Disruptive Discharge in Air. 187
was arranged so that more pipes than are usually provided for
could be attached to it. Its base being removed, the bolt
which had held it to the base passed through a hole in the
table ; and the nut being screwed up the pump was firmly fixed.
The Discharging Tubes.—These consisted of two cylindrical
glass tubes about 4 feet (1:33 metre) long and nearly 3 inches
diameter. At one end of each was a tap, the brass pipe from
which ended in a ball which formed one of the discharging
terminals. Holes in the side of the brass pipe admitted the air
from the tap to the tube. At the other end was a stuffing-box,
in which a brass rod slid ; at the end of the brass rod was a
point which could either be placed in contact with the ball or
withdrawn some 3 feet from it. The end of the rod was kept
always in the axis of the tube by means of three little glass
arms, which were stuck into an ebonite collar fixed on the
discharging rod a little behind the point. The two tubes were
supported in a horizontal position, parallel to each other and
about 18 inches apart, on four ebonite legs about 18 inches high.
The tubes were joined to the air-pump by means of the pipes and
taps shown in the figure (Plate III.), which were so arranged
that the tubes could be at once connected to each other, to the
external air, to a gas-holder, or to the pump. Between the
tubes and the pump the metal pipe was cut, and a piece of
glass tubing about 18 inches long, well varnished with shellac,
was inserted, so that the electricity might not pass to earth
through the pump*.
When the tubes were shut off from the pump, air could
always be let into the glass pipe to prevent the discharge pass-
ing to earth inside it, as it would do at low pressures. The
distance between the point and ball in each tube was measured
as follows. They were placed in contact, and an ink mark
was made on the discharging rod just outside the collar of
the stuffing-box. When the rod was slid out, the distance of
this mark from the collar was equal to the distance between
the point and ball. The pressure was given by a U-gauge,
about 4 feet high, attached to the air-pump at one end, open
to the air at the other.
The pressure P was given by the formula
P= {height of barometer} — {difference of level of mercury
in the two arms of the U}.
Before being admitted into the tubes, the air was dried by
being drawn through sulphuric acid. When it was desired
* Mr. Apps informs me that it is injurious to the coil to connect either
secondary terminal to earth when using long sparks.
188 Mr. J. BE. H. Gordon on the Effect of Variation of
that the pressure of the air in the tube should equal that of the
external atmosphere, air bubbled through the acid as long as
the difference of pressure inside and outside the tube exceeded
that of the inch of acid which had to be displaced, and then
the tap was opened direct to the outside air. The external
diameters of the tubes were about 2°94 and 2°76 inches respec-
tively, and the diameters of the balls °94 and °92 inch.
The Experiments.
In the experiments which are the subject of the present
paper, one of the tubes (A) was left open to the atmosphere,
and its discharging point placed at a standard distance either
6, 8, or 10 inches from the ball; and the other tube (B) being
nearly exhausted, experiments were commenced at the low
pressure, and then a little air was let in between each observa-
tion. The tubes were so connected to the coil that the dis-
charge would pass in whichever tube offered least resistance.
The discharging-distance in B was then varied and adjusted to
the shortest distance, which caused the whole discharge to pass
in A. The distance between the points of B being noted, the
points were then brought nearer together till they reached the
longest distance at which the whole discharge passed in B.
The mean of these two distances was taken as the distance
which, at the pressure then being worked with, interposed in B
a resistance equal to that of the standard length in A of air at
the pressure of the atmosphere.
Let us call this mean “mean B spark.” Now, if the law
that the spark is inversely proportional to the pressure holds,
we should have for the same series of experiments,
{mean B spark} {pressure in B} =const. ;
and to compare different sets made with different distances in
A and with the barometer at different heights, we should have
{mean B spark} {pressure in B}
wl a ee COM at
{distance in A} {height of barometer}
If the two tubes and the discharging points were precisely
alike, this constant would be unity. Any slight difference in
the shape of the points and balls, however, would cause it to
differ from unity, but would not affect its constancy.
The Table (pp. 190, 191), which explains itself, gives the
results of several sets of experiments arranged in ascending
order of pressures.
The results which I deduce from it are :—
(1) From a pressure of about 11 inches up to that of the
Pressure on the Length of Disruptive Discharge in Avr. 189
atmosphere Harris’s law approximately holds good. No va-
riation from it indicating any other law is observed.
(2) No law can be said to be more than approximately true ;
for when the density has almost reached the discharging limit,
any slight accidental circumstance, such as the presence of a
grain of dust, a little burning of the point by the last dis-
charge, &c., will cause the discharge to take place. Professor
Clerk Maxwell has compared the experiment to the splitting
of a piece of wood by a wedge. It is possible to determine
the average pressure on the wedge which will split the wood ;
but in any particular experiment it is impossible to say that
the wood will split exactly at that pressure.
(3) When the pressure is diminished below 11 inches, the
product in column Vil. rapidly diminishes. This shows that
at low pressures the spark produced by a given electromotive
force is much shorter than is required by Harris’s law, or that
the electromotive force required to produce a spark of given
length is at low pressures greater than that required by Harris’s
law. This agrees with what Mr. De La Rue has told me,
namely that he finds that at all pressures, however low, the
discharge is disruptive, and none of it passes by conduction.
If any portion could at low pressures pass by conduction, we
might expect that a smaller and not a greater electromotive
force would be required than that calculated by Harris’s law
from experiments at high pressures.
It is also not inconsistent with the result of Sir William
Thomson’s historical experiments (mentioned above) “On the
Hlectromotive Force required to produce a Spark.” For he
writes*, ‘ Greater electromotive force per unit length of air
is required to produce a spark at short distances than at long.”
For the words in italics I substitute ‘‘at low pressures than at
high.”” We may then both write “ with a low air resistance
than with a high one,” or “ with few air particles between the
points than with many.”” Sir William Thomson says of his
result, “it is difficult even to conjecture an explanation ;”’ I
can only say the same of mine.
I cannot say exactly at what pressure M. Knochenhauer’s
experiments show a change in the law—as he evidently con-
siders the change to be due partly at least to experimental
errors, and introduces corrections, some of which are appa-
rently suggested by peculiarities in his apparatus, while others
are intended to adjust the experimental results to the supposed
law. As far as I can see, the change was first beyond the
reach of his corrections when the barometer fell to about 2
inches.
* Papers on Electrostatics and Magnetism, § 323, p. 248.
f
won O
t
r
rf Varia
ect ¢
4
Mr. J. &. H. Gordon on the -
190
OZO-U
CLA wumyjoo) x (“A uuimyoo)
(*[ wumyoo) x (‘AT uumyjoo) —
V m oanssoad x y ur yavds yo yysuery
q ut oanssoid x g ur yards jo y48uery
‘ITA
0¢-6é 8 &I1 €-€1 é-GT L-91
aa YA, 7 i |) Ry eo OOLT OBL £9]
G9-66 8 cV-Fl 0-F1 6-FI F6-91
09-66 9 CV-GI Gl 9-1 ¢0-9T
09-66 9 8-11 on | V1 LCI
09:66 8 co-FI 6-E1 G1 [-¢l
rrrttfessees Gy @grensereeeleerterees yp eereceetlireeee ses: oe Mg ce reridere QQ peeelees 2 Ogee feces PPI
G9-64 8 £91 8-ST 8-81 66-F 1
09-66 9 CL-E1 ET oI vG-F1
05-66 8 Co FT 6-ET @-Gl GE
0L-62 Ot 9-14 P61 8-€6 6-11
a |) 9) ei CO a CLE, Ri tercaiew |r BIE Berl BLE
09-66 9 9-91 0-9T G-LT PL-AL
G9-6% 8 6-L1 8-9T 0-61 89-11
¥9-6é 9 G6-9T GOT LLT 6F-6
69-66 8 €9-06 SP-6I L-1Z FE-6
GQ.ggit ttle cee Sslacenat ene rr refer g gpereters Ose Z8.2
OL-66 01 6-€% PIG 8-92 8-£
49-66 9 G9-06 9-8T LG 6S-F
OL-62 Or 8-08 GGG L-9€ GE
$9-66 9 GL-9G 6-26 9-08 GPG
SoYOUT soyout saqout soyour | soyout soyout
« yleds gy uve ,, : .
‘TA WuwNjoo UI WeATS a Vv
qy soy JV spueys ojou0.4
eq Ut “A UTUNTOO UT UOATS
yysusy Jo ave ur yaeds wv soonp
oad YOIYM OLOF OATIONLO.T}
-oo]o ours oyy Aq poonpoad
“7 uUINTOO Jo oansso.td ye ‘st
yorya yauds JO yysueyz 07 yenbo
‘TIT pure TT suumypoo jo uvepy
‘TA “A “AI oles a ‘I
"a9NVS-(]
ey} ur Arno
ur Ajo soxyd | -xour Jo suum]
oyvy 0} OSavyo -00 JO s}ys1ey
-SIp oy} posnva jo oouodoyIp
Yor gf UT szutod) snurtu zaojoutod
jo yavde oounysrcy | -vq Jo yyStoy=
q Ul asso
‘y urowmsserd =| *w utsyutod jo
= Joyoutoreg =| gavde couvystqy
191
ur.
2
tive Discharge in A
Pressure on the Length of Disrup
er oneene
eeeoestareoere
“8 GQ.ag ot
¥9-66
09-66
09-66
¥9-66
0-66
OL
9
or
9
Ballncmineees ‘open
8
9
al gon Hane 7 (eae ecto
= =
=
eoleesecance
SCOOWODMDDOSHONOSCONCOLENDE
L om
ee eeerne eleaet rh eeeseesee
=
[|
us
WEDD AS OOH S SOD He
—
ie)
= =
1 SH De st SHO DT HR HERS OD OO OD ODO IID N
=
ier)
okies
Co
[on
a es
.
ite)
RRA AOND
Pty dewiat [a mesa eta ulet eee CZ-ZI
(—! |]
FIL | G68E 1-66
GC 9-6 49-66
GZl | 9-81 9-86
6-¢ a) 9-8
[le | Ol eee
98 LOL LLB
9-9 gL F-L6
z9 9.9 66:92
Ser | eel ¥-9Z
wen aoa ees be
Lg GL 6F-Sz
Gel | SFI P&Z
0-01 L-€1 1-2
OL £8 8-FZ
Poe apr etal es) a
6-9 8-L PL-FS
[Il | lel 1-62
8 9-6 1-83
Ler | 8-1 9-82
Segre SUE = utce
LL 8 ¥o-26
Let | 8S1 BBE
Lit | 8-91 6-12
ZS ra FO-1Z
OS el gepeton: Bg
¥-6 9-01 1:08
911 | 981 8-61
ect | L91 9-61
3-6 eI 67-61
Soe ORT etehal
Lat | 8FI P81
Lor | Vel 381
UL ol 2-00 POLL
BLt | 1-6L 9-L1
reo ges
AXVI. Hydrodynamic Problems in reference to the Theory of
Ocean Currents. By K. Zopprirz*.
HE aim of the following pages is to show what are the
motions admitted by an unlimited stratum of liquid under
external influences acting only upon the surface, supposing
that friction takes place in the liquid (as it does in water and
ul other known liquids to a greater or a less amount).
The differential equations for the motion of frictional liquids
are as follows :—
ae | Ges Oy ee
dt Ox
- +592 _y—“ oxo,
a =e —Z, Ea et
ou 7 - + on =0;
in which u, v, w are the velocities in the directions of the rect-
angular coordinates x,y,z; X, Y, Zare the components of
the external forces; p is the pressure, w the density, & the
coefficient of friction of the liquid, and A the symbol for the
sum of the three partial differential quotients of the second
order according to #, y, and z.
The surface-conditions can be expressed most simply thus :—
(1) The particles of the surface of the liquid will always remain
in contact with those of the adjacent body; that is, both must
have the same velocity-components perpendicular to the sur-
face. Naming these vy and ,, then must at any time
This condition includes, if the adjacent body is itself liquid or
gaseous, the necessity that the pressure normal to the surface
be equal on both sides, because otherwise the connexion ex-
pressed by the preceding equation would be broken. (2) The
difference of velocity of the particles of the liquid against those
of the body in contact, parallel to the plane of contact, is pro-
portional to the tangential component T of the internal pressure-
forces acting upon the surface, and has the opposite direction.
Accordingly, if 7 and 7, denote the tangential velocities of the
* Translated from a separate impression, communicated by the Author,
from the Annalen der Physik und Chemie, new series, vol. 11, pp. 582-607.
M. K. Zéppritz on the Theory of Ocean Currents. 193
liquid and the contiguous body, the equation
T=A(7,—7)
will subsist, in which 2X is the constant of the external friction,
depending only on the nature of the two bodies in contact. If
wetting of a part of the surface takes place, we must there put
T=T7, consequently A= 0.
Let the liquid be spread over a solid plane. Of external
forces gravitation only acts perpendicular to this plane. Let
its direction be the positive X-direction ; then is
Xo, ,L=—LZ—0:
Let the solid plane be wetted, so that the liquid particles
adjacent to it always remain at rest. This requires that for
them w=v=w=0 always. The body in contact with the other
surface will at every point have equal velocity and in the same
direction, but in general dependent on the time. If the initial
_ motion of the liquid was parallel to that of the contiguous
medium, or was also =0, then, in accordance with the second
surface-condition, only motions in the same direction can at
any time take place. Consequently, if we place the plane of
XZ parallel to this direction, v is always =0. The differen-
tial equations then become
du _1 Op k ‘a
i a
dure Op vk a
OU Vows.
Spas ea
The conditions for the particles in contact with the solid
surface are }
: y—y,=0, T=A(j,—7).
If the angles made by the normal to the surface with the
X- and Z-axes be denoted by (n, x) and (n, z) respectively,
the 1st equation gives
(u—) cos (n, x) + (w—wy,) Cos (n, z)=0;
while the 2nd splits up into the two following :—
Tsin (n, #)=AMwy—u); Tsin(n, z)=rA(w,—w).
These equations are satisfied if we assume the surface to be
horizontal—that is, put
cost, v)— 1, Feosi( 1m, 4) — Costa, <}—=0-
Phil. Mag. 8. 5. Vol. 6. No. 36, Sept. 1878. O
194 M. K. Zoppritz on some Hydrodynamic Problems
so that the stratum preserves the constant depth h, and if we
further put w=u,;=0 and
lop _
ary: 2
consequently
p=Nt+pu92.
N denotes then the pressure for #=0, consequently (if the
origin of coordinates is transferred to the upper boundary
plane) the pressure, taken as constant, exerted by the conti-
guous medium upon the surface. Hereby becomes
ray 8 aii
Oz oy
Since moreover the first of the differential equations is iden-
tically satisfied, there remains, for the determination of w, only
the third,
dw _koO'w
dt pox
because the fourth merely expresses that w is independent of
z, and thereby causes the second differential quotient according
to 2 to be omitted in the present equation.
In the condition-equation which must subsist for «=O,
P now signifies the pressure-component exerted, parallel to
the Z-axis, upon an element of the surface perpendicular to
the X-axis. According to F. Neuman and Kirchhoff’s nota-
tion,
=—1 (8! + +o),
w
iv aa: =(w,—w).
In the most general case, w,=¢(t) is a given function of
the time.
The application is not limited to cases in which only low
velocities occur, the squares of which can be neglected against
the first power : for since
- _ ow , ow Ow Ow
Oe)" Oe eae ee ;
therefore here
but here
Ow 0,
u=0, i), Set
in reference to the Theory of Ocean Currents, 195
for the present problem
dw Qw
dt. Ot
cannot be neglected.
The problem now is, consequently, so to define the function
_ w that, within a space bounded by two planes perpendicular to
the X-axis and at the distance h from each other, it satisfies
the differential equation
ee ay se
and the equations
(for 2=0) — 2° + pw=pd (8), UOIOROROZD
(for z=h) jo OOS OLAS DRED
and, finally, at the time t=0 takes a given initial value—thus,
ORME — One try (sk. OHA GE)
For simplification, wis supposed =a, and ; ae
Hereby, however, the problem is reduced to a well-known
thermal problem—to the determination of the temperature in
a partition, of which one boundary-plane is kept at the tempe-
rature 0, while the other radiates freely into a medium of a
temperature given as a function of the time. The long-known
solution of this problem shall be considered in what follows,
in its relation to some important phenomena of ocean-currents.
The simplest case for calculation, but practically the most
important, occurs when the velocity w, of the medium in con-
tact is independent of the time, and the motion has become a
stationary one and is consequently likewise independent of the
time. In this case the differential equation becomes
dw
det ="
and is therefore free from the coefficient of friction. Its solu-
tion has the form
w=atbe;
and the constants are determined by the two conditions for
a=0 and z=h; so that w becomes
196 M. K. Zoéppritz on some Hydrodynamic Problems
The velocity in the surface becomes
= ph
Wy = Wy eh
and, when / is very great, changes into w, itself. Accordingly
w can also be written
i he
w= Wo
This simple equation solves the important question how the
velocity is distributed in a very extensive sheet of water of
uniform depth, which is in stationary motion under the influ-
ence of winds acting constantly onits surface. It shows that,
if the bottom stratum is at rest, motions in the direction of the
wind take place in the rest of the strata, with velocities that
increase proportionally to the elevation (h—.) above the bot-
tom, from 0 to the value wy in the surface. The question put
by various authors, mostly geographers, To what depth does
the influence of the trade-wind reach? is therefore to be
answered thus :—So far as the motion of the ocean under that
influence may be regarded as stationary, it extends to the bot-
tom of the sea, and even the deeper strata obey it according
to the measure given by the above law, provided that no other
causes (¢. g. displacement-currents) put these strata into other
motion. In the case of the deeper strata being kept by an
extraneous cause in motion in exactly the opposite direction
to that of the upper strata, there must exist between them a
plane where the velocity is =0. If this be considered as the
lower boundary plane of the upper bed, and its distance from
the upper surface be denoted by /,, for the motion in the upper
mass the following equation holds good :—
The distribution of the velocity in the upper mass is there-
fore the same as if the lower were.a solid mass.
The velocity found for stationary motion is dependent on
the friction-coeflicient & only through wy) (a dependence which
vanishes when / is very great); it will consequently diminish
with the depth according to the same law in a very viscous
liquid as in a very mobile one. In stationary motion the in-
fluence of friction appears solely in the participation of all the
strata in the motion which is communicated from without to
the upper surface only.
Dependence on the coefficient of friction first comes in with
the consideration of periodically variable motions, and gives
(to use a favourite expression with many writers) a measure
in reference to the Theory of Ocean: Currents. 197
for the depth of the penetration of the surface-impulse within:
a fixed time.
The general solution of the differential equation (1), with
the accessory conditions (2), (3), (4), was given by Poisson*.
It can be derived more elegantly according to the method
(probably originated by Dirichlet) which, in Riemann’s Lec-
tures on Partial Differential Equations, p. 140, is applied to
the somewhat simpler problem when there is no "free radiation,
but a given temperature at the surface.
The function w may be composed of two functions u and v,
which satisfy the general differential equation (1) for w,. and
fulfil the following conditions :—
For z=0. For «=h. For ¢=0..
-& +pu=0, (eal bs We),
—S + pv=p¢(t), vO. v=0..
Their sum, «+v=w, obeys then the conditions (2), (3); and
(4).
If m denotes the infinite number of collectively real roots
of the transcendental equation
meosmh+psinmh=0, z. ~ . +» (5)
the demands for u are fulfilled by the following expression
(which is to be summed over all the roots m):—
2mcosmx+tp sin mx
u=2> Pf
h
ea mat oe
é hin? + p(hp +1) {71H cos m& + p sin &)dé.
Those for v are fulfilled by
A(t) —x) 2 2m cos mx + p sin ma:
ph+l “© @ m(hm? + p(hp+1)
>. =m cos mx + p sin m2) ( : Ae
Dap Skim cos me + p sin mx) Ae~ Malev, (7
a ape hn? + p(hp +1) ie us ‘ %)
The first member serves only for representing the function for
«=(Q, and vanishes as often as 0<wXh; for its second term
is nothing more than the development of the first according
to the sine of the argument (h—w) multiplied by the roots of
the transcendental equation (5), and consequently disappears
together with the first term whenever 2>0. For the applica-
tion to internal points this first member can therefore be
* Journal de U Ecole i cea ci cah. xix. p. 69; and Théorie Mathé-
matique de la Chaleur, p. 327.
(6)
198 M. K. Zoppritz on some Hydrodynamic Problems
omitted. Accordingly, for such points it is :—
= sme+tpsinme _ 4” ;
pases 7 SOS TE BP Be ove a) S(&)(mcosmé + psin mE) dé
5 Chm? +p(hp +1) :
mcosme+psin mst (* _ rata)
The first of these two members, which proceeds from the
initial state, vanishes if f(7)=0, consequently if at the time
t=0 the entire mass was at rest; but it vanishes also with any
value of f(x) if ¢ is very great—that is, if the initial state lies
in a very remote past. In both cases the motion in the inte-
rior of the fluid is represented by the last member alone. The
regularities which result from this expression relative to the
motion at different depths and at different times are for this
problem partly the same as those pointed out by Fourier in
the simpler problem when the temperature of the surface is
given; for they agree so far, that they depend on the integral
according to X, which is common to both problems.
If d(¢)=w, is a given quantity independent of the time,
this integral becomes
t
w
(“oyema n= : (L—e-mat)
on me
co
+2apdm.
0
and the part which is independent of the initial state
Why SMCOSME+ PSM MK, aye |
— gion (RET EAD) “ayes (1 —e- 8) a) a
From this it is evident, first, that after an indefinitely long
time the exponential vanishes, and v in the limiting case is ex-
pressed by the sum of which it has been above remarked that
it becomes
- i hE) oe Wa l
= WwW, ph+1 aka | ae ae et ° . ° . ( 0)
as had resulted from the direct consideration of the stationary
state.
If at any time 0 <ta change of the velocity w, affecting the
surface occurs to the amount of +-+y, then is
P(rA)=w, from rA=0 to rA=4,
p(A)=w,+¥ from A=86 to A=t;
consequently the above integral divides into two and has the
value
Wy
Te (1 — e~neat) ze = Cas sod Cee)
The second member, which accordingly is added to v, repre-
in reference to the Theory of Ocean Currents. 199
sents the influence of the change of velocity y aa ea in
_ the interior. If¢ and @ are enormously great, but their dif-
ference little, the second member approximates to the value
yéi—@).
The influence of that alteration is then at every depth propor-
- tional to its duration and amount.
If the velocity of the contiguous medium is, at the surface,
a periodic function of the time—for example,
$(t) = cos (at—b),—
then, if i—XA=p be introduced as a new variable, becomes
t ‘t
\ e—matt—A) cos (aN—b)dd = cos (at) { e~™8 cos ap dp
0 ;
t
+ sin (at—t){ e~™a¢ sin ap dp.
0
After an indefinitely long time these two integrals become
constant with respect to the time, and consequently the velo-
city at every depth becomes a periodic function of the time,
of the same period — as that of the contiguous medium,
but of changed amplitude, dependent on x, and with shifted
period of occurrence of maximaand minima. If $(¢) is a pe-
riodic function of general character, it can be represented under
the form
f(t) =w, + w’; cos (at—b,) + w’, cos (2at—bz) +...
Putting this value in the integral, we obtain for w an ex-
pression, the first member of which changes, for t= , into
upon which follows a series of members with cos (nat—6) and
sin (nat—b), of the same sort as in the previous more simple
case for n=1.
If we wish to calculate the mean velocity during a period
T="
: 7, all terms affected with sine and cosine vanish from the
ee and there remains
a p(h—«)
a wdt = wy Fe
as the mean velocity, consequently the same as with the sta-
tionary motion.
200. M. K. Zoéppritz on some Hydrodynamic Problems
In the problem of the determination of the temperature in
the interior of a mass bounded only by one plane, and unli-
mited in the positive X direction, when the temperature of the
plane is given, some other simple laws respecting the increase
of temperature with the depth can be deduced, which will be
eommunicated infra. Such laws cannot be obtained for the
present problem. If equations (5) to (8) be applied to a stra-
tum of infinite thickness, putting therefore h=o , for the so-
lution of the transcendental equation
mh cos mh + ph sin mh=¢ cos $ + ph sin $=0
it isonly necessary that
sin d= sin mh=0,
and therefore
mh=nt7,
where x denotes a whole number: x then becomes a quantity
that increases continuously from 0 to ©; for the difference
between two successive roots m becomes
7
(Ns
h
Accordingly we obtain from equation (8),
bye 2 Cont 2 COS M2 +p Sin mx paper 1 :
wontons ¢ RENT ne aml AEN (meosme-+p sin m 3)dé
0
Qap ( * m(m cos ma +p sin ma’) : wtaeeny
+ P| a am) $0} dn. (11)
Of this, only the second part, v, independent of the initial
state, shall be further considered, and, indeed, for the case that
$(A)=w, is constant. By inserting after » the value already
used in equation (9) of the integral then resulting, and noticing
that the sum (independent of ¢) takes the value of equation
(10) and therefore for h=oo the value w,, we get
2pw, (°” cos max 2p7u, (7 sin mex
v=W4— fe 5 ee dm — iat: ——5— 5 eatin.
a \ me +p a J, mm +p)
These two definite integrals can be reduced to Kramp’s inte-
gral. The reduction of the first is carried out in Riemann’s
Vorlesungen tiber partielle Differentialgleichungen, pp. 166-169.
If for abbreviation we put
pv at=F, 5 aE =,
in reference to the Theory of Ocean Currenis. 201
then is
“cos mz a 2
2p a: emai = / me? er Cqudaken e~*dz}.
0 Me +p T+é T—é
The second integral is obtained from this by integrating ac-
cording to « from 0 to z. The resulting double integrals are
- reduced by partial integration to single ones ; and we get
2 2 e sinme _ —at
P , mm p)o om
eo fe os
=/ me” { errs ( e~*dz—e-* ( e~*dz+ 24 dge-?-#},
|
wtté et—z
With this becomes
201 (2 i — 2 |
w=WUy—- ee tper Ca dz+e-P o
7 0
Sia (12)
ee
eso 2vVat
To obtain from this the more general expression for w;= (A),
we have only to take the second part with the plus sign, insert
(t—X) in the place of ¢, multiply by $(A)dA, and integrate
from 0 to ¢.
The velocity in the surface-stratum is obtained from equa-
tion (12) by putting therein z=0 :—
y= wr} 1— > aed Lp i. 3
pv at
The second part of this expression approximates, for in-
creasing time, to the reciprocal of pV vat, and therewith to 0
Putting this in words, it means :—The velocity of the surface-
stratum continually approaches nearer to that of the conti-
guous medium.
This necessary inference of the theory, however, draws a
limit to its applicability to the theory of ocean-currents, Ex-
perience teaches that nowhere do the surface-waters of the sea
take the mean velocity of the masses of air blowing over them,
because, when the wind is rather high, periodic motions of
those strata (waves) arise, on the sides of which the wind acts
in quite another manner, namely by pressure on the side-
surfaces, so that, with still more augmented difference of ve-
locity between air and water, breaches of connexion take place,
discontinuous, turbulent movements. Therefore the surface-
condition above laid down can only for very inconsiderable
velocities correspond to the reality ; for greater velocities the
water-surface as a whole cannot fulfil it. In this case it is
202M. K. Zoppritz on some Hydrodynamic Problems
better to introduce into the problem the progressive motion of
the superficial stratum of the ocean (which, indeed, can every-
where be easily determined by observation) as a given quantity,
as a known function of the time (eventually as a constant).
Thereby a much simpler problem is obtained, which can be
mathematically deduced from the foregoing, if in this we put.
p=. The surface-condition then reads, for <=0, w=(¢);
and the transcendental equation is transformed into sin mh = Oz
the roots of which are
gh aa
Therewith the general expression of equation (8) for p=
changes into the following :—
% Cc wT 2 cy h
w= 7 Se CG) sin ( 48) sin "Ea
by L 0
Be é nn?
- Zar (—1)rtn a = pore Gar, (13)
1 : i)
For the stationary state we get the same formula as before ;
but now w)=}.
In reference to the periodic motion in different depths the
same holds which was indicated above for the more general
expression. But if the following formula be applied to water
of infinite depth, therefore to h=«, we still get the laws
already mentioned. If, namely, in the expression (11) we put
p=, the second part, above denoted by v, becomes
a t
air We sinmadm\ h(rAje~™#e-Ndn.,
aE. 0 0
The integral according to m can be completed ; for it is
oo d (o_o)
{ m sin maze!’ dm = — ai cos mxe7Y™dm.
0 0
x
But the latter integral is well known. It is, namely,
2 1 Py pacts
cos mxze7!’" dm = 5 Ve rag Sy:
0 fy
Accordingly
msin mxe7’"dm= © Vr e 4y,
0 Are
Consequently
Sif APQVEr BW 2 (9 (inl e ) :
= —_—— fF eee >F_= tt —* det tt
; a=! (t—r)2 i / 1 ia faz? )° te
in reference to the Theory of Ocean Currents. 203
Now, if ¢(¢) is constantly =wo, it is at once evident that v
becomes the same for pairs of values x, ¢ and 2’, t’, for which
the lower limit of the integral is the same; therefore
£ a’
ee a
i. €. the same velocity occurs at different depths which are to
one another as the square roots of the times.
The formula that is valid for a constant superficial velocity
Wo, namely
x
2w) (* Q (2vat
v= Taf eede= wo{ 1 = Ja) edz}
2 Vat
ean be made use of to calculate, with the help of the Tables
that exist for the value of Kramp’s integral, the time that
elapses before a point in a given depth reaches a certain velo-
city. The velocity w, of the surface first reaches a point after
an infinite time. If we take a point at the depth #=100
metres, and inquire after what time it will possess the half-
velocity of the surface (v=3$w)), we have to solve the trans-
cendental equation
20 #
1— —=J e-*dz
z V7). ?
in which, for @, its value (see p. 195) is put. Herein c=100
metres, and instead of k and w their values for the liquid in
question, are to be inserted. Since, according to Encke’s
Tables in the Berliner astronomischen Jahrbuch for 1834, the
integral value 0°5027 corresponds to the upper limit 0°48, the
time sought, ¢, is very approximately determined by the equa-
tion
Rae, Ee =(0°48.
QV t k
The coefficient of friction for water and very dilute salt-
solutions is, at ordinary temperature, according to O. H. Meyer*,
about 0013-0015. Taking 0-0144 and still putting w=1,
from which the density of sea-water differs only in the third
place of decimals, we can put for application to the ocean
/t=a4
ko - O12
* Pogg. Ann. vol. cxiil. p. 400.
204 M. K. Zoppritz on some Hydrodynamic Problems
k contains as unit the square centimetre ; therefore « must also
be expressed in centimetres, and be put =10000. We thus get
nif 5000
0°48 . 0°12
which gives the value of ¢ in seconds, and we find
t= 7,537,000,000 seconds = 239 years ;
so that, if the particles of the surface of an ocean of very great
(properly infinite) depth, at rest, begins at a point of time
t=0 to move forward with a constant velocity, half the velo-
city of the surface will first prevail at 100 metres depth after
239 years.
If we inquire, After how long a time has a tenth part of the
surface-velocity penetrated to 100 metres depth? we find it is
41 years. According to the principle expressed in equation.
(15), at 10 metres depth the same velocities will prevail at the
end of 2°39 years and 0-41 year respectively.
These numbers are very appropriate for giving an idea of
the slowness with which changes of velocity are propagated
downward ; for what has just been calculated for the propa-
gation of a commencing surface-movement in a liquid at rest
is just as valid for every change of motion in a moving liquid,
since the velocity already present and that which has newly
entered are algebraically added together. A stationary cur-
rent diminishing in velocity linearly with the depth will on
this account be only extremely little altered by passing changes
of velocity affecting its surface (as, for example, by head-
winds or storms), except in the strata nearest to the surface.
There will much rather prevail at every deeper-situated point
a mean velocity but very slightly variable with the time, and
determined by the mean velocity at the surface. The latter
velocity has the direction of the prevailing winds, and falls and
rises with them according to a law which cannot be more pre-
cisely determined. This fact of the limitation of considerable
action of transitory causes to the strata in the vicinity of the
surface is an additional justification of the assumption, made
to facilitate the calculation, that the ocean is of infinite depth.
If the velocity of the surface is a periodic function of the
time, as are all winds dependent on the seasons of the year
and hours of the day, it must be possible to express them by
a finite series of the form
p(t) = po + pi cos (= —m) + Pz COS ce —3) Pas oe
As has been already shown in the preceding more compli-
in reference to the Theory of Ocean Currents. 205
cated problem, v must then be representable by a series of
cosines and sines of the same period. By making use of for-
mula (14) we obtain the following series *:—
aa mit mar
V=P y+ ZpPme 2zk COS (hae ae)
- from which we see immediately that the velocity at every
depth has the same period 2g, but that the amplitudes,
Co. doen? wae
diminish as the depth increases. In sea-water
ih
yZ=uis U7.
If x be expressed in centimetres and 2q in seconds, for
z=100 metres and the period of one year (consequently for
m=1, 2g=1 year) the exponent of e becomes about —26;
therefore the amplitude of this oscillation already diminishes
to a vanishing fraction, with e=10 metres to e~?6= 138°
If the depths diminish in an arithmetical series, the ampli-
tudes of oscillation diminish in a geometrical series, so that in
four depths 21, #2, v3, 2, so situated that #,—x;=2,—w, the
amplitudes 6, 0, 03, 0, are in the ratio
6, : G20. ° 6.
A maximum and its succeeding minimum of an oscillation
of the duration 29 are ever simultaneous in depths separated
by a distance
my — a= a / 20,
pe
which for 2g=1 year gives
&g— X#1=11°9 metres.
in order to get a numerical representation of the time re-
quired by a surface-velocity wy commencing at time t=0, and
remaining constant, to introduce at the bottom of a previously
still ocean of the finite depth h the state of velocity opposite
a) the above formula (13)
must be employed, in which f(€) must be put =0 and $(r) =w.
We then get
c) é ar \2k
w= 210) <> (—1)"'n sin “| aula oe, a.
phe ; h Jo
to the stationary (when w=w
* See the expansion in Riemann’s Vorlesungen, p. 137.
206 M. K. Zoppritz on some Hydrodynamic Problems
or, after carrying out the integral,
4 QD © __1)\nr-1 nr \2k i
wa { o—2 3 ee mt sin ee A
hk Se n h
Since
* = 01491,
m
for a mean sea-depth of 4000 metres, to be expressed in cen-
tims., the exponent of e becomes
0:1421 ,
a See
400000?
extremely little as long as ¢ is not enormously great, the series
consequently very feebly convergent. If t=10000 years, four
more terms must always be calculated in order to obtain an
approximation to within one thousandth of accuracy. If the
amount of the velocity w,, in the half depth of the ocean, con-
sequently for «= . be required, all terms in the series vanish
which contain exact multiples, whilethe remaining sines assume
the value +1. We then get, for t=10,000 years, exactly,
within 0°001,
n=} t— 2 (em —4¢e7*5) ‘ =0:037 Wo.
Since after an infinite time the velocity 0°5w) must prevail
at this place, it is evident how inconsiderable a portion of the
definitive velocity has penetrated to such a depth only after
10,000 years. On the other hand, for ¢=100,000 years wy,
becomes
=} 2 evn} EAGhae
Therefore the velocity has, after 100,000 years, already arrived
very near to the definitive value; after 200,000 years it differs
from it only 0-002.
From the foregoing theoretical considerations two results
especially are obtained, which more or less contradict views
hitherto accepted :—first, that the stationary motion proceed-
ing from an invariable surface-velocity makes itself perceptible
with linearly diminishing velocity right to the bottom in an
unlimited sheet of water, while the view has frequently been
expressed that the influence of such surface-currents (as, for
instance, the impulse generated in the equatorial regions of
the ocean by the trade-wind) extends downward to only very
limited depths. Secondly, we have found that all periodic or
in reference to the Theory of Ocean Currents. 207
aperiodic variable changes in the forces acting upon the
surface are propagated into the depths with extreme slow-
ness, the periodic with very rapidly diminishing amplitude.
From the combination of these two propositions it follows that
the motion of the main body of a sheet of water subject to
periodically variable surface-forces is determined by the mean
_ velocity of the surface, and that the periodic changes are per-
ceptibly only in a proportionally very thin superficial stratum.
It is hence obvious that hitherto the influence of the fric-
tion has in one direction been underrated, and overrated in
another :—underrated, inasmuch as it has been believed that
that influence could not be regarded as penetrating to such
depths; overrated, inasmuch as it has been customary to attri-
bute to friction much too considerable an influence in regard
to the propagation of the motions of variable currents. Its
action has been still more overrated in another direction, of
which the following investigation will give some explanation.
Up to the present time the liquid layer was presupposed un-
limited in two dimensions ; but the case of laterally bounded
currents is also capable of treatment*, and therewith the influ-
ence of the sides (the shores) upon the flow can be recognized.
Let the liquid have again the depth h, but be bounded by
two parallel perpendicular sides with the distance 26 between
them, which are wetted by the liquid, and at which, therefore,
the velocity is =0. Ifthe X-axis be situated as before, but
the axis of Y placed perpendicular to the two sides, and the
point of origin in the centre of the upper-surface line of the
cross section, then the velocity w parallel to the sides is given
by the differential equation
de _& (dhe , Oe)
dt w\da? * Oy?
and the conditions :—
For «=0, 0" +pw=ph(i,y); forzt=h, w=0;
for y=), w=0; for y=—b, w=0.
For the case of stationary motion (which shall exclusively
be further pursued here), we have
moreover the velocity of the contiguous medium must be in-
* The corresponding thermal problem Lamé has taught us to handle in
the briefest and most elegant form in his Legons sur la Théorte Analytique
de la Chaleur, p. 327.
208M. K. Zippritz on some Hydrodynamic Problems
dependent of ¢, and therefore only =(y). These require-
ments are satisfied by the function
12 Gin (Qn+ lj =
wo= FT
0 Sin(2n +1) Cae
“a cos (2n+ 1) 57 St
Cof(2n+ Ls
iF (A) cos (2n+ Lr dh,
in which, for brevity, the hyperbolic sine and cosine are repre-
sinted by Gin and Gof; so that
Gine=4(e"—e-*), Cofa=hk(e*+e-*).
If the velocity of the air be taken as independent of y, and
consequently $(y) be put =wy, ei becomes
(=1 Gin (2n + Lyn" © cos (Qn+ l)w
m+" Sin(2n + 1) eo Baga snee
If herein we put the breadth oe O, ie resulting ee
will be the same as that for the velocity of the stationary mo-
tion in an entirely unlimited sheet. The fraction under the
symbol of summaticn takes for 2b=00 the form . By dif-
ferentiating both numerator and denominator according to = 3h
we get, after inserting 2b=0,
4w, pih—2) 5(—1)"
= ae EEL 2 aa cos (2n + 1)m 5
But this sum is, for all positive values of y aan are less
than b (the value y=6 itself is excluded), equal to t ; so that
in reality w receives the above-found value (10).
The motion in the surface, consequently for «=0, if the
assumption be retained that ¢(y)=, is represented by
_ Aw © (1) Cos (2n+1)r se
Ts neT 7 = OOF Got Qn+ In,
which expression, for p= aaa into wy, itself.
If this series were capable of summation, although only for
y=0, it might be possible by suitable experiments to ascer-
in reference to the Theory of Ocean Currents. 209
tain, at least approximately, the value of p with low velocities.
For if we imagine a. very long canal of given rectangular cross
section (for the sake of simplicity let it be taken as square,
consequently 2b=h) set in stationary motion by a gentle wind
with the velocity w, blowing parallel to its axis, the velocity
_in the middle line of its surface (y=0) will be
pals (7b)
=
ie (Qn+1){ 1+ "te “EM Got Qn+ tr }
Remarking that, for n=0, Cot 7 is already =1:0037, and for
higher values of n the value of Cot (2n+1)z continually ap-
proaches nearer to unity, we find as a very close approxima-
tion :—
=} ay ed Saar sail 1 \
— w Lphtmw aph+3mr Sphtba OSS
If next we consider only two terms of this series, we get for
ph the quadratic equation
pl? (8w,—d37wy) + ph. 47(8w, — 37rwy) — 97? wo) = 0.
according to which
h =2r} ie CO ei : ;
P es 4(8w— dw)
Were, for example, w= 4m, wo) =2m, consequently w, : wo =2,
we should obtain ph=0°8877, or
2°07
al al
and the first neglected term in the above series would be
Woo =
Woo
= a cs while the first term is = 188-5 = =e The error would
therefore amount to about 3 of the value, and would be re-
duced to about =), by taking a further term into account.
It appears, however, that p between water and air is very
great, and on that account the ratio w;=2w, possible only
when the canal is very narrow, while with a greater width wo,
approaches much nearer in value to w,;. Many more terms of
the above series would then have to be taken into account.
The greater the value of p the nearer does the value of wy come
to that of w,; consequently the curve which represents w, as
a function of the distance y from the middle approximates to
a straight line parallel to the axis of Y. The same can he said
of the velocity in any horizontal line at the depth 2. It is
therefore evident that, in case p is very great, the banks exert
a very inconsiderable influence on the distribution of the ve-
locity.
Phil. Mag. 8. 5. Vol. 6. No. 36. Sept. 1878. i?
210 On the Theory of Ocean Currents.
The stationary state here also is independent of the friction-
coefficient.
It follows, moreover, from these considerations, that, in a
liquid layer of constant depth, two currents parallel to the
same straight line, but flowing in opposite directions, can well
be adjacent without disturbing one another. Their dividing
surface is then a vertical plane parallel to their directions, in
which the velocity is 0, and which behaves exactly like a solid
bank. As long as the forces brought forth by each of the cur-
rents continue unchanged, the motions of both remain sta-
tionary, and neither current disturbs the other.
The complete analogy shown by the distribution of velocity
in a mass of liquid possessing friction, with the heat-distribu-
tion in a solid body, gives a hint to pursue it also in another
direction. It has already been shown above, how extraordi-
narily slowly the velocity present at the surface is propagated
into the depths, provided here the velocity 0 has previously
prevailed. From this it can be conversely inferred that the
after-effect of the initial state vanishes with the same slowness.
This is represented by the hitherto neglected first term of the
formule (8), (11), and (13). If in them we put for f(&) a
constant or a linear function of &, the integral according to
can be at once carried out, and the entire term dependent on
the initial state becomes in all three formule a sum of the
same form as that which was obtained for the term dependent
on $(X) when ¢(A) was put = a constant. Since the expo-
nents of e are the same in both cases, the above calculated
numbers are valid for the vanishing of the initial state.
If, for example, about 10,000 years ago (therefore at a
period of which we have no historic information), by any
cosmic event the equilibrium of the sea was so considerably
disturbed that strong currents resulted therefrom, the influence
of the then existing motions would certainly not yet have
totally disappeared from the present condition of the currents
—indeed it would at the present time predominantly deter-
mine the motion of the ocean in its greater depths—if the
earth were entirely covered with an ocean of the uniform depth
of 4000 metres. The interruption of the continuity of the
ocean by continents and island-masses of irregular shape will
contribute to soften down considerably that after-effect of pre-
vious states of motion, not so much by the increased friction
on the sea-bed as by the reflex and displacement currents
everywhere breaking in. Nevertheless, after the above nume-
rical proof of the slow spread of the influence of locally acting
changes of motion penetrating the mass, a caution is necessary
not to put aside the difficulty of more accurate calculation, as is
Motions in Dilute Acids on Amalgam Surfaces. 211
usual, by saying “ All these motions are rapidly consumed by
friction.”
It would be possible to determine by observations whether
any after-effects of former motions are still present in the
ocean. For this purpose it would only be necessary to insti-
tute comparative observations of the currents at the most va-
‘rious depths in the central portions of the great equatorial
currents and the region of calms. Yet we could not hope to
demonstrate small remnants of former motions with a certainty
like that with which this is possible in relation to the after-
effect of the former higher temperature of the earth by mea-
surements of subterranean temperatures.
Further, those above-calculated numbers give a hint how
remote, at the least, we have to imagine the initial state to
have been from the present time, or for how long a period, at
the least, we must imagine that the trade-winds have blown
in their present extent and strength, to justify the assumption
that the present state of motion of the equatorial currents is
approximately stationary. For this about 100,000 years are
required if we take for a basis a mean sea-depth of 4000 metres
and take no account of the damping influence of the conti-
nents and islands, which must somewhat lessen that number.
That every initial state, however, finally vanishes, and, from
the simple law of distribution laid down, gives place to a sta-
tionary one, is evident from the form of the series for w, and
has, besides, been shown generally for all temperature-problems
by K. von der Miihll*.
Giessen, January 5, 1878.
XXVIT. Motions produced by Dilute Acids on some Amalgam
Surfaces. By RoBERT SABINeET.
N the December (1876) Supplementary Number of the
Philosophical Magazine I stated an opinion, supported
by experimental evidence, that the motions which Erman,
Draper, and others have observed in certain electrolytic liquids
when in contact with mercury surfaces, and in the circuit of
an electric current, are due to displacements caused by oxida-
tion and deoxidation at different points.
In following up the subject since, I have made further
experiments, and have noticed some phenomena which are in-
teresting (although perhaps of no practical value), to which, I
believe, attention has not hitherto been directed.
* Math. Annalen, ii. p. 648.
+ Communicated by the Author.
212 Mr. R. Sabine on Motions produced by
Exp. 1. A rather rich amalgam of lead was filtered through
a paper funnel into a clean shallow dish, so as to produce as
bright a surface as the nature of the amalgam would allow.
Then a drop of very dilute nitric acid was carefully placed
upon it by means of a pipette. The acid-drop did not lie still
(as it would do upon a surface of pure mercury), but set itself
at once into a jerky motion. It gradually contracted its area
and then suddenly spread out again, then gradually contracted
again, and again suddenly spread, the pulsations being irre-
gular. That portion of the amalgam surface which was ex-
posed by the contraction of the drop was very bright and
smooth, and appeared to be free from floating particles of
foreign metal which roughened the surface at other points.
In a repetition of the experiment with weaker acid, the drop
was observed to march bodily over the amalgam surface, going
from one side to the other, and sometimes returning.
Dilute sulphuric, hydrochloric, oxalic, and acetic acids be-
haved similarly to nitric acid, but in somewhat different
degrees.
Amalgams of tin, antimony, zinc, and copper behaved simi-
larly to lead amalgam, but also in different degrees.
It was found that, in order to produce these motions, the
acid must be sufficiently diluted to avoid the perceptible for-
mation of gas. The extent to which the dilution might be
carried appeared to depend upon the richness and nature of
the amalgam. Weak motions were observed with the fol-
lowing :—
Amalgam of 1 oz. water to
COPpely sess sseceeeesnee 1 drop nitric acid.
ZVNG Ae ain satus sees ZiGEOPS | es
ARUN OD Ft .enelne ses Owe ”
Dine 2a se cee eeaeeeas OS. e
Liead gris cesses epee nee LDF a.5 3
Lixp. 2. Instead of the foregoing metals, which in very di-
lute nitric acid appear to be all positive to mercury, amalgams
of platinum, gold, and silver were next tried, these metals being
all negative to mercury. On placing the acid-drop on the
clean newly filtered surface, no motion whatever was observed.
When a trace of positive metal, however, was added, slight
motions were observed.
Eup. 3. A dish containing lead amalgam having a drop of
dilute nitric acid on its surface was placed under a small glass
receiver. The motions of the acid-drop were observed to be
irregular, the edge darting out first in one direction and then
in another. The air in the receiver was changed by the steady
Dilute Acids on some Amalgam Surfaces. 213
injection of oxygen ; and it was observed that the motions im-
mediately became more rapid and, at the same time, more
regular all round. When the supply of oxygen was stopped
and atmospheric air substituted, the motions resumed their
original irregularity.
Hap. 4. The foregoing experiment was repeated by allow-
ing a drop of acid water on the amalgam surface to fall into
motion underneath the receiver, and then changing the atmo-
sphere to one of hydrogen. ‘The motions immediately ceased.
On letting in the air again, the motions were resumed. In
carbonic acid, nitrogen, and coal-gas the motions were in-
stantly arrested ; and by covering the amalgam surface under
the receiver alternately with one of these gases and with either
atmospheric air or oxygen, the motions could be stopped and
reestablished at pleasure.
Hep. 5. On a surface of lead amalgam a drop of dilute nitric
acid was placed, and the tip of a lead wire suspended in the
drop. Between the lead wire and the amalgam was inserted
a delicate reflecting galvanometer. By means of an adjustable
shunt across the galvanometer, the first current was reduced
until the index fell nearly to zero. Then the shunt resistance
was increased so as to obtain the greatest sensitiveness, whilst
retaining the light point upon the scale. In this position,
whilst Mr. McHniry observed the motions of the acid-drop, I
observed the motions of the galvanometer, each givinga signal.
In this way it was found that each spreading of the drop was
accompanied by a slight excursion of the light-point. The
direction of the permanent deflection showed that the amalgam
surface was positive to the lead wire. The direction of the
excursions indicated a slight diminution of this permanent
current, or that at the moment of expansion of the acid-
drop, the amalgam surface became slightly less electropositive.
In the intervals between the expansions, the tendency was for
the needle to move in the other direction. Lead is positive to
mercury in dilute nitric acid; therefore this reduced electro-
positiveness may indicate an increased proportion of mercury
on the covered surface at the instant of spreading.
The conclusion which I draw from these experiments is,
that the motions in question are due to a portion of the surface
of the amalgam becoming alternately oxidized by the air out-
side the acid-drop, and deoxidized by electrolysis in the inte-
rior of the drop. ‘The reciprocal play of these two actions is,
I venture to suggest, as follows:— When the acid-drop is placed
upon the surface of the amalgam of a metal specifically lighter
than mercury, it finds the surface to consist of mercury in
which are floating innumerable particles of the foreign metal,
214 Mr. R. Sabine on Motions produced by
The latter, in rich amalgams, are distinctly visible to the eye,
producing a somewhat roughened surface. Hlectric currents
are generated between the mercury and the particles of foreign
metal, through the acid. When the foreign metal is positive
to mercury, the latter (which by contact with the air is always
more or less oxidized) becomes deoxidized underneath the drop
of dilute acid and therefore cleaned. The drop has less afli-
nity for the clean than it had for the oxidized surface. Its
adhesion is therefore diminished ; and it draws itself together
in consequence, leaving a surrounding ring of deoxidized
mercury, in which the eye can detect few or no floating par-
ticles of foreign metal ruffing the smoothness of the surface.
Oxidation of this exposed clean portion of mercury, however,
gradually sets in; and when the mercury up to the boundary
line of the drop is sufficiently reoxidized, the acid reasserts its
affinity for the oxide, and the drop is enabled to spread out
again to its original dimensions. Interior deoxidation then goes
on again by means of the small surface couples ; and the play
of alternate contraction by reduced adhesion, due to deoxida-
tion, and spreading by affinity for the oxide formed by the
outer atmosphere, is kept up so long as positive metal and acid
last.
The contraction due to deoxidation by the current would
necessarily be slower than the spreading due to chemical affi-
nity between the acid and oxidized surface:
In explanation of the acid-drop travelling bodily over the
amaleam surface, I would suggest that if, from any reason, the
oxidation were more energetic at one side of the drop than at
the other, it must lose equilibrium and go on travelling in the
direction of the more energetic action, because the mercury
surface on that side of the drop would be ready oxidized, whilst
on the opposite it would be continually left deoxidized.
Supposing that the foregoing explanation is the right one,
there are two points well worthy of noting. First, it would
follow that the electropositive metal in the amalgam is to some
extent electrically independent of the mercury—asserts, in
fact, a certain electrical integrity. Secondly, it would be ne-
cessary that the electromotive force between the for eign metal
and mercury (say lead and mercury) when in very dilute acid
must be greater, or at least have a greater decomposing action,
when the one metal-is in a state of minute subdivision and its
particles in intimate electric contact with the other metal, than
we should be led to expect from the behaviour of the metals
in separate masses.
An analogy appears to exist between this behaviour and the
augmentation of chemical affinity of the couples constructed
Dilute Acids on some Amalgam Surfaces. 215
by Dr. Gladstone and Mr. Tribe by the deposition of a nega-
' tive upon a positive metal, described by them at the British-
Association Meeting at Bristol in 1875.
Connected with the same subject, but susceptible probably
of a different explanation, is the following experiment :-—
On a clean dry surface of rich lead amalgam a drop of strong
nitric acid is placed. The acid spreads itself out, the amalgam
surface underneath it, in the course of a second or two, assu-
ming a dull leaden-grey colour. Suddenly, with a flash, this
colour changes to a whitish tint, which gradually deepens
again in colour until, after another second or two, another
flash restores the whitish tint. This alternation of colour is
sometimes repeated steadily many times in succession during
several minutes, until an energetic action at length sets in and
gas is evolved.
The change from grey to white is always abrupt; the change
from white to grey always gradual.
Instead of employing a vessel with lead amalgam, the flash-
ing was equally well observed with the amalgamated surface
of a piece of common sheet-lead. A galvanometer placed in
the circuit showed that at the instant of the flash the covered
surface became less electropositive.
A quantity of lead amalgam placed in a shallow dish and
completely covered with strong nitric acid showed changes of
colour as before. At each flash it was observed that the area
of the amalgam was suddenly contracted ; and it reexpanded
during the change of colour from white to grey.
A drop of strong nitric acid placed upon a bright surface of
lead attacks it gradually, and produces a dull grey colour
which is slightly opalescent.
A drop of strong nitric acid placed upon a bright surface of
mercury attacks it energetically, producing white crystals and
evolving gas plentifully.
The behaviour of the separate materials suggests an expla-
nation of what may happen in the case of the amalgam, viz.
that while the surface is turning to a grey colour, the nitric
acid is attacking lead; and when it suddenly flashes white, the
acid is attacking mercury. The strange part of the pheno-
menon is the apparent passivity of the mercury for some time
after placing the acid upon the amalgam. ‘The explanation
which appears to me to be the most probable is, that the first
contact of the acid with the amalgam surface results in the
production of a thin stratum of lead-salt, which floods the mer-
cury surface and tends to keep the nitric acid for a time sepa-
rated from it. The acid in course of a second or so, however,
diffusing through this stratum, commences an attack upon the
216 Mr. J. Ennis on the Origin of the Power
mereury, which is stopped by the stratum of mercury-salt
which is formed, and which enables the lead particles to reas-
sert their electropositiveness and. be further operated upon.
Then a fresh diffusion ensues and the play is repeated.
XXVIII. The Origin of the Power which causes the Stellar
Radiations. By Jacos Eynts*.
“ba is important for scientific men to acquire the habit of
regarding all matter as having been diffused equally, or
nearly equally, through all space. This is the initial point in
our history of creation, the earliest period which we know.
From this universal diffusion we can trace, by the operation
of well-known forces, the origin of the stars. We can under-
stand how the vast sidereal systems, stellar nebule, were
formed, and how they must remain stationary in space. We
can understand the origin of solar and planetary systems,
and how these latter systems are all moving through space
with inconceivable velocities. We can learn (as I proved in
my paper in the ‘ Philosophical Magazine’ for April 1877)
that gravity is the force which imparted their velocities
to all the stars and to all stellar systems. And now I
am to prove that in this same universal diffusion of all
matter we can behold the reservoir, the illimitable reservoir,
of that force which radiates the undulations of heat, light,
and actinism from all the stars. I will point out also
that, in the condensation from that primitive diffusion,
we can behold the origin of those modifications of matter
which we call the simple elements. In that condensation also
we can see the first manifestations of several of the physical
forces, such as electricity, magnetism, cohesion, heat, and light.
The three primitive forces, of whose origin we know nothing,
are repulsion, chemical force, and gravity.
The diffusion of matter in a gaseous form, by the ordinary
repulsive force, is a store of heat; and this store is greater or
smaller in proportion to the amount of diffusion. It is analo-
gous to the removal of a pound weight from the surface of the
earth: the further it is removed the greater will be the amount
of heat produced by its fall. It has been found that when our
atmospheric gases expand from one volume to two, their tem-
perature is lowered, and just 144° I’. of heat are absorbed and
rendered latent. very addition of the original volume by
expansion renders latent an additional 144° of heat ; that is,
so much heat loses its character and form of heat, and it reap-
pears as repulsion or diffusion. When compressed again, that
* Communicated-by the Author.
which causes the Stellar Radiations. WNT
diffusion is annihilated, and the same original amount of heat
is reproduced. By a thermometer in the receiver of an air-
pump the loss of heat by expansion is seen clearly enough ;
but in the sinking of an oil-well recently in North-western
Pennsylvania it was manifest on a magnificent scale. Instead
of striking a reservoir of oil, the auger entered an accumula-
tion of gas (a hydrocarbon); and as this gas expanded on
issuing with amazing force from the orifice of the well, its own
heat was converted into repulsion, and it absorbed the heat
from the surrounding atmosphere and from the ground. The
watery vapour in the gas and in the air fell down as snow, and
the ground all around was frozen: it was like the freezing of
carbonic acid by its own expansion.
From the well-ascertained fact that a gaseous diffusion ab-
sorbs 144° F. of heat by every increase of its original volume,
which heat is converted into the form of repulsion, and is called
latent heat, we are enabled to calculate the amount of latent
heat in all the higher strata of our atmosphere. A volume of
air rising three and a half miles (more accurately 3°43 miles)
becomes two volumes, and contains 144° of latent heat; on
rising double that distance (6°86 miles) it becomes 4 volumes ;
therefore 3 new. volumes are added, and it contains 432° of
latent heat ; at 10°29 miles it becomes 8 volumes, and 7 new
volumes are added, and therefore it contains 1008° of latent
heat ; and so on upward, according to the following Table (p.
218), which (with other columns here omitted) was constructed
by Mr. Benjamin V. Marsh,merchantand, like Benjamin Frank-
lin, an amateur of science in Philadelphia. It first appeared
in the ‘ American Journal of Science,’ July 1853. His paper
on many accounts is valuable; and the subject is further car-
ried out in my own paper on Meteors in the Proceedings of
the American Association for the Advancement of Science for
1871.
The appearance of meteors is a proof that our atmosphere
extends upwards more than 200 miles, and that its loftier
regions are wonderfully charged with latent heat. In my
paper on Meteors I gave two instances, one in Europe and the
other in America, where meteors travelled more than a thou-
sand miles through the air from 40 to 100 miles high, and
continued vividly bright through the whole distance until they
passed from view. Last year another passed in the same in-
eandescent manner a thousand continuous miles over the
United States. I also gave other instances of vertical descents,
when invariably the light of the meteors went out before reach-
ing the ground. They prove that in these cases the very bright
light comes, not from the meteor itself, but from the air in its
218 Mr. J. Ennis on the Origin of the Power
front, which is compressed and made to give out its abundant
latent heat. Had the meteors themselves been so vividly in-
candescent, their brightness would have continued another
twinkling of an eye before they struck the earth. Had friction
been the cause of the heat, their light would have become
brighter in the dense lower atmosphere, where inyariably their
light goes out, albeit gravity hastens their velocities. I pointed
out in that paper the fallacies in the reasonings of high autho-
rities who thought they had proved that meteoric light is due
to friction.
Number of grains
of air in cylinder
| 1 mile long and
Number of volumes 1 foot in diame-
| Height, corresponding to Number of degrees of ter. Weight at
in miles, 1 volume at the surface latent heat. surface of the
of the earth. earth = 2342847
grains, = 334°69
pounds ayoirdu-
pais.
3°43 2 144 1171424
6°86 4 432 585712
10°29 8 1008 292856
| 1e72 16 2160 146428
Was 32 4464 73214
20°58 64 9072 36607
24°01 128 18288 18303
27°44 256 306720 9152
30°87 512 73584 |. 4576
34°30 1024 147312 2288
YET! 2048 294768 1144
41°16 4096 589680 572
44°59 8192 1179504 286
48°02 16384 2359152 143
51:45 32768 4718448 72
54:88 65536 9437040 36
58°31 131072 18874224 18
61-74 262144 37748592 9
65:17 ‘s 524288 75497328 4
68°60 1048576 150994800 2
102:90 1073741824 154618822512 sts
137-20 1099511627776 158329674399600 Sc1SEE
17150 | 1125899906842624 | _162129586585337712 | ssestascs
205°80 /1152921504606846976 |166020696663385964400 |saa7svacase5
The point of most intense interest in the Table of Marsh
is the wonderfully large amount of latent heat in an almost
infinitesimally small amount of the air. Look at the lower
line in the Table ; how immense is the physical force ! and how
minute is the amount of matter! and yet the two are physi-
cally coupled. Here is a wonder which leads to the very
gravest consequences. Itis an image of the sun. The amount
of matter in that great orb is infinitesimally small when com-
which causes the Stellar Radiations. 219
pared with his physical foree—that force which has sent out
the solar radiations many millions of millions of years. Now
mark the origin of that solar force. When our sun in its ne-
bulous period was expanded less than halfway to the nearest
fixed star (a Centauri), it was 666,000,000,000,000,000 times
more rare than hydrogen. It was more rare than the highest
strata of our atmosphere; and its repulsive force, latent heat,
was in greater proportion than in the last line of the Table of
Marsh. That force is indestructible. It cannot be lost.
During the condensation of the sun it must be stored up in
the solar elements, and pass off as solar radiation. I speak
not now of the falling together of the materials of the sun by
the force of gravity, and the consequent liberation of heat from
that source. That is exceedingly small, not worth counting, al-
though it might continue the solar radiations 20,000,000 years.
But in the repulsive force which so vastly expanded the
nebulous sun we behold only one of the sources of its present
power. ‘There was still another and a greater power then resi-
ding in our nebulous sun. It was a power great enough to
overcome the repulsive force, to condense the nebulous sun to
his present liquid condition, and to store up all that infinity of
latent heat in the chemical elements of the sun. This para-
mount and overcoming power was the chemical force. When
all matter was diffused through all space, its condensation
could not have been caused from the loss of its heat by radia-
tion—in common phrase, by ‘the cooling of the primitive fire
mist.” If all space had been thus filled by sensible heat (“fire
mist),’’ then that heat must have remained. It could not radiate
away ; for there was no other space where it could go. There-
fore we must look to some other well-known cause for the
condensation of the primitive solar gases. The only other
cause we can think of is chemical action; and that is an ad-
equate, a normal, and a familiar cause. The chemical force,
indeed, is the great condensing-power in the universe. Oxygen
and hydrogen, when under its influence, are rapidly condensed
nearly 2000 times in volume to form water: but the repul-
sive force of these gases is not lost; it is converted partly into
heat and light, and partly into cohesion.
We will now attend to some well-known facts to illustrate
how the chemical force may overcome the repulsive forge, and
imprison in a dense solid ora liquid vast stores of many kinds
of physical forces. Gunpowder, nitroglycerine, dynamite, and
mercurial fulminating powders are examples. In all these
cases the original repulsive force has been overcome and ap-
propriated by the chemical force. As being most familiar, we
will confine our analysis to gunpowder. Its power is stored
220 Mr. J. Ennis on the Origin of the Power
up in its chemical force, and in the repulsion of its three gases,
oxygen, nitrogen, and carbonic acid. These gases were
floating about in the air until the chemical force laid hold on
them, and pressed them down into the small solid materials of
the powder. The nitrogen and oxygen were quietly combined
as nitric acid, and then united with the potassa of the earth,
forming nitrate of potassa, or saltpetre. The gaseous carbonic
acid was absorbed through the stomata of plants, then dissolved,
and its carbon hardened into wood, or rather the charcoal of
the wood. This saltpetre and charcoal, with a very little sul-
phur, are the only components of ounpowder. We know how
the least spark liberates these imprisoned gases ; and how ter-
ribly their native repulsive power shows itself, not only with
thundering sound, but with the power of thunder, and with
the heat of lightning.
The materials of gunpowder show this power, not only in
the thunder-like explosion and the lightning-like heat, but
also in vast stores of chemical force. One of the elements of
saltpetre, composed of oxygen and nitrogen, is the violent -
aqua fortis, or nitric acid. Two other gases, hydrogen and
chlorine, are combined and condensed by chemical force into
a very different material called hydrochloric acid. These two
acids when combined show their power by dissolving gold as
a lump of sugar is dissolved in a cup of tea. Hydrogen and
co)
nitrogen also are combined and condensed by. the chemical
force into the violent ammoniacal gas. This ammonia com-
bines with the nitric acid, and the two are hardened by the
chemical force into a solid, the nitrate of ammonia. All these
are striking instances of the way the repulsive force may be
overcome and converted into the chemical force, this chemical
force being lodged in vast abundance in small amounts of the
resulting solids and liquids. How inert and comparatively
feeble are the chemical properties of the four gases which
form aqua regia (oxygen, hydrogen, nitrogen, and chlorine) !
But the force residing in them in the form of repulsion is
great beyond expression, beyond measurement. Think of the
wonderful mechanical force lately found necessary to reduce
them to a liquid condition—still retaining their repulsion and
ever ready to burst out into their native gaseous state. As they
can be so easily reduced to the solid condition by the chemical
force, this is an impressive illustration of the great power of the
chemical force in overcoming and appropriating to itself the
repulsive force. The oreat idea here conveyed is that the
repulsive force of these gases cannot be annihilated. It com-
pletely disappears as repulsion when these gases are solidified
or liquified ; but it is converted into the chemical force.
which causes the Stellar Radiations. 221
Two great ideas are now clearly proved. First, the incon-
ceivably large amount of repulsive force coupled with every
single infinitesimally small portion of the sun when in the ne-
bulous condition, as illustrated by the last line of the Table of
Marsh. Secondly, the still greater amount of chemical force
then residing in the nebulous sun, which overcame the repul-
sive force and compressed the sun to his present size—as illus-
trated by that same force when it compresses oxygen and
nitrogen into nitric acid, and when it compresses oxygen and
hydrogen into water—in the case of nitric acid, retaining a
vast store of chemical force, and, in the case of water, produ-
cing a large amount of heat and also of cohesion, as I will
soon show.
Both these stores of original force, the repulsive and the
chemical, must now reside in the compressed sun, the same as
great stores of force reside in compressed gunpowder. And
no finite mind can pretend to say how long that reservoir of
solar force may be able to send out the radiations from the sun.
Count up millions of years as we may, we cannot begin to
touch the problem. We stand before itsimmensity bowed in
reverence, as when we contemplate the infinity of space and
the eternity of time.
In this condensation of the nebulous stars, our sun included,
we behold the origin of the so-called simple chemical elements.
These are not eternal entities. They are mere modifications
of the primitive gaseous diffusion, formed successively as con-
densation went on. The proofs I cannot epitomize here, as
they are already condensedly stated in my volume, ‘ The Origin
of the Stars,’ where they occupy nearly the entire Second
Part, more than forty pages. In the meteorites there are only
about 22 chemical elements, the same monotonous catalogue,
more or less complete, coming down at every meteoric fall,
In our Earth, after a longer condensation and a more powerful
chemical action, the catalogue became extended to 63. In
the Sun, after a still longer and more powerful action, the
number of simple elements, judging from the fixed lines, must
be several hundreds or several thousands. All the stars have
different sets of fixed lines, showing that the modifications of
matter which we call chemical elements are infinite in number.
The same is seen in the planets. Mercury is nine times more
dense than Saturn; and therefore the two are composed mainly
of different elements. Greater heat might indeed expand the
elements of Saturn more than those in Mercury, but not so
much as nine times. This is impossible. All solids and liquids
fly off into vapour long before even a double expansion.
Moreover there is no estimating the millions of years which
Saturn had to cool before the origin of Mercury.
222 Mr. J. Ennis on the Origin of the Power
In that same Part I collected many facts to show the hete-
rogeneity of matter, and how the peculiar elements of the Sun
may possess many thousand times more chemical force than
those in our Earth, and thus continue through periods illimit-
able to burn and to impart solar radiations. The same is true of
the facts ‘ dissociation,’ which have been insisted on so much.
The oxide of gold is dissociated with truly an insignificant
amountofheat; the oxide of mer curyr equires only a littlemore;
but the dioxide of carbon requires many tens of thousand
times more heat for its dissociation, if indeed such dissociation
by heat be at all possible. The peculiar elements of the sun
may require we know not how much more. To say that the
great heat of the sun must necessarily dissociate its elements,
is to say what we do not know, and that in the face of the
strongest reasons to the contrary.
I said there are three primitive forces whose origin is unknown
—repulsion, chemical force, and gravity. But we perceive that
from the operation of these three all the other special forces
become manifest, through the great principle of the conversion
of force. From the chemical force in ordinary burning come
light and heat; from the same force in the galvanic battery
come electricity and magnetism. ‘The great force of cohesion.
is no exception. In the nebulous cendition of the sun, at its
greatest expansion, we cannot conceive of the operation of the
cohesive force ; it was the product of the chemical force while
overcoming the repulsive force of the nebula. This we see
beautifully illustrated in oxygen and hydrogen. By the che-
mical force they are condensed into water; and Dr. Henry, of
the Smithsonian Institution at Washington, first proved that
the cohesion between the molecules of water is probably equal
to that between the molecules of ice. In raising up a disk
1 inch square from the surface of water, a force equal to the
eAipkt of only 53 grains is required ; but this is because
lever after layer of the water is broken successively, like a
strong cord when its many strands are broken one by one
(his experiments are described in the fourth volume of the
American Philosophical Society, Philadelphia),—whence he
comes to the conclusion that the tensile force necessary to
break a cubic inch of water, instead of being 53 grains, must
be several hundred pounds. The difference between water
and ice is not in the amount of cohesion, but in the fixed
polarity of the molecules of ice, which by the action of heat
are allowed in the water to turn in every direction.
I have now pointed out in a very brief manner some of the
many consequences flowing from the primitive diffusion of all
matter through all space, and its slow condensation into stars
which causes the Stellar Radiations. 223
by the chemical force. A few words more are necessary on
the source of solar heat. My paper opposing the mechanical
theories of solar heat, the fall of meteorites in the sun, and the
fall of the materials of the sun towards its centre, was pub-
lished in the ‘ Proceedings,’ for 1867, of the Academy of
Natural Sciences of Philadelphia; and at its close I expressed
a hope that the subject was put at rest for ever. But Mr.
Croll has lately brought out an addition to the mechanical
theory. He admits the failure of the meteoric theory; and he
concedes that the falling together by gravity of the materials
of the sun would produce heat enough for only twenty millions
of years—an insufficient period. But he supposes that two
unluminous stars, each half the mass of our sun, must have
been propelled together in opposite directions with velocities
of 476 miles per second, and that their collision must have
produced heat enough to supply the solar radiations for 50:
millions of years. This vast amount of heat would have ex-
panded our sun very widely in a nebulous condition; and by -
the falling together of this nebulous mass, heat enough wonld
be produced to last 20 millions of years more of solar radia-
tions. These 50 millions of years of heat derived from the
collision, and these 20 millions derived from the falling together
of the solar materials, make together 70 millions of years of
solar light and heat. Many objections oppose all this.
1. If the solar heat for 20 millions of years would be pro-
duced by the falling together of the materials of the sun, then
precisely the same amount of energy, or heat, would be con-
sumed to expand the sun to its nebulous condition. And this
would be subtracted from the heat of collision, 50 millions of
years. Instead therefore of 70 millions of years, his period
would remain only the original 50 millions from collision.
2. Mr. Croll has not proved, nor attempted to prove, that
the heat of fifty millions of years would be sufficient to expand
our sun far beyond the furthest planet, so that in condensing
the solar system might be formed. When expanded only to
the orbit of Neptune the sun was 14,000,000 less dense than
hydrogen. By the Table of Marsh this would absorb and
render latent a wonderful amount of latent heat, which Mr.
Croll must prove could be produced by his theoretical collision.
3. If our Sun were expanded beyond the orbit of Neptune
by a sudden production of heat from any cause, then, in order
to contract to nearly his present size, that heat must first ra-
diate away. According to this scheme, the very fact of solar
condensation presupposes the loss of heat by radiation. But
after the loss of all this heat which caused the expansion (the
heat of 50 millions of years), none at all can be left for solar
224 On the Power which causes the Stellar Radiations.
radiation after the formation of the planets. The theory leaves
the solar system from its first creation in total darkness and
inconceivably cold.
4, Mayer, the author of the meteoric theory, could not
account for the former fused condition of our globe, and its
present interior heat, by the fall of meteorites. He therefore
supposed that two opaque stars had collided to form our Harth
in a molten condition. Then he is bound to do the same with
the other planets. In each case two planets must have collided,
leaving the resulting planet in a nebulous state to form its
satellites by condensation. And, mirabile dictu, all the colli-
sions must have been so nicely adjusted that the resulting
planets should rotate in the same direction on their axes, and
revolve in the same plane and in the same direction round the
sun, the same direction that the sun rotates, and nearly in the
solar equatorial plane. The chances against all this scheme of
collisionsare infinite ; and therefore itis impossible. Mr. Croll’s
theory is about the same. The sidereal systems are as orderly
as our solar system. Our own sidereal system is composed
chiefly of the ring of the galaxy, like the ring of the asteroids,
and like the rings of Saturn. The ring in Lyra, with other
sidereal rings, and other regular forms of sidereal systems,
shows the legitimate working of the nebular theory, but not
the chance collisions of wandering stars.
5. Mr. Croll has to assume velocities for his colliding stars
such as could not have been produced by the force of gravity.
This is his own admission. But I have proved that gravity is
the force which in the beginning put all the heavens and the
earth in motion. No other force can be conceived to cause
the stellar velocities ; and that force is sufficient*.
6. Mr. Croll’s theory is, that originally all the stars were
dark and cold, and in the most rapid motiou—far beyond the
velocities which could be produced by the force of gravity.
The collisions, he says, have stopped them and made them
shine: ‘‘ The fixed stars are suns, and they are visible because
they have lost their motions.”” But the fixed stars haye not
lost their motions. Hvery astronomer knows that they have
their “proper motions,” velocities more rapid than those of
the planets. 61 Cygnimoves nearly 2000, and Arcturus nearly
3000 miles per minute.
7. There are sound reasons for believing that collisions
among the stars is an impossibility. I have proved that the
* See ‘The Origin of the Stars,’ Triibner and Co., 1st London (from the
4th American) edition, and papers therein referred to; also the article on
the Physical and Mathematical Principles of the Nebular Theory, in this
Journal-for April 1877.
M. Dvorak on Acoustie Repulsion. 225
fixed stars in our sidereal system are all under each other’s
influence through gravity. Two stars approaching each other
through gravity would at the same time be under the influence
of other neighbouring stars, drawing them from the right line
towards each other’s centre. Therefore they would not col-
lide; but they might approach very near to each other, so as
to remain permanently within their powerfully gravitating
force, and form a binary system. This isa mode of accounting
for the ten thousand double and multiple stars already known,
besides the mode of explanation by the nebular theory. More-
over the nebular theory necessarily gives very high velocities
to all the stars, but to all in the same direction. If afterwards,
by perturbation, they receive contrary directions, still the mo-
tions of any two precisely toward one another would be the
most improbable of events.
Therefore the mechanical theory of stellar light and heat
utterly fails in all its phases. The only true theory for the
‘jones eterni’”’ is that of chemical action. This also has been
abruptly denied, but only by those entirely unacquainted with
the foundations of that theory as explained by myself in ‘ The
Origin of the Stars’ and in subsequent papers.
XXIX. On Acoustic Repulsion. By V. DvoRAx*. Witha
Note by Prof. A. M. Mayzr.
1. A COUSTIC Repulsion of Resonators which are open at
one end only.—In a previous article, “On Acoustic
Attraction and Repulsion,” I have conclusively proved by
theoretic considerations, as well as by experiments, that the
average pressure at the node in a column of air vibrating in
stationary waves cannot be equal to zero as long as the ampli-
tude of vibration is not infinitely small.
In a resonator open at one end, as, for example, a cylinder,
we find a node at the closed end. In the interior of the cy-
linder near its closed end there exists a greater pressure than
on the outer surface of this end which is touched by the out-
side air, as can easily be shown by means of a sensitive mano-
meter.
To obtain resonance the opening of the cylinder is turned
toward the source of the sound ; and the cylinder is then re-
pelled by the excess of pressure within. Resonators not having
a cylindrical form, but open at one end, are also subject to such
repulsion. In my previous communication I have indicated
* From the American Journal of Science and Arts for July 1878.
Translated from the Annalen der Physik und Chemie, Band ili, No. 3;
dated Agram, November 19, 1877.
Phil. Mag. 8. 5. Vol. 6. No. 86. Sept. 1878. Q
226 M. Dvorak on Acoustie Repulsion. —
means for observing the acoustic repulsion of resonators. As
the method described there is not very sensitive, I have replaced
it by the following. The resonators here employed are usually
made of stiff drawing-paper covered with gum-arabic, and
have the shape of a cylinder, with a little paper tube, hf, at
one end (fig. 1, A). This little tube may also be omitted (as
Fig. 1. Fig. 2.
in B): in that case the resonator is ‘tuned by increasing or
diminishing the little opening, fg. Hven a cylindrical tube
open at one end, OC, may serve our purpose as a resonator.
Spherical resonators of glass, D, which a practiced glass-
blower can make as light as paper resonators, are excellent.
The note of the resonators is determined by gently blowing
over the opening or by tapping. : :
The resonator is fastened with sealing-wax to the end ofa
light wooden rod, the other extremity of which is provided
with a counterpoise of lead, O (fig.2). The centre of the rod
has a glass cap, H, which rests on a needle-point.
The best source of sound is a resonant box of a tuning-fork
(fig. 2). The repulsion is so great that it is apparent even with
an ordinary brass Helmholtz resonator weighing, with the lead
counterpoise, 142 grams*. With every tuning-fork we must
first ascertain whether the air in the resonating box vibrates
with sufficient energy, because this is not always the case even
with accurately tuned boxes. As the elasticity of the different
boards which form the elastic system of the box is not equal,
their vibrations may hinder the formation of the node at the
bottom of the box; in this case the air on the bottom of the
box will vibrate but feebly. We can easily ascertain this fact
by accurately tuning the box to the note of the fork, and then
observing whether the note is considerably weakened by par-
tially covering the opening. If it is not, then the air in the
* The apparatus represented in fig. 3 may also be used to show acoustic
attraction by turning the closed end of the resonator toward the box.
M. Dvorak on Acoustic Repulsion. 227
box has but little vibration, even if the tone of the fork is pow-
erful. J have, for example, two boxes with excellent tuning-
forks by Ko6nig (of 256 vibrations per second), in which the
air would in no wise vibrate powerfully. The strength of the
vibration of the air was considerably affected by the degree of
tightness with which the fork was screwed to the top of the
- box. The fork is always vibrated powerfully with a bow; and
two bits of rubber tubing must be on the bottom of the box.
I generally use the fork A;, of 435 vibrations per second, by
Konig. Repulsion is then plainly visible with glass resonator
at a distance of 10 centimetres from the opening of the box.
With a large C fork of Konig (of 128 vibrations) which sounds
for more than ten minutes, it was apparent at a distance of
20 centimetres.
The resonators may be tested either by the reinforcement of
the sound produced with a tuning-fork, or by the weakening
of the sound on approaching them to the opening of the box*.
It is not possible to obtain the repulsion of resonators from the
prongs of a tuning-fork alone, as their aerial vibrations are
too weak (compare Pogg. clvii. p. 42). I formerly tried in
vain to obtain acoustic repulsion from vibrating bodies with-
out the aid of resonance. I suspended small resonators before
the end of a glass tube vibrating longitudinally, and provided
with a cork to increase the vibrating surface. The open end
of the resonator was probably too near the end of the fork,
and so produced a lowering of the tone and acoustic attraction
instead of repulsion. Attraction is probably present in all
cases, and can assert itself only when not counteracted by
greater repulsiont. Later I obtained repulsion very easily in
a longitudinally vibrating glass tube 127 centims. long and
27 millims. in diameter, on the end of which was a cork 46
millims. in diameter. One of the resonators used was sphe-
rical (fig. 1, D), and another cylindrical (C).
I also obtained powerful repulsion with a circular disk 31
centims. in diameter and 2 millims. thick, made by K@nig.
The plate was fastened in the centre in a vertical position and
made to vibrate in six segments, producing a note of 208 vi-
brations. ‘The resonator was made of stiff paper of the form
of B (fig. 1); ab equal 80 millims., cd 140 millims., fg equal
* This is perhaps connected with a conversion of the aerial vibrations
in the box into the work of repulsion, The vis viva of the sound-vibra-
tions disappears to reappear as work.
+ These experiments were also described in a previous communication.
In the apparatus represented (fig. 2), repulsion is easily converted into
attraction by diminishing the opening of the resonator with wax, and so
throwing it out of tune.
Q 2
228 M. Dvorak on Acoustic Repulsion.
17 millims.; and its opening was placed in front of the ce
of a vibrating segment, or ventre.
2. The Acoustie Mill.—A_ continuous rotation is ¢
tained, on the principle of the acoustic repulsion of resor
by fastening four very light paper or glass resonators upon
two wooden rods, op, g7 (fig. 3), crossing at right angles, —
and balanced on a glass cap; all the openings of the resona-
tors fronting one side in the direction of tangents. The whole
apparatus is placed before
the opening, K, of the reso- Fig. 3.
nating box and fork, in the
manner indicated in fig. 3.
The open end a of resonator
1 is repelled from K; the
closed end 6 of resonator 2
is attracted: but in general
this attraction does not in-
crease the rapidity of rota-
tion, because it counteracts
rotation the moment the re-
sonator (2) has changed its
position about 45°. It is
therefore not possible to ob-
tain continuous rotation by
means of acoustic attraction, : |
as I have shown by numerous experiments*. The resonator
(1) continues to move by reason of its inertia, and resonator
(2) takes its place, being in turn repelled, and so on.
A very rapid rotation is obtained by using a large Kundt’s
tube and placing a small acoustic mill before its open end.
The glass tube (Kundt’s), which vibrates longitudinally and
produces the tone, is fastened to a heavy table, and protrudes
only a short distance through the cork into the glass tube,
placed upon a separate table so that its open end projects
somewhat beyond the edge of the latter. The length of the
rod was 127 centims., the diameter 27 millims. ; the half wave-
length of its note, a equals 104 centims. ‘The length of the
tube was 45 centims.; the length of the vibrating column of
air, corrected for the open end, was 35 =F Hs ; the inner dia-
meter was 5 centims.
* Instead of the resonators (fig. 3) I used vertieal paper vanes, varying
e curvature, without achieving any results, notwithstanding the fact that
there was a pretty streng acoustic attraction for each separate vane.
M. Dvorak on Acoustic Repulsion. 229
3. The Acoustic Torsion-balance.—If we hang by a wire a
le rod provided with a resonator, like the beam of a
’s torsion-balance, in a case having an opening in the
urned toward the resonator, we can compare the inten-
sity of notes having an equal number of vibrations by means
_ of the repulsion of the resonator ; but further experiments are
necessary to test the practicability of this method. The sound
proceeded from an open pipe, having the note A (of 435 vi-
brations). To prevent the current of air which passes through
the pipe from striking the resonator attached to the balance,
we must cut the pipe exactly in the middle of its node, and
insert a slack membrane softened with glycerine. To prevent
the air issuing from the mouth of the pipe from impinging on
the resonator, a broad box is used which surrounds the mouth
of the pipe air-tight. This box is open on the side opposite
the resonator, so as not to impair the tone. The pipe is
sounded by means of a KGnig’s acoustic bellows with a uni-
form blast of air. The distance of the resonator from the
mouth of the pipe must be at least 2 or 3 centims., to avoid a
change of pitch.
4. Production of Aerial Currents by Sound.—It may easily
be proved by simple theoretic considerations that the mean
pressure at the node of a column of air is greater than at its
ventre ; and that it steadily diminishes in passing from the
node to the ventre, provided that the amplitude of vibration
is not infinitely small.
It would seem that this difference of pressure would be
neutralized by the passage of the air from the node to the
ventre. There would then be produced a mean pressure in
the whole column, which would be greater, however, than that
of air at rest; consequently air would issue from the opening
of the vessel in which it forms stationary waves. I have not
succeeded, so far, in making the whole process clear; for in
reality no perfect balance of pressure takes place. The mano-
meter always shows a slight excess of pressure even at the
ventre; but this excess increases as we pass to thenode. All
my previous experiments indicate moreover that a current of
air passes from the node to the ventre, at least in Kundt’s
tube, in which the air-waves are very powerful. This prin-
eipal current lasts as long as the air vibrates. Besides, the
same experiments show a continuous secondary current, close
to the walls of the tube and in a direction contrary to that of
the principal current; so that the whole air in the tube is in
circulation. The cross section of the principal current is nearly
as great as that of the tube, while that of the secondary cur-
rent is a very narrow ring.
230 M. Dvorak on Acoustic Repulsion.
The excess of pressure as shown by a manometer at the node
is always less than the theoretical pressure, because in the
latter the air is not supposed to move from the node and to
equalize the pressure. Of course the excess of pressure at
the ventre is not equal to zero, as theory requires. Probably
the friction of the walls has much to do with these phenomena.
It may be expected from what has been said, that the air will
issue from the vessel in which it vibrates in stationary waves.
The manometer shows, in the first place, that the excess of pres-
sure is not equal to zero in the plane of the opening of a reso-
nator, because a portion of the air immediately in front of this
opening partakes of this stationary wave-motion, and because
there is always a small excess of pressure even in the ventre
of a stationary wave. ‘There is no doubt that a partial equali-
zation of pressure takes place at the opening; experiments
show, furthermore, that there is a continuous exit of air, which,
as in Kundt’s tube, is probably neutralized by a secondary
and contrary current.
The exit of the air can easily be proved as follows: a sphe-
rical glass resonator is placed before the resonant base of a
tuning-fork ; the resonator is filled with tobacco-smoke; strong
vibrations are given to the fork, when the smoke will be seen
to rush from the resonator.
The current of air proceeding from a resonator is well shown
by means of a Chladni plate, by means of lycopodium, which
accumulates upon the ventres in little heaps when the plate is
sounded. If now we place the opening of a bottle (or bottles)
of a resonator, D, over such a heap, the lycopodium is imme-
diately blown about in a circle, and may be scattered in any
direction by giving suitable inclinations to the resonator. A
glass plate held over a heap of lycopodium produces the oppo-
site effect by causing it to contract.
I have succeeded in producing comparatively strong cur-
rents of air in still another manner; but I have not yet found
an explanation of these complicated phenomena.
A cone made of stiff paper was held with its large end oppo-
site the opening of a large Kundt’s tube. The size of this
cone may vary; but its effect is greatest when it vibrates to
the same note as the Kundt’s tube, and so. forms a resonator
open at both ends; the diameters of its open ends are 37 an
7 millims., and its length 90 millims. ;
When the Kundt’s tube begins to sound loudly, a current
of air issues from the narrow end of the cone with such vio-
lence that it easily blows out the flame of a candle ata distance
of 20 centims. This current rushes through the cone with a
peculiar noise, and is easily felt with the finger.
eS ee
?
M. Dvorak on Acoustic Repulsion. 231
The cone may be replaced Fig. 4.
by a cylinder having the
width of the Kundt’s tube,
open at the end turned to- ‘ IN
ward the latter, and closed >
all but a small hole at the
end; but the current is much
weaker; nevertheless it will
move a small wheel with ver-
tical paper vanes (fig. 4).
In the experiments with the tuning-forks, it is essential
that the cone should vibrate to the same note as the fork;
otherwise the current is too weak. For the fork A (of 4385
vibrations) the openings of the cone have diameters of 82 and
3 millims., and its length is 373 millims. The opening at the
apex of the cone must be very small to obtain an appreciable
current.
On conclusion of this investigation, Dr. R. Konig kindly
communicated to me that Mr. Alfred Mayer in New York
| Hoboken | had previously succeeded in producing continuous
rotation by means of sound. The communication was as fol-
lows :—‘ Professor A. M. Mayer showed me a very similar ex-
periment last summer (1876). He suspended by a thread two
large well-tuned flasks attached to a rod, and caused the whole
apparatus to revolve by means of a tuning-fork. I informed
him in consequence that you had previously demonstrated the
phenomena ofrepulsion in resonators; for he was not acquainted
with your paper™ on acoustic attraction and repulsion.”
Note by Professor ALFRED M. Mayer.—My connexion with
the discovery of the sound-mill is as follows :-—
In January 1876 I made the discovery (first reached by
theoretic deductions) that there was more pressure on the inner
surface of the bottom of a resounding cavity than on the outer
surface of the bottom, which touches the outer air. I subse-
quently proved the truth of this conclusion by experiments on
suspended resonators, and by observations on the motions of
precipitated silica powder and films of soap-bubbles placed at
various points in resonators of different forms. My first pub-
lication of these results was on May 22, 1876, on which day I
read a paper on this discovery before the New-York Academy
of Sciences, and exhibited before the members an apparatus
formed of two + arms of light wood, with a resonator attached
to each arm, as in fig. 8 of Professor Dyorak’s paper. On
sounding an organ-pipe, or a fork on its resonant box, in tune
with these resonators, they were successively repelled from the
* Read before the Royal Academy of Sciences, Vienna, in 1875.
232 M. Dvorak on Acoustic Repulsion.
pipe, or fork, and a continuous rotation was exhibited. At
the same meeting this experiment was preceded by those on
the motions of silica-powder &c. in resonators. }
On the 8th of July, 1876, there appeared in the ‘ Scientific
American’ a report of this meeting of the Academy, in which
my experiments on Acoustic Repulsion are thus referred to :—
“In the next place, Professor Mayer exhibited an apparatus
constructed by him to produce motion by means of sound-
pulses. Four glass resonators on cross-arms were suspended
by means of a string. On sounding an organ-pipe in tune
with the resonators and bringing it opposite the mouth of one
of them, the resonator was repelled and the apparatus com-
menced to rotate. This experiment was the more striking
from the fact that, so far from any current of air proceeding
out of the mouth of the organ-pipe, the air is actually sucked
in, as may be rendered visible by means of smoke from a cigar.
The smoke is carried up the pipe even when the latter is closed
at the top with cotton wool so as to smother the sound. On
substituting disks of cardboard for the resonators, they were
drawn up to the mouth of the organ-pipe with considerable
force. When fine silica-powder was placed in the resonators,
it was thrown into violent motion on sounding the pipe.”
In the same month (July 1876) Dr. Rudolph Konig visited
me, and I exhibited the same experiments before him.
The discovery of the acoustic repulsion of resonators and
the invention of the sound-mill were made independently by
Professor Dvorak and myself. It is another instance of men,
even so far distant as Agram and Hoboken, led into the same
path of research by the natural growth of science.
Dimensions of the resonators and reaction-wheels used, in
millimetres :—
(1) Fork C, of 128 vibrations. Glass resonator of form H
(fig. 1),ab equalled 90; hi, 25; Ak, 20; kf, 33; fg,8. Its
weight, together with its leaden counterpoise, was 70 grams.
(2) Fork A, 485 vibrations per second. (a) The glass
resonator used in the experiment represented in fig. 2, and to
show the current of air by means of smoke, was of the form D
(fig. 1): ab equalled 58; Af, 22; fg,10. (6) The glass
resonators of the acoustic mill were of the form D: ab equalled
384; hf, 12; fg, 3. The length of the arms from the middle
of the glass cap to the middle of the resonator was 52 millims.
The weight of the whole wheel was 23 grams. (c) Paper re-
sonators of the acoustic mill (fig. 3) were of the form A (fig. 1):
ab equalled 34; cd, 50; hf, 63; fg, 9. The length of the
arms was 65 millims., the weight of the whole wheel 9 grams.
Geological Society. 233
(3) Kundt’s tube, me equals 105 millims. The glass reso-
nators of the acoustic mill were of the form D (fig.1): ab
equalled 24; hf, 2; fg, 7; length of the arms 30 millims.
It is a striking fact that very small resonators may give a
very deep note: with fork A, 1 used a glass resonator of the
form D (fig. 1), in which ad equalled 24, Af 14, and fg 1
millim. ‘The volume was about ninety times less than that of
the resonant box of the fork, to whose note the resonator was
tuned. Notwithstanding its smallness it showed acoustic re-
pulsion.
XXX. Proceedings of Learned Societies.
GEOLOGICAL SOCIETY.
[Continued from p. 153. ]
“June 5, 1878.—John Evans, Esq., D.C.L., F.R.S., Vice-President,
in the Chair.
HE following communications were read :—
1. “On the Quartzites of Shropshire.” By Charles Callaway,
Hisq., M.A., B.Sc., F.G.S.
In a former paper (Q.J.G.8. xxxiil. p. 652) the author indicated
that part of the so-called quartzites of the Wrekin are “ Hollybush
Sandstone ;” in the present communication he shows that the
whole, both in the Wrekin and Church-Stretton areas, are of Cam-
brian or Precambrian and not of Caradoc age.
In the Wrekin area the quartzites rest unconformably against the
volcanic axis in a nearly continuous band, dipping away from it at
angles of from 30° to 55°, their present position being due to its
elevation. The volcanic rock is a bedded Precambrian tuff, which
reappears in Lawrence Hill and the Ercal, also accompanied by
quartzites overlain by Hollybush Sandstone. Caer Caradoc belongs
to the same volcanic series ; and the quartzites reappear on its 8.H.
flank, overlain by Hollybush Sandstone containing Kutorgina cin-
gulata and Serpulites fistula, above which follow the Shineton Shales,
and next, separated by a fault, the Hoar-Edge grits (Lower Caradoc).
The author believes that the apparently conformable succession here
is due to parallel faults. Along the S.E. flank of the Wrekin the
quartz rock dips 8.E., while the volcanic rocks dip N., and fragments
of the latter are contained in its base. ‘The author is inclined to
consider this a friction-breccia, and the junction a faulted one. He
also regards the junction with the Hollybush Sandstones as a faulted
one, and maintains that in any case the quartzites are older than the
latter rocks, which are sometimes considered the equivalents of the
Ffestiniog group, and by Mr. Belt to be Menevian. The quartzites
can hardly belong to any part of the Upper Cambrian; and the
author passes on to consider the various positions which they may
be held to occupy, and gives reasons for thinking that they are Pre-
234 Geological Society: —
cambrian. The only fossil that has been found in them is a sup-
posed worm-burrow. In conclusion the author expresses the opinion
that the Stiper-stones quartzites are of Arenig age.
2. “ On the Affinities of the Mosasauride, Gervais, as exemplified
in the bony structure of the fore fin.” By Prof. Owen, C.B., F.R.S.,
F.G.S., &e.
3. “On new Species of Procolophon from the Cape Colony, pre-
served in Dr. Grierson’s Museum, Thornhill, Dumfriesshire; with
some Remarks on the Affinities of the Genus.” By Harry Govier
Seeley, Esq., F.L.S., F.G.S., &c., Professor of Geography in King’s
College, London.
4. “On the Microscopic Structure of the Stromatoporide, and on
Paleozoic Fossils mineralized with Silicates, in illustration of
Kozoon.” By Principal Dawson, LL.D., F.R.S., F.G.S.
5. “ On some Devonian Stromatoporide.”
Esq., F.G.8.
6. “*On a new Species of Loftusta from British Columbia.” By
George M. Dawson, D.Sc., F.G.8., Assoc. R.S. M., of the Geological
Survey of Canada.
By A. Champernowne,
June 19, 1878.—John Evans, Esq., D.C.L., F.R.S., Vice-President,
in the Chair. .
The following communication was read :—
1. “On the Section of Messrs. Meux & Co.’s Artesian Well in the
Tottenham Court Road, with notices of the Well at Crossness, and
another at Shoreham, Kent; and on the probable Range of the
Lower Greensand and Paleozoic Rocks under London.” By Prof.
Prestwich, M.A., F.R.S., V.P.G.S.
The well-known boring at Kentish Town in 1856 showed the
absence at that point of Lower Greensand, the Gault being im-
mediately succeeded by hard red and variegated sandstones and
clays, the age of which was at first doubtful, but which were finally
considered by the author to approach most nearly to the Old Red
Sandstone near Frome, and to the Devonian sandstones and marls
near Mons, in Belgium. The existence of some doubt as to this
identification rendered the boring lately made at Messrs. Meux’s
brewery particularly interesting ; and the method of working adopted
by the Diamond Boring Company, by bringing up sharply cut cores
from known depths, gave special certainty to the results obtained.
The boring passed through 6524 feet of Chalk, 28 feet of Upper
Greensand, and 160 feet of Gault, at the base of which was a seam,
3 or 4 feet thick, of phosphatic nodules and quartzite pebbles.
Beneath this was a sandy calcareous stratum of a light ash-colour,
passing into a pale or white limestone, and this into a rock of oolitic
aspect. Casts and impressions of shells found in this bed showed it
to be the Lower Greensand, whose place it occupied. The boring was
carried further in the hope of reaching the loose water-bearing
sands of this formation ; but the rock became very argillaceous; and
oe -
Prof. J. Prestwich on Artesian Wells. 235
when 62 feet of it had been passed through, the boring entered into
mottled red, purple, and greenish shales, dipping at 35° in an
unascertained direction. These beds continued through a depth of
80 feet, when, their nature being clearly ascertained, the boring was
stopped. The fossils of these coloured beds, which included Spiri-
fera disjuncta, Rhynchonella cuboides, and species of Edmondia,
Chonetes, and Orthis, show them to be of Devonian age. ‘Thus the
existence of Palzozoic rocks at an accessible depth under London,
and the absence of the Jurassic series, as maintained long since by
Mr. Godwin-Austen, are experimentally demonstrated.
These facts are of interest in connexion with the question of the
possible extension of the Coal-measures under the Cretaceous and
Tertiary strata of the south-east of England. The beds found at
the bottom of Messrs. Meux’s boring are of the same character as
the Devonian strata which everywhere accompany the Coal-mea-
sures in Belgium and the north of France, being brought into juxta-
position with them by great faults and flexures. The author refers
especially to a remarkable section at Auchy-au-Bois, in the western
extremity of the Valenciennes coal-field, which is particularly inter-
esting from its furnishing evidence that the Hardinghen coal-field,
between Calais and Boulogne, is a prolongation of that of Valen-
ciennes, and because the same strike and a prolongation of the same
great fault observed at Auchy-au-Bois through Hardinghen would
carry the southern boundary of any coal-field in the south-east of
England just south of Maidstone, thence passing a little north of
London. Hence it is in the district north of London that there is
most probability of the discovery of the Carboniferous strata. The
extent of country in which shafts could be sunk to the Paleozoic
strata, however, will be limited by the presence of the water-bearing
Lower Greensand, which probably reaches close to London in the
south, reappears in Buckinghamshire and Bedfordshire 30 or 40
miles north of London, and probably extends some distance towards
the city under the Chalk hills of those counties and Hertfordshire.
The nature of the representative of the Lower Greensand in the
boring, and the characters of the fossils contained in it, lead the
author to the conclusion that in it we have a deposit produced near
the shore of the Neocomian sea, here probably consisting of cliffs of
Devonian (or Carboniferous) rock. From these cliffs the calcareous
material which here replaces the usual loose sands of the Lower
Greensand was perhaps derived by the agency of springs; and the
shore-line itself must be situated between the south end of Totten-
ham Court Road and the Kentish Town boring. The sandy beds of
the Lower Greensand will probably be found to set in at no great
distance to the southward, presenting the conditions necessary for
storing and transmitting underground waters. A test boring made
by Mr. H. Bingham Mildmay at Shoreham Place, about 5 miles from
Sevenoaks, and in which the Lower Greensand was met with at
about the estimated depth (450 feet) and furnished a supply of
water, seems to confirm these views.
[ 236 ]
XXXI. Intelligence and Miscellaneous Articles.
ON SOME PROBLEMS OF THE MECHANICAL THEORY OF HEAT.
BY PROFESSOR LUDWIG BOLTZMANN.
PRE first section of the memoir has for its subject the relation
between the Second Proposition and the calculation of probabili-
ties; the second, the thermal equilibrium of a heavy gas. To these
the author adds the following communication:—In the Bezblatter to
Wiedemann’s Annalen der Physik, Band II. Stiick 5, is a treatise
by S. Tolver Preston, in which the diffusion of gases is brought
into relation with the Second Proposition of the mechanical theory
of heat. This cannot (as, according to the notice in the Beiblatter,
the author seems to think) serve for the refutation of that proposi-
tion; but it may well be a new and interesting application of it.
There is in the same Stick of the Bezblatter a notice of a memoir
by M. Clausius on this subject. Now, knowing nothing more of
the contents of the memoir than what may be ‘gathered from this
notice, and not in the least wishing to forestall it, I will merely
mention that, as it appears to me, the most essential problem that
here comes into question, namely the calculation of how much heat
can be transformed into work without any other compensation than
the mixture of two dissimilar gases—or, to use the terminology of
M. Clausius, the calculation of the transformation-value of the
mixture of two dissimilar gases—is only a special case of some cal-
culations which I have carried out in my treatise ‘On the Relation
between the Second Proposition of the Mechanical Theory of Heat
and the Calculation of Probabilities as regards the Propositions re-
specting Thermal Equilibrium.” Lhave, namely, there considered
quite generally the case that in any mixture of substances, whether
it be the mixture or the distribution of velocities or of directions of
velocities, the entropy does not perfectly correspond to the definitive
final state, and have shown that then it must always be less than
in the definitive final state, so that consequently, on the transition
into the latter, heat may be converted into work; and I have given
a formula (formula 51) by which the difference of entropy, and con-
sequently also the amount of the convertible heat, can be calculated.
From this formula (51) it immediately follows that the entropy
of a mixture of several gases is exactly equal to the sum of the en-
tropies which would belong to the individual gases if, at the same
temperature and under the same partial pressure, each were alone
peta in space. If V is the volume, T the absolute temperature,
k the weight of the gas, c and c' its two specific heats, then its en-
= , @Q being = the heat intro-
duced) is ae cd +k(c'—c) iog V.
We will now consider two cases: first, two different gases are
present in two different spaces V, and V,, under equal pressure p
tropy (by which I understand {
Intelligence and Miscellaneous Articles. Dat
and at the same temperature T ; secondly, the same gases are mixed,
at the same temperature, in the space V,+ V,, while the total pres-
sure is equal to the previous pressure of each separate gas. In the
first case let H, be the entropy of the first, H, that of the second
gas; in the second case let H,, be that of the mixture. According
to the rule given above, E,, E,, and E,, can be calculated by means
of the above formula. We thus find
1(H,,—E,—E,)=T(y' — yYUV,4+ V.)¢V,+ V.)—VLV,—V.LV, |.
But this is the expression for the quantity of heat which can be
converted into work without any other compensation than the mix
ture of the two gases. Therein is y'—y the product of the weight
of unit volume into the difference of the two specific heats, which
product has the same value for both gases.
The total work which can be gained from this heat is, according”
to known principles,
PLY, ste VK, a ve) a Vie A ele
To gain this total work, of course we should not have recourse to
the expedient of diffusion through porous partitions, but convey the
one gas into the other by means of a substance that chemically com-
bines with one of the gases under partial dissociation (as quick-lime
with carbonic acid), of course taking care that the process always
remains reversible. We should, for example, first indefinitely
expand the first gas, then with the substance above mentioned
transfer it very slowly into the other, while, again, it would be
continually compressed so that the partial pressure of the first gas
was always equal in both vessels. Lastly, the mixture of gases
must be so far expanded that its volume shall be equal to the sum
of the volumes of the original gases. Since all these processes can
easily be accompanied by calculation, it will be easy in this way to
verify the above-given formula.—Kuiserliche Akademie der Wissen-
schaften in Wien, mathematisch-naturwissenschaftliche Classe, June 6,
1878.
ON THE RELATION OF THE WORK PERFORMED BY DIFFUSION TO
THE SECOND PROPOSITION OF THE MECHANICAL THEORY OF
HEAT. BY PROF. R. CLAUSIUS.
In ‘Nature’ for January 1878 (vol. xvii. p. 202), Mr. Tolver
Preston has specified a process by means of which mechanical work
can be gained through diffusion of gases. The reflections he makes
upon this fact are very ingenious, and in relation to theory very
interesting on account of the conclusions to which they give occa-
sion; only in one point J think I must express a view different
from his: he thinks, namely, that the result of his process contra-
dicts the second proposition of the mechanical theory of heat; and
in this I cannot coincide.
The substance of his process is as follows. He imagines a ecy-
linder divided into two sections by a movable piston. ‘The piston
consists of a porous substance, such as pipe-clay or graphite. In
the two divisions of the cylinder two different gases are present,
oxygen and hydrogen for instance.
238 Intelligence and Miscellaneous Articles.
If, now, both gases have initially equal pressure, a change is soon
produced therein by diffusion. The hydrogen penetrates through
the porous piston more quickly than the oxygen; hence the amount
of gas present on the hydrogen side diminishes, while that on the
oxygen side increases. This produces a lessening of pressure on
the hydrogen side, and an augmentation of pressure on the oxygen
side, so that the piston can be put in motion with a certain force,
and mechanical work performed capable of beg made useful ex-
ternally. At the same time, with the movement of the piston the
gas on the side where it expands becomes cooler, and becomes
warmer on the side where it is compressed; and consequently heat
passes over from a colder to a hotter body.
These two circumstances, that work is gained in the process
without there being any difference of temperature present initially,
and that simultaneously heat also passes over from the colder divi-
sion into the hotter, are regarded by Mr. Preston as contradicting
the second proposition of the mechanical theory of heat.
To this inference I cannot assent. Ifthe conversion of heat into
work and the transference of heat from the colder to the hotter
body had taken place in such manner that the variable material at
the end of the operation were found in its original state, so that we
had to do with a cyclical process, then certainly there would be in it
a contradiction to the second proposition of the mechanical theory
of heat. But the matter does not stand thus. We haye, in the
process, as variable material the two gases. These are at the com-
mencement unmixed, and at the conclusion mixed; and therefore an
essential change has taken place with them, which may be regarded as
a compensation for the conversion of heat into work and the trans-
ference of heat from a colder into a hotter body. Since the gases,
through the molecular motion which we call heat, tend to mingle,
and indeed in such wise that the higher the temperature the more
quickly does the mixture result, we have here to do with an action
of heat comparable to the expansion of a gas by heat; and hence
we must ascribe to the mixed gases a greater disgregation than to
the unmixed. Now, since the increase of disgregation is a positive
change, it may be compensated by the transformation of heat into
work and the transference of heat from a colder into a hotter body,
both of which are negative changes.
It is therefore evident that, although it is true that the present
case possesses certain peculiarities by which it is superficially di-
stinguished from other cases, yet in the essential points with which
we are concerned in the mechanical theory of heat it is in complete
harmony with the cases usually treated, and contains nothing con-
tradictory to the second proposition of the mechanical theory of
heat.—Wiedemann’s Annalen, 1878, pp. 341-343.
ON MOSANDRUM, A NEW ELEMENT. BY J. LAWRENCE SMITH.
Having read the interesting communication from M. J.-L. Soret
to the Academy relative to the absorption-spectrum of the gadolinite
Intelligence and Miscellaneous Articles. 239
earths in the ultra-violet rays*, I hasten, with a view to my own
interest, to bring to the knowledge of the Academy that the earth
designated X was discovered by me more than a year ago: the dis-
covery was publicly announced, in the course of the proceedings of
the Philadelphia Academy of Natural Sciences, in May 18777; a
communication to the same effect was also sent to the said Academy
in November of the same year.
My conclusions were based entirely on chemical principles ; for
it was proved that the earth which I had discovered was distin-
guished by its properties from all those known to belong to the
yttria and cerium groups, although it came very near those earths,
the chemical properties of which shade almost insensibly into one
another. A short time after announcing the discovery, I sent a
specimen to M. Delafontaine, of Chicago, who thought that it would
prove to be either Mosander’s terbia or some new earth. It was,
however, impossible for me to make its properties agree with those
at that time attributed to terbia. ,
I was desirous as far as possible to rid this new earth of the pre-
sence of earths already known, in order to study its properties and
constituent parts. Jor better success I required a little of the
terbia which M. Marignac had recently extracted from gadolinite.
I wrote therefore, in March, to that able chemist. He possessed
too small a quantity of that earth to let me have any; but he ex-
amined my new earth and the nitrate, which I sent to him; and in
communicating to me the result of his examination he says (inter
alia), “‘ Not only am I convinced of the identity of your earth and
my terbia, but I may add that you have obtained it in greater purity
than I.” After M. Soret had examined my earth by means of the
spectroscope, he said to me, “I can have no doubt about the iden-
tity of that chemist’st [M. Delafontaine’s] and my terbia and your
earth.”
The spectroscopic observation of M. Soret placed beyond doubt
that the earths of samarskite contain a new metal, as I announced
in May 1877, my first specimen then obtained giving the absorp-
tion-spectrum marked No. 2 in his communication. I no longer
hesitate to give to this metal the name of mosandrum, in honour of
the distinguished chemist whose researches and remarkable disco-
veries in this class of earths form a brilliant epoch in the history of
metallic chemistry.
In giving the following succinct history of this discovery, I
* This has no relation to the Ural samarskite, in which I, concurrently
with other chemists, have found oxide of cerium.
+ Comptes Rendus, April 29, 1878.
** Professor Lawrence Smith made some observations on the anomalous
properties of the earthy oxides of samarskite, and stated the reasons which
led him to believe that those oxides do not contain cerium, and that most
of what is regarded as cerium is a new element.”’—Amnnals of the Phila-
delphia Academy of Natural Sciences, May 8, 1877.
{ In the course of more recent researches M. Delafontaine believed he
had discovered another new earth; but M. Soret’s experiments and M.
Marignac’s conclusions make it evident that this earth is identical with
that discovered by me.
240 Intelligence and Miscellaneous Articles.
acknowledge my obligations to M. Delafontaine for the numerous
suggestions with which he has kindly aided my investigations.
Towards the end of 1876 I was engaged in the mineralogical and
chemical study of the American minerals containing niobic acid, and,
among others, of samarskite, a considerable quantity of which had
been found in North Carolina. In so doing I discovered two new
minerals, a report on which was addressed to this Academy. In
separating the earths from the samarskite I gained the conviction
that they contained no acid oxide of cemwm, or at the most only
slight traces—a fact which is recorded in the publication of my
results*, Other chemists who examined this samarskite (as Mr.
Hunt, Mr. Allen, and Miss Swallow) concurred with each other in
finding in it some oxide of cercwn; M. Delafontaine, in a private
letter dated 4th May 1877, writes to me, ‘I have ascertained no-
thing that can make me doubt the presence of cerium ;” and in a
letter of the 21st of the same month he passes in review the causes
which might have misled me in my conclusions, ending with these
words :—‘ But I suppose you have an equally good method; and
we may expect to receive from you a monograph upon 4 new ele-
ment—which, I avow, would give me great pleasure; for it has
already seemed to me that the hypothesis of the existence of such
an element would give a satisfactory explanation of certain incon-
eruities in the properties of the other earths.” In a still more recent
letter he says, in regard to the samarskite earths, “‘ 1 am convinced
now of the absence, almost if not absolutely total, of the oxide of
cerium; and no one has any longer a doubt on this point.”
M. Delafontaine, to whom I remitted a little of the earth, which
I had purified as much as it was then possible for me to do so, and
also a large quantity of the mineral, concluded that it was either
terbia or a new earth. Not finding, however, the chemical proper-
ties correspond to those then known of terbia, I addressed a report
to the Paris Academy of Sciences, msisting on my first conclusions,
asserting that the new earth is distinguished from that of the yttria
group by the action of sulphate of potass’, from the oxide of cerium
by its solubility in extremely dilute nitric acid and in a solution of
alkalies supersaturated with chlorine, from lanthanum by the colour
of its oxide and of its salts, from didymium by the absorption-lines
of the latter in the bright part of the spectrum. I abstained from
giving any definite name to the metal constituting the base of this
earth, because I knew it was necessary to proceed with great cir-
cumspection, working, as I did, among a group of oxides which
figure among the elements as the asteroids among the planets. But
the spectroscope, in the skilful hand of M. Soret, has supplied what
was wanting; and I seize this opportunity of announcing that the
existence of the element, which I suspected in 1876, is no longer
hypothetical, but real—Oomptes. Rendus de 7 Académie des Sciences,
July 22,1878, tome Ixxxvii. pp. 148-151.
* Archives des Sciences Physiques et Naturelles, March 1878, p. 283.
+ Being precipitated by a concentrated solution of that salt in the pre-
sence of crystals of the same salt, especially when heated, but less readily
than the oxides of cerium, lanthanum, and didymium.
iis eal
THE
LONDON, EDINBURGH, axn DUBLIN |
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FIFTH SERIES.]
OCTOBER 1878.
XXXII. On the Measurement of the Curves formed by Cephalo-
pods and other Mollusks. By the Rev. J. F. Biase, 1.A.,
i Ge. S:
[Plate IV.]
i® ery years ago Professor Moseley pointed out (Phil.
Trans. 1838) that the curves affected by discoid and
turbinated shells were derivable from the logarithmic spiral ;
and after him Naumann gave the name of concho-spiral to an
allied curve, in which the differences of the radii in the same
direction form a geometrical progression, but the initial radius
is not one of the series. By such a modification he hoped to
bring the measurements of actual shells more into harmony
with calculation. The errors of observation, however, are
always greater than this change would correct—if founded on
fact, which is doubtful; and all practical advantage is lost by
the complication of the equations.
In working through the fossil Cephalopoda, I have been
obliged to obtain some clearness of idea as to their mode of
origin and consequent connexion with each other, and to find
some means of recognizing in fragments the nature of the
whole ; and I have thus been led to the following results,
2. If we examine the shell of a Nautilus in which the earlier
are preserved by the later whorls, we find that the shell bends
back upon itself as in fig. 1. Let ARB be the section of the
earliest stage, which in the Nautilus is nearly a semicircle.
On the growth of the shell, A B (the line inwhich the embryonic-
* Communicated by the Author.
Phil. Mag. 8. 5. Vol. 6. No. 37. Oct. 1878. R
242 Rey. J. F. Blake on the Measurement of the
shell section cuts the plane of growth) becomes D EH, and DE
subsequently GF. We have now only to suppose two laws of
growth to make both inner and outer edges equiangular spi-
rals. These are, that the shell-forming animal grows always
obliquely to its present edge, and that the outside grows at a
faster rate than the inside in a constant ratio. It is easy then
to see, by similar triangles, that all the edges will meet in a
common point C, which, when the growth becomes continuous,
is the pole of the curve which the polygon becomes. If a be
the angle between the radius and the tangent (in other words,
represent the direction of growth), we may write the equation
to the outer curve,
i 0 cot a
The initial radius is taken as unity for simplicity, the applica-
tions being always relative. The inner curve in the same way
may be written
ey)
ye? cot e,
or
— o(0—f) cot
rel 8B) co a
taking 2, the ratio of growth, to be e~*°t*. This shows that
we may consider the inner as an earlier portion of the outer
curve, and look on its growthas retarded. The two elements,
therefore, which completely determine the form of the section
are a the spiral angle, and 8 theangle of retardation. It thus
appears that the form of the central section of a Nautilus is
independent of the shape and size of the embryo, depending
only on the direction and relative rate of growth.
If, now, we consider turbinated shells, a new element is in-
troduced. The direction of growth is no longer in one plane,
but makes a constant acute angle with a fixed plane; and
this, in combination with the variable angle which the direc-
tion of growth makes with a fixed line in that plane, produces
a curve of double curvature, which, as it partakes of the nature
both of a helix and a spiral, may be called a helico-spiral.
This third constant angle, which will be the complement of
the semi- vertical angle of the enveloping cone for a fixed point
in the surface of growth, may be called the angle of elevation,
and be denoted by y. :
_ These three angular elements, together with the equation to
the trace on any plane through the pole making a finite angle
with the direction of growth thus determined, of the outline
of one whorl of the shell, are sufficient completely to deter-
mine the form of the whole shell so long as the growth is uni-
form; and these, therefore, or their equivalents ought to form
Curves formed by Cephalopods and other Mollusks. 243
part of the description, when complete, of every regular mol-
luscan shell.
3. As an example, suppose the trace elliptical, which is very
often the case.
To jind the equation to the surface of a turbinated shell of
elliptical section.
Taking the pole as origin, and the axis of the shell as that
of z, let X, » be the radial and vertical coordinates of the centre
of any one of the elliptic sections; a, b the semiaxes; e the
angle the major axis makes with that of z. Then the equation
to the ellipse is
{(z—p) cose+(r—2r)sinel? | {(r—2) cose—(z—p)sin e}
a is b?
Taking the centre as the point of reference, if y be the angle
of elevation,
p=Atany;
and if & be the spiral-angle,
A= & cot Oe
Also, if 8 be the angle of retardation of the inner end of the
major axis behind the centre,
— nee a __ 9(8—B) ney cosec = e cot iG: fae cot =) cosec €
= ¢? lq cosec e, say.
Putting b=«a and making the above substitutions, the equa-
tion to the surface becomes
Ks (z—e8t* tan y) cos e+ (r—e? *) sin eh?
+ {(2—e°* tany) sine—(r—e?°*) cose}?
ae eRCNSEE. la ete eee yet a A eA)
which may be immediately transformed into one between «x,y,z
y
by the substitution of «+? for r*, and tan’ for 9, or into
a polar one by substituting pcos ¢, psing for z and r; which
will bring it into harmony with the more general functional
but unmanageable equation given by Professor Moseley. In
most cases, except among the Gasteropoda, e may be assumed
= ee
4, By giving different values to the constants in this equa-
tion we can obtain all the varieties of shells of elliptical sec-
tion, and in a similar manner those of any other form of
section. Thus for all the Brachiopoda the value of y is zero.
In both these and the Lamellibranchiata ¢ is never much less
than unity, and often greater; and at the same time « is small
R 2
2
=i
244 Rey. J. F. Blake on the Measurement of the
and equal in the two valves among the Lamellibranchiata, but
greater in the ventral valve among the Brachiopoda. The
various forms among the latter class are produced partly by
changes of form of the tracing curve, partly by differences in
the value of o. Thus such transversely oval forms as Obolus
have approximately «>1, and the inner edge coinciding with
the axis, or c=1; while elongate ovals, as Siphonotreta, have
kK<1. Where the hinge-line is straight, as in Spirifera and
other genera, the ellipse, in which usually «>1, overlaps the
axis, and consequently ~<a, which involves ¢>1; to ob-
tain which the angle of retardation must be imaginary, as it
must be therefore in all shells in which we assume a curve
cutting the axis. Then also the ratio of growth of the inner
edge, which does not, so to speak, exist, is imaginary ; but o,
with which we have practically to deal, is real. We can in
these cases nevertheless speak of the angle of retardation as
being that of the centre over the outer edge, unless the centre
itself is on the negative side of the axis, when the phrase be-
comes useless and g is negative and >1. In such conical
forms as Discina « is nearly zero, and y has a moderately
small positive or negative value, the latter corresponding to
the flat valve. When, as is usually the case, the two valves
turn in opposite directions, we must reckon « negative in the
dorsal valve ; but when that valve is concave, as in the Pro-
ductide, « is still positive, but has a different value, less than
that of the ventral.
In the Lamellibranchiata these same differences are com-
bined with a very small but not zero value of y. They all, with
few exceptions, principally among the Ostreide, have the
values of a of epposite sign in the two valves, and they pre-
sent a greater variety of tracing curves. Their values of a,
however, are larger than we find among the Brachiopoda,
whose maximum values belong to the Pentameri. Of this we
have notable examples, combined with a considerable value of
y, in such shells as socardia and Diceras, and with a very low
value of y in Caprinella.
Among the Gasteropoda (for a considerable number of
which the value of « has been observed by Professor Nau-
mann), we have «=O for the limpets, while 8 is very small
for the Dentaliade and very large tor Haliotis. The suitable
values for the other mollusks (the Pteropoda and Cepha-
lopoda) will immediately suggest themselves—as we may say
generally that the curvature depends on a, the involution on P,
and the elevation on y. |
The direction of the major axis of the generating ellipse in
Gasteropoda is generally oblique—being approximately parallel
-
Curves formed by Cephalopods and other Mollusks. 245
to the opposite slope of the shell in those with a small apical
angle, and parallel to the adjacent slope when the vertical
angle is large, becoming parallel to the axis when y=0. It
has also the same direction in Turrilites.
5. To find the conditions that the whorls should intersect on
the same or on opposite sides of the axis.
In equation (A) put z=7 tan y, whence
(r— te) Vx(tan y cos e+ sin e)” + (tan y sine—cose)?
== a Kae“ eosee €,
or
paeneted 1x KO COSEC € COS \.
sin (e+y)V «* + cot? (e+y)
If the whorls touch on the same side of the axis, the larger of
these values must equal what the smaller becomes when 0 + 27
is written for 0—if they cut, greater—if out of contact, less,
since the similarly placed ellipses must touch if they meet on
the line joining their centres. The whorls therefore intersect
or not according as
a Ko COSC € COSY
sin (e+) «+ cot? (e+ 7)
> or <erentad oe KO Sune ?
sin (e+y)V «+ cot’ (e+y) 5S
as
Ko COSC € COSY e2m cota __]
: : ee PP) (IS eae 1
sin (e+y)V «7+ cot’(e+y¥) ermecota 1 | (1)
If corresponding whorls on the opposite sides of the axis
touch, the greater value of z when r=0 in equation (A) must
equal the smaller value of z when @+7 is written for 0, and r
again put equal to 0, since it is easily shown that if the two
ellipses meet on the axis they must touch. The condition for
this may be deduced in a similar manner to the last ; and we
find accordingly that shells are umbilicated or not according
as
{(«’ cot” e+1) tan y+ cot e(x?—1)}(e™~t*—1)
> or < cosec’e kV a(x’ cot?e+1)—1(e™*+1). (2)
Such an umbilicus, however, will be spiral ; a straight one,
caused by the generating curve not meeting the axis, will exist
when the radical is impossible, 7. e. when
oV« cot?e+l<l.
246 Rey. J. F. Blake on the Measurement of the
Very few shells make the expressions above compared equal
to each other. Cyclostoma and Scalaria are examples in which
this nearly happens in both cases. Some Turrilite also ap-
proximate to making (1) an equality, and (2) somewhat less
closely.
As an example of the application of these equations, the
shell of Cyclostoma elegans may be taken. Jn this the value
of y, ascertained by measurement, is 783°, e= 156°, «=°87315,
and o may be calculated, either directly from the equation
defining it or by methods to be presently noted, tobe 46. Also
erecta by observation = a Substituting these values in
9
Ko COSEC € COS Y
sin (e+) Ve + cot(e+y)
we obtain ‘216 approximately, while
E27 cota __ 1
gratag ol
The whorls therefore, according to this calculation, are slightly
out of contact; and it will be seen in the shell that the outline
deviates slightly from the elliptic form in order to bring them
into contact. Similar substitutions in the expression of (2)
make the left-hand side 2°679, while the left is -841. The
whorls therefore cut the axis, but leave a spiral umbilicus.
6. In the case of discoid shells we need only discuss the
condition of contact on the same side of the axis. Here y=0
and e=90°, and (1) becomes
e27 cota
| o> or <Greotay ]’
showing that contact or overlapping is independent of the shape
of the whorls. Indeed it is obvious that they will be in con-
tact or not according as the retardation of the inner edge is
greater or less than 360°. As the retardation increases from
this value the whorls more or less overlap, becoming com-
pletely involute when # is infinite, in which caseo=1. When
the axis is cut by the whorls, as in the case of the Nautilus,
whose shape is best represented by half an ellipse rapidly
rounded into the umbilicus, the inner edge of the major axis
becomes non-existent, 8 beingimaginary. It is by the varia-
tion of this element alone that such genera as Crioceras and
Gyroceras are separated from Ammonites and Nautilus. They
are therefore less distinct than Turrilites and Toxoceras, which
differ in addition by the whorls of the first always cutting
ee i.
Curves formed by Cephalopods and other Mollusks. 247
the axis. The genus Trochoceras indeed lies between them
in this respect.
7. Similar methods to the above may be adapted to other
generating curves besides the ellipse. For the circle, of course,
we have only to putt=1. In many cases no simply expressed
equation can represent the shape; but there are a few that do
admit of this. Thus, in the Ammonites of the group Cordati
the curve is nearly represented by the cardioid whose equation
is
p=a(1+ cos ¢).
Here the retardation of the pole from the apex being
Zoe “a ePeota— |) — Joe say, and tany—0,
the equation to such an Ammonite will be
ip—e) *)(¢—(1 ati Gye ote) ai ZV CR (7 — eB cota)? + 2°} d
8. It is to be noted that, if a plane section through the
middle point of growth have an elliptical or any other curved
outline, the trace on any other plane through the same point
will not be of the same character ; and though the assumption
(say) of an elliptical section in a plane perpendicular to the
direction of growth of the middle point may be as near an
approximation to nature as the one chosen, and the corre-
sponding equation may be worked out, yet the results are
quite unmanageable, and have no particular relation to the
laws of growth already enunciated. The curve assumed in
the above investigation is that exposed by a longitudinal sec-
tion of the shell through its axis. It has therefore no neces-
sary connexion with the form of the aperture, which may be
in another plane, or, indeed, have a curve of double curvature
for its outline.
This difference is particularly to be noticed in conical shells,
such as the Orthoceras, which correspond to the value «=0.
In these we cannot take a plane through the pole (i. e. the
apex) as the surface of growth. Nor can we consider one
side more retarded than the other. Fundamental differences
are thus revealed between the laws of growth of such shells
and those which are curved. We may, however, connect them
both theoretically and by natural links. To turn an equian-
gular spiral about its pole through a given angle is to bring
an earlier point in the curve into any particular radius; so
that the apical angle of a conical shell corresponds to the
angle of retardation in a discoid one: only in the latter case
the inner curve stops on the extreme radius of the outer, while
in the former it is continued to be of the same length. In
some Cyrtocerata and in the opercula of Gasteropods we may
248 Rey. J. F. Blake on the Measurement of the
have a curved shell (see fig. 2) in which the ornaments ap-
proximately run at a constant distance from the pole, while
the septa approximate to a radial direction. Thus one law of
growth is illustrated by the inside and another by the outside,
9. The several elements of the shell have hitherto been con-
sidered constant; the results of their variation may now be
indicated. The rapid increase of « produces such shells as
(QHkotraustes, a subgenus of Ammonites; and the rapid diminu-
tion to zero, Scaphites, Ancyloceras, and Lituites. Its more gra-
dual increase with age is shown in Pupa and some Bulimi;
and its diminution in many Orthocerata, which are curved in
youth. An increase of 6 alone produces a more involute shell,
as many Goniatite and Bellerophon expansus—and in combi-
nation with a decrease of a, shells such as Succinea and Siga-
retus. Its decrease contracts the body-chambers of many
Orthocerata. Analteration of y, combined in some cases with
an alteration of a, takes place in all those Gasteropods whose
whorls cannot all be touched by the same cone, and whose
spire may be called concave or convex. As the former is the
the commoner of the two, it follows that y most often decreases
with age. The changes in Vermetus and Siliquaria seem to be
brought about by an increase in y alone. Its rapid decrease,
on the contrary, bringing it to a negative value, produces the
depressed spires of some Cones and of the Cypree. When
all three vary simultaneously, the effects may be so masked as
to be ascertainable only by careful measurement.
In the Cephalopoda, which have part of their shells parti-
tioned off, some authors give among the characters both the
length and the capacity of the body-chamber. ‘These two are
evidently deducible from each other, whatever may be the
shape of the shell, provided its growth continues constant;
for if the length of the body-chamber =(1—«) whole length,
the capacity =(1—x’) whole capacity: if therefore it can be
measured independently, it will show if any contraction or
expansion has taken place.
It remains now to show how the three elements of shells
may best be observed, and especially on imperfect specimens
such as fossils very commonly are.
10. To find the spiral angle of a discoid or turbinated shell.
Since in a turbinated shell all the radii from the apex and
arcs of the curve lying on one cone are multiples of their pro-
jections on the plane perpendicular to the axis, we need only
consider discoid forms at first. Let. A BCD (fig. 3) be sucha
form; AC, B D two diameters at right angles through its pole.
Then, from the properties of the equiangular spiral, it is obvious
that we have a choice of several methods of determining e, by
\.. ae
Curves formed by Cephalopods and other Mollusks. 249
which results may be checked, or the angle ascertained on
small fragments of the shell; and since the outer and inner
curves have the same angle, observations on either will suffice.
Thus e7°'* is given by any of the following ratios :—
AO AE EO EK |
Ter ee. OG Nez
so e™te is oven by ae , a value chiefly useful for fragments ;
and ¢2°"” by
BO en OG © NEG
BD’ HD’ FH’ FL
The first of these series gives the best result on unornamented
shells, and the second on ornamented. To facilitate the ob-
taining the angle from the observed ratios, the following Table
of solutions of the equation cot «= pg aH has been prepared,
sy
which may at once be applied to the others by squaring or
extracting the root :—
. oO
Table of Solutions of cote= 228
ey || B - || ® ise eee ees, MON a
| Oo 1 ° i | ce) i O° i
101 | 89 49 || 1:26 | 85 48 || 1-51 | 8232 || 1-76 | 79 48
102 | 8938 || 127 | 8539 || 1-52 | 8224 || 1-77 | 79 42
103 | 8928 || 128 | 8530 | 1:53 | 8217 || 1-78 | 79 36
104 | 8917 | 1-29 | 8522 || 154 | 8210 || 1-79 | 79 30
105 | 89 7 || 1:30 | 8 14 || 1:55 | 82 3 |, 1:80 | 79 24
106 | 8556 || 131 | 8 5 || 156 | 8157 || 1:81 | 79 18
Pe esas 132° | 84 57 |! 1:57, || 81 50 || '1-82' | | 79-12
108 | 8836 || 133 | 8449 | 1:58 | 8143 | 1:83 | 79 7
109 | 8826 || 1-34 | 8441 || 1:59 | 8136 | 1-84 | 79 1
110 | 8816 || 1:35 | 8433 || 1:60 | 8129 | 1-85 | 78 55
111 | 88 6 || 136 | 8425 | 1-61 | 8123 || 1:86 | 78 49
1:12. | 8756 || 137 | 8417 || 1-62 | 8116 || 1:87 | 78 44
Vig | 87 46 || 1:38 | 84 9 || 1-63 | 81 10 || 1:88 | 78.38
114 | 8737 || 1-39 | 84 1 || 164 | 81 3 || 1:89 | 78 33
115 | 8727 || 1-40 | 8353 || 1-65 | 8057 || 1:90 | 78 27
116 | 8718 || 1:41 | 8345 | 1-66 | 8050 || 1-91 | 78 22
117 | 87 8 || 1-42 | 8338 | 1-67 | 80 44 || 1-92 | 78 16
1:18 | 8659 || 1-43 | 8330 ||. 1-68 | 8037 || 1-93 "| 78 11
1:19 | 8650 || 1-44 | 8323 || 1-69 | 8031 | 194 | 78 5
1:20 | 8641 || 1-45 | 8315 || 1-70 | 8025 || 1-95 | 78
¥21 | 8632 || 146 | 88 8 | 1-71 | 8018 || 1-96 | 77 54
122 | 8623 | 147 | 88 || 1-72 | 8012 || 1:97 | 77 49
123 | 8614 | 1-48 | 82 53 | 173 | 80 6 | 198 | 7 44
124 | 86 5 || 149 | 8246 || 1-74 | 80 199 | 77 39
125 | 85 56 | 1:50 | 8239 || 1-75 | 79 54 || 2 77 33
When the ratio is > 2, we generally have to deal with evolute
250 Rev. J. F. Blake on the Measurement of the
shells, in which the angles of the different species do not lie
so close together ; and the following inverse Table will be suf-
ficient to check the direct measurement of the angle by the
observation of ratios :—
Table of Solutions of R=e7™*+,
a. Lie a. | R. a R.
fe}
89 1:06 69 3°25 49 11°8
88 1:12 68 3°44 48 12:7
87 1:18 67 3°66 47 13°7
86 1:25 66 3°88 46 14:8
85 1:32 65 4:12 45 16-0
84 1:39 64 4°38 44 17°3
$3 1:47 63 4°66 43 18°38
82 1:56 62 4:95 42 20-4
81 1:65 61 yo feeea|| aterm 22-1
80 1:74 60 562 || 40 24:0
79 1-84 59 599 all 739 26°3
78 1:95 58 6°39 38 28-7
a 2-05 57 6°82 37 31°5
76 2-16 56 7:28 36 34°6
795 229 eae 778 30 38:0
74 243 | 54 8°32 34 42-0
73 2-55) oil) oe 8:92 33 46°4
72 DF) | eee 9:55 32 51-4
71 2°89 51 10-3 31 57°3
70 3°06 50 11:0 30 64:0
11. These methods suffice for recent or complete shells ; but
sometimes a fragment of a single whorl is all that is presented
to observation, in which case there are two or three possible
methods.
1st. Suppose the inner as well as the outer edge of the
whorls preserved, as A B, C D(fig.4). Then, if we draw any two
parallel tangents, as EG, FH, the straight line joining the
points of contact must pass through the pole. Hence GHF
is the angle required. And evenif neither edge be preserved,
any pair of longitudinal strize or other ornaments will suffice
for the purpose.
2nd. Let the directions and lengths of a pair of transverse
ornaments, which we may assume to make the same angle
with the radius, be available (fig. 5) as AC, BD. Then the
angle between AC, BD equals the angle between the radii,
=6 say: we have therefore AG = cote. which oivesiea: am
terms of known quantities. |
3rd. Let the outer edge alone be available. Here we have
the simple problem, Given an arc of an equiangular spiral, to
find its pole and spiral angle. This admits of two easy solu-
tions :—
Curves formed by Cephalopods and other Mollusks. 251
(1) Let two tangents DB, DA (fig. 6) be drawn to the
curve. Then, if O be the pole, since OA D, OBE are equal,
a cirele described round DBA will pass through the pole:
this point may thus be determined by the intersection of two
or more such circles and the angle e=D BO observed. This
method, though theoretically simple, requires so much accuracy
in determining the actual points of contact of the tangents as
to be generally inapplicable.
(2) If p1, p2 be the radi of curvature at two points of an
equiangular spiral, and s the arc between them, then
cota = MP2.
S
Now the value of p, at A can be very closely approximated to
by measuring the distance AC at which a constant small offset
CD is made by the curve ; and this accuracy may be increased
if the offset be small enough by placing it on both sides of the
point of contact, and assuming the point to be midway between
its two positions. If AC =2,, and the offset pw,
2 2
A= pedal approximately ;
2h
whence, if 2 be the corresponding distance of the same offset
when the tangent is at B,
2 2
HX: dk
ona = Le
pes
If 2s be chosen to be 100 units, the calculation is very simple,
and gives results closely concordant with those derived from
the complete shell.
12. These formulze may be exemplified on Ammonites ob-
tusus. ‘Two diameters at right angles measured 224 and 188
millims. respectively, whence e2 *'*=1:19, or R=1:41. Two
others measured 208 and 176 millims., whence R=1°39. The
breadths of two whorls along the same diameter measured 76
and 56 millims., whence R=1°39. Two others were 64 and 46
millims., whence R=1°39. ‘Two parallel tangents were drawn
and the points of contact joined ; these made an angle of 834°
with the tangents when care was taken that the tangents
should be at similar points, the outline of this Ammonite being
slightly polygonal. With the same precaution, an offset of 5
millims. was 353 millims. on each side of one point of contact:
at another, distant 187 millims. of arc, measured by carefully
rotating the shell along the ruler, the same offset was 324 mil-
lims. on each side; whence cot a=1:079, whence a=83° 50’.
Extracting from the table the angles corresponding to R=1:39
252 Rey. J. F. Blake on the Measurement of the
and R= 1-41 and taking the mean, we find the angle a= 83° 52’.
This example will illustrate the amount of coincidence that may
be hoped for from careful measurements.
13. All these methods lead, of course, to erroneous results
when the shell has suffered distortion, except those derived
from measures taken along a single straight line. Tor ex-
example, the value derived from the ratio = ought to give
D
the same result as a (fig. 3), whatever the distortion: butthese
ratios will not be the square of HD’ If the shell has been
elongated in the direction AC in the ratio 2: 1, we have
AK’ — pm cota A :
Pum eky Mivahnta am GAO),
whence a Ae
i AE GC
HD FED
which gives a measure of the distortion.
An example of this may be taken from specimens of
Goniatites, which are often distorted, in which state they
have been called Hilipsolithes. Four whorl-breadths at right
angles were measured at 20, 174, 144, 122 lines respec-
; Al HD a
tively, whence aq 1h 878, BE =1°372 (fig. 3), the differ-
ence being due to errors of observation on ill-preserved shells.
The mean may be taken as 1:375 for the true ratio. The
: . Ale Ea
values of the ratio derived from squaring the ratios HD’ Go
as respectively are 1:306, 1:456, 1:293. The first and third
of these differ only from errors of observation: but their va-
riation from the true ratio is such as would be produced by
distortion, the value of which is either , 1306 _.947 or
1-293 | geet
1456 ga U4 ; that is, the diameter of the shell in the di-
rection AC has been diminished by compression in the ratio
“94, A
14, The value of the angle of retardation depends, of course,
on the two points assumed. When the section is an ellipse,
and the centre and extremity of major axis are compared, it
depends on the length and:position of the major axis. Butin
the more general case, whatever be the shape of the curve,
especially if the whorls intersect, and in discoid shells, it is
Curves formed by Cephalopods and other Mollusks. 258
more convenient to compare the outer edge with the intersec-
tion of the whorl with the one next to it inside.
To determine the angle of retardation of the inner edge behind
the outer in a discoid shell.
This element is given by the ratio of the umbilicus and of
the outer whorl to the diameter. If and wp be these ratios,
1 —eBeota
Hea F coke, b= eC
whence 4
8 log R= —T log» and — ire sa
or 7 logr
BS log (1—’—p) — log w
In the description of Cephalopoda we often meet with such
an expression as “ inner whorls two thirds concealed.” Ifthe
inner whorl be concealed in the ratio of 2: 1,
e727 cota __ p—Bcota 1t—RAX
C= e727 cot &__ p(—B—T) cot a = A 3
whence, if R is known, \ and then @ may be deduced; which
might sometimes be convenient in the case of a fragment. In
this case, however, another method may be followed. If },
and b, be the lengths of two lines measured in the direction of
the radii, and s the are of the outer curve between them,
then
b; —bg=s cos a(1 —e7Ft*),
_As an example Ammonites margaritatus may be taken. In
one diameter of the septate portion of the shell, of length 1664
millims., the umbilicus was 51 and the last whorl 72; this
gives X = 307 and w =°432. In another perpendicular dia-
meter of 131 millims. the umbilicus was 424 and the last
whorl 55; whence AX=°'324 and w="41. The values of Rde-
duced from these are 1:65 and 1°64. The decrease in the value
of ®X and the corresponding increase of u shows that this spe-
cles grows more involute with age; in other words, 8 varies.
In the earlier whorls it is 820°. It might be thought that
Professor Naumann’s conchospiral would in this instance pro-
duce closer approximations to the observed values; but the
value of R deduced from the radii at right angles is 1°69;
whereas it ought to be less than that derived from whorl-
breadths, if the inner and outer curve were both conchospirals.
Another example taken was Turrilites scheutzerianus. Here
the diameter at the last whorl was 56 millims., the penultimate
diameter 43 millims. ; the last whorl had a horizontal breadth
254 Rey. J. F. Blake on the Measurement of the
of 29 millims., being a vertical ellipse. In this case the um-
bilicus, not being approximately in one plane, has to be cal-
culated: we obtain R= 1378, whence
A=1 (1+ qare):
56 1378
log Arie dsb (oslo eee E
PTR aogR "05626 eae
or the inner edge of the shell represents the surface nearly
fifteen whorls behind.
The other two formule may be illustrated on Ammonites
leviusculus. The measurements along one diameter of 50
millims. were—outer whorl 214, umbilicus 14, remainder 142 ;
whence R=1°47 and 7X='28. Substituting these values,
we obtain z= ee — = ‘67. From actual measure-
ment the whorls are 74 concealed, 7. e. °66. The value of a
corresponding to R=1°47 is 83°. The breadths of the whorls
at two points distant 67 millims. of arc are 143 and 20 mil-
lims. respectively ; whence
5°6667 =67 x ‘1218 (1—2),
which gives X='32. This latter measurement is the least
trustworthy, especially if the direction of the radii cannot be
accurately ascertained.
15. In turbinated shells whose elliptic axis is oblique, we
require to know the retardation of the inner extremity of the
major axis, i. e. the value of o. This is best done by compa-
ring the diameter perpendicular to the axis with the major
axis of the last whorl. To determine this diameter we must
add the two radii obtained from the condition that z shall have
equal roots in the equation A which correspond to @ and @— a.
This condition gives us
p=eiete | +oV/ x’ cot?e+1).
The smaller of these values corresponds to the radius, if any, of
the open umbilicus, as in § 5; the larger is the one we require.
Therefore, if d be the measured diameter,
d= cP (1 + e-7*) S14 Ve cot Pe +1;
and since a=e' oa cosec e, ;
do cosece=af1+e-7#t {1 +0V 2 cot? e+ 1}.
For example, in the Cyclostoma elegans before mentioned,
Curves formed by Cephalopods and other Mollusks. 255
d=12 millims. and a=3°7; also iis
e='87315, e=156°, R= =
w. 12 x 2°45860=3°7 x 180178 $1 +02°2216};
“. 14°6926c=6°6666, and c=°46.
The value of o may also be calculated from an equation, to be
given hereafter, for determining the angle of elevation y from
the angle of the tangent cone, whenever the value of y can be
measured directly.
16. In the case of the conical shells of the Orthocerata, in
which we can no longer speak of the angle of retardation, but
must measure the apical angle of the cone, the above methods
are not applicable. Here, however, the apical angle can
always be directly observed on the sides of the shell: or if it
have a known number of longitudinal ornaments, by taking
that multiple of the angle between two of them and dividing
by 27 we obtain the sine of half the required angle if the sec-
tion be circular. It may also be obtained for any particular
plane, whatever be the section, by the formula
d,—d, Gm B . ° B
D5 = tan 5 or sin 5?
if d,, d, be two diameters in that plane, and s the distance be-
tween them measured either on the axis or on the slant side.
It would be unnecessary to remark that it is the difference
and not the ratio of the diameters which gives us the apical '
angle, were it not that this ratio is given by some paleeontolo-
gists among the shell-characters, where of course it is per-
fectly useless. Methods quite analogous may be used for
curved shells where the pole is known. For if with pole as
centre any circle be described cutting the two curves, the angles
between the tangents or between the radii corresponding to
the points of intersection will be the 8 required. Or if d,, dp
are the distances between these points for two circles,
d,—d, aS a8 B dy—dy _ . B
a) ae 9, Sing «cosa,
71, 72, being taken on either curve (see fig. 8).
If the transverse section of a conical shell is elliptical, the
apical angle will not, of course, be the same in the planes of
the major and minor axis, though, the ratio of these being
constant, one angle may be deduced from the other. When
curvature takes place in the plane of the major axis, the curves
formed by the ends of the minor axis do not lie in one plane,
\
256 Rey. J. F. Blake on the Measurement of the
14+”
: 1—
the major axis being supposed to be perpendicular to the axis
of the shell. This, of course, is not the tangent cone to the
whorls. It follows that if the curves in the plane of the major
axis remain regular, and yet one plane can be made to touch
the surface at the extremities of all the minor axes, the shell
must either be unsymmetrical or the shape of the section must
vary ; and the latter will certainly be the case when two such
planes can be found. We cannot, therefore, measure the apical
angle of a Cyrtoceras or Dentalium, in a plane perpendicular
to that of the curvature, with perfect accuracy.
17. When a discoid shell has suffered distortion (that is,
compression in the plane of the major axes), @ may still be
found if more than half a whorl be left ; but no method sufh-
ciently simple to be of use can give either « or 8 on distorted
fragments. A more important case is when the compression
is perpendicular to the plane of the major axis. This has no
effect on a, but increases 8 at the expense of x. In measuring
the apical angle of Orthocerata, we therefore require the fol-
lowing :
Given the semi- vertical angle of a cone of elliptical section
when the excentricity of the section is e, to find it when the
same is compressed so that the excentricity is e’.
Describe a sphere with the vertex as centre; then the cone
will cut this sphere in a curve of double curvature, the length
of which will remain constant when the excentricity is altered,
since the area of such a cone will be unaltered by compression.
If 7—2w be the vertical angle of the cone in the plane of
but on a cone whose vertical angle 2dis given by cot 8=x
the major axis 2a, and h the height, then : = tan o.
Let ¢ be the complement of the excentric angle at any point
of the ellipse, whose excentricity is e, and p the radius from the
centre of the section 6, do the element of the arc on the sphere,
ds of the ellipse, d@ the angle between p and p + op, A the radius
of the sphere; then
do = Adé,
p'd?? = ds’ — dp’,
and p= Vi? +a*(1—e’ cos’ db),
and ds=aV/1—e’ sin? dd;
. doagv ¥ AGA) Shean
i? + a?(1—e cos’ d)
pong J/ sec? w —e?(1 + tan? w sin? ¢)
®) J
sec? a —e’ cos’ h ,
Pag,
Curves formed by Cephalopods and other Mollusks. 257
whence the required relation deduced from the equality of the
areas is
(? / sec? w —e?(1+ tan? w sin’ d) dd
0
sec? w—e” cos’ d
_ (5 V sec? w/ —e(1 + tan’ o’ sin Pag
i sec? w’ —e” cos’
The impossibility of exact measurements on fossil shells
which have been compressed renders the working out of these
integrals, representing the correct solution of the question, a
waste of time, if a fair approximation may be made some other
way. No very close approximation which is practicable to
work has been found. If, for example, we take for the length
of the are the sum of the chords subtending the arc of a
circle passing through the ends of the major axis and the sphe-
rical projection of the minor axis, and if a, w; be the angles
subtended at the centre by the semiaxes, then
tan Wo
== ’
tan @,;
and
A(1— cos @; COs @»)
radius of circle = ——
/ 1—2 cos @, COS @) + COS @1
COS @, (COS W)— COS @1)
1— cos @, COS @2
oe Oy / / 2(1— cos @; C08 @2) — sin a; ,
4” 2/ 2(1— cos @; COs @2) ;
and if the chords be assumed constant, we have
cos 6=
whence
C= (1— cosa, cosw:)? ——-2(1—cos @ cos@,) —sin a1
2(1— COS @; COS Ws ) — sin? @, x/ l-cos @1 COS W»
or :
3 } ee
(1— cos @; cos @2)? (1— cos w’; cos oy)?
/2(1—cos@,cos@.)+sino: V 2(1—cosw,/cosw,’) + sinew’,
If this relation is satisfied between two shells, one may be the
compressed form of the other.
For example, a specimen of Orthoceras annulatus has its
minor axis decrease from 20 to 16 lines in 38, the major axis
at the larger size being 32; to compare this with M‘Coy’s
description “ tapering 1 in 8,”’ the uncompressed section being
Phil. Mag. 8. 5. Vol. 6. No. 37. Oct. 1878. S
258 Rey. J. F. Blake on the Measurement of the
circular. Here
as We
8 4 16
tan @= 5 x 38 = 9R?
a
tan o/, = tan o’,= 3
In this case the two above expressions become respectively
‘0071 and :0048. Hence the tapering in the compressed shell
compared is more rapid. Ifa conical shell be perfectly flat-
tened and its transverse ornaments become circular ares, the
length of any semicircumference =7ra gives the original dia-
meter of the shell when circular.
18. In the case of a curved shell of elliptical section being
compressed perpendicularly to its median plane, we may
assume that the area remains constant, and find the effect on
the angle 8.
If a=e°t*o, the element of area
= e%eota gr/ 1 —e* sin? 6dd(1—o sin $)dé
when ¢ is measured from the end of the minor axis towards
the pole, and the same with 1+osin ¢ instead of l—osing
when measured away from the pole. Integrating with respect
to @ between the limits @ and —«, the area may be written
oe29 cota is
Jeota | ¥ 1—e’ sin’ h(1 +e sin $d.
g
Now, denotin “| /1—e’sin? ddd by H(ed) as usual, and
( /1—e’ sin’ ¢ sin ddd by M(ed),
2/9
6 cota
oer) cot ZC z) + H(ed) + oM(e 7 )—oM(ed) \.
Hence, # remaining unaltered, the condition that a compressed
and uncompressed shell may belong to the same species is
o(¢ z) +oH(eg) + eM(0 = —o(Med) = { o/E(e z)
i o/H(e’¢’) ah o"M(e! 5) — a" Me’) le cot «(8'—8) (1)
area =———_
2 cota
Curves formed by Cephalopods and other Mollusks. 259
To find M(e@), put cosd=z ;
: Pint sin d sin d6dd= cle s
=— 8) vI-e tee ae
2te
When
ate a+ = ee
MSU, w=sls
ee SERS 5
, M(ep)=$ { = + ~ log (1+ +) — S88 y [=e sin?
eer iL SS
: log (cos $+ = VI=e sin? d
—e f ecos@+ /1—e’sin ¢,
Ze
=1.(1—cosdvV 1—e’sin?¢ Ts
consequently
7 bees ae
M(e 5)=3 7h logiz
It now remains to determine o and ¢ in terms of R and A,
and @’ in terms of 6. If 6, ¢, be the complements of PBN,
PAN respectively, we have from the figure (fig. 9),
o sin @=(1—A— do)( = | (2)
R’ sin ¢+ sin ¢,= <> (= — oe (G)
R? cos $= cos $,(=Gp): coke he ee a)
from these we obtain :
Seer ed <i Weestioan al Dn ee,
By the compression of the shell the radii, and therefore the @’s
corresponding to them, will be enlarged ; and this will take
place so that the sum of the ares of the ellipses i in one plane
may be constant. This gives
cdots fu (o7)4 BBCH+HCS, }
2 Ley /
i), cto B(e'S) += K(e pee ,) iy (6)
whence, making the necessary substitutions in (1), we obtain
the condition for identity. te
Lee ae
260 Rey. J. F. Blake on the Measurement of the
When the whorls do not intersect, we must put o=5 in (1)
and cancel the fractions in (6): the rest are not required.
The only important application of these conditions is when a
shell has been completely flattened in shaly beds. In any case
crumplings of the surface may be induced by resistance to
lateral expansion, when the expression for the area of the com-
pressed shell will come out less than it ought; but if it comes
out greater, the two shells compared could not have had the
same original form. An example may be take in Ammonites
planorbis, which, when uncompressed, has been called Ammo-
nites erugatus. In an example of the latter we find R=1:33,
rX='431; whence by (5) o=:449; and by (2) sn d="838.
The last whorl on which these measures were taken was 10°83
millims. in breadth; .°. 10°833—a=°838 a, or a=5°894. The
thickness of the same whorl was 8°33 millims., whence e=°7065.
The elliptic integrals are best observed directly by measure-
ment of the arc; and if the values differ slightly from the
theoretical values, the correction has probably to do with the
deviation of the form from a perfect ellipse. In this case
204 E (2-5) +E(e) iN
= the circumference of the whorl between its intersections
with the inner whorl = 26 millims, whence
E (c,5) + E(e/p) = 2-205.
Also, on substitution,
M(o$)="408, and M(e,2) =-811.
Hence the first side of equation (1) becomes 1:071. In the
flattened shell as seen in the type, R=1-33 and A\/=:384,
whence o/=°49 and o’ sin ¢’="428. Also, e’ being unity,
m
E (C = + E(e’,¢)=1+sing’, and Mp) =,
Mi (c, o) = 4.
Hence the second side of the equation reduces to
1°:038 y e2(8'—8) cot a
Now we have seen that
u («, 3) + E(e, 6) =2°205 ;
and
Curves formed by Cephalopods and other Mollusks. 261
and by direct measurement we find that
Ke, ¢) + Ee, $,)=1°087 ;
whence, from (6),
e2(9'—8) cot « 17139
(the coefficient on the right-hand side becoming 1+o’). The
second side of (1) becomes now 1:184. This value does not
agree sufficiently with 1:071 for the difference to be due to
any errors of observation; and it follows that Ammonites pla-
norbis was produced from a more inyolute shell than that called
Ammonites erugatus: and such more involute varieties occur
in the south of England.
19. To find the angle of elevation in a turbinated shell.
The point in the tracing-curve whose angle of elevation is
measured must, of course, depend on the shape of that curve.
When it is such as to form a complete cone, as in Hulima, the
angle for any point on the surface is directly measurable.
When the curve is such as the ellipse, the angle measured by
the tangent lines does not correspond to the y already used,
but is connected with it by an easily expressed relation ; for
if w be the semi- vertical angle of the tangent cone, the equa-
tion (A) must give equal roots when rcot@ is written for z,
which requires that
tan y= cotw+avV «(cot cote+1)?+ (cot a— cote)’.
When, as is often the case, w=e, this reduces to
COosS@+oK
CU a ae aie
It is obvious that when @ and y can both be observed directly,
this gives an equation to find a, as noted in § 15.
An example of the use of this equation may be taken from
the previously quoted Cyclostoma elegans. Here
o='46, w=24°, e=156°, «='87315,
whence
tan y=4°874= tan 78° 24’,
the angle derived from direct measurement being 783°.
20. The semi- vertical angle of the cone for any particular
point may also be calculated by means of other angles often
more easily measured. Let be such an angle, andi the angle
between the tangent at that point and the axis. Let AB (6c)
be an element of the curve at that point, DB its projection on
the plane of zy (6s). Then
dz=docosi, ds=dssini, dz=drcotw, dr=dscose;
262 Onthe Measurement of the Curves formed by Mollusks.
whence
tano=cosatani. . °. . . Tae
If y be the angle between the tangent and the radius from the
vertex,
dzsec@=de cos y:
.". COS @= CostseC’y.” . |. |. =
The values, therefore, of i and y are sufficient to give o
and «. This last equation was obtained by Professor Moseley
by a different method, and the first, under a different form, de-
duced from it. It follows from (1) that 7 increases with in
the same shell, and hence that the angles must be measured at
corresponding points. In the same way y is dependent on o,
since from (1) and (2) we may deduce
tany=tanesine. . . 2 7
The angle y is the only one which can be an pe on
specimens, and 7 only on figures. The “sutural angle”
ployed by D’ Orbigny i is different from either of these, bisinld
the angle between “the line joining the ends of two radii cor-
responding to 6 and @+7a7 with “the smaller of them. The
connexion of this with the drawing of the suture is only ap-
proximate, as the latter does not lie in one plane. If be
this angle, we have
e= cota — sin v 5
sin (+20)
or
’Rsin 2@
tan b= 12 Bean ° ‘Det . ° (4)
If w be found from the tangent lines to the shell, w must be
measured from the points of contact and not in the suture—
whence the term “sutural”’ angle is inexact for a second
reason. This method has the advantage, however, of being
applicable to very little more than a complete whorl, the rest
requiring one and a half. When less than one whorl is pre-
served, it is sometimes possible to measure the angle between
the projections of two tangents to the curve at points separated
by half a whorl, on a plane through the axis perpendicular to
that containing them, i i. e. between BG (fig. 10) and the corre-
sponding line on the opposite side. If 2 be this angle, we
have
dz
eT ee cot w tan a.
rd
One important value of these equations is to serve as a
check on the separate measurements, and thus to gain obser-
tan d¢=
On the Matter composing the Interior of the Earth. 263
vations for drawing an average, as there is no doubt that
spiral shells are not absolutely geometrically constant, and all
measures are therefore more or less approximate.
One example of their use will suffice: this may be Phasianella
striata. In this we have w=16°; i by observation is 79°.
Also R=1:2; to this value corresponds in the Table 86° 41’.
Substituting these values of w and « in (1) we obtain i=78° 41’.
Again, substituting in (4) for Rand a, we obtain ~=91° 36’;
by observation the same angle is 92°. These results are suffi-
ciently close to prove the regularity of the shell formation in
this case.
It has not been thought worth while to study the effects of
compression on turbinated shells, because from their shape no
assumption can be made as to the direction of pressure that
could be considered generally applicable.
XXXII. On. the Limits of Hypotheses regarding the Properties
of the Matter composing the Interior of the Earth. By HENRY
Hennessy, /’.2.S., Professor of Applied Mathematics in the
Royal College of Science for Ireland™.
qd, ROM direct observation we are able to obtain only a
very moderate knowledge of the materials existing
below the solid crust of the earth. The depth to which we can
penetrate by mining and boring operations into this crust is
comparatively insignificant ; and these operations give us little
knowledge of the earth’s interior in comparison with what is
afforded by the outpourings of voleanos. Two hundred active
volcanos are said to still exist, while geologists have established
that many thousands of such deep apertures in the earth’s crust
have existed during remote epochs of its physical history.
The source or sources of supply for all these volcanoes have
poured out a predominating mass of matter in a state of liquidity
from fusion. Evidence is thus furnished that matter in a state
of fluidity exists very widely distributed through the earth.
The supposition that this fluid fills the whole interior, and that
the solid crust is a mere exterior envelope, is usually designated
as the hypothesis of internal fluidity. From this hypothesis
_ mechanical and physical results of primary importance in ter- .
restrial physics may be deduced.
Newton, Clairaut, Laplace, Airy, and other illustrious ma-
thematicians have used an extension of this hypothesis in dis-
cussing the earth’s figure. They supposed the particles com-
* Communicated by the Author, having been read before the Mathe-
watical and Physical Section of the British Association for the Advance
ment of Science, Dublin, August 1878.
264 Prof. H. Hennessy on the Properties of the
posing the earth to retain the same positions after solidification
as that which they held before it. JI ventured, for the first
time, to discard the latter portion of the hypothesis as useless
and contrary to physical laws. I now venture to say that, in
framing any hypotheses as to the physical character of the
matter of the earth, we should not affix any property to the
supposed matter which is opposed to the properties observed in
similar kinds of matter coming under our direct observation.
Observation has disclosed that liquids are in general viscid,
and that they possess what has been designated internal fric-
tion in a high degree*. Observation has recently shown that
among the three states. of matter (gaseous, liquid, and solid)
a law of continuity exists. Observation also discloses that
gases and vapours are, of all forms of matter, the most com-
pressible, that liquids are much less compressible, and that
solids are still less compressible. Thus, for instance, water is
about fourteen times more compressible than copper or brass.
2. If these general comparative properties of liquids and
solids are admitted, it follows that in the hypotheses regarding
the earth’s internal structure we should most carefully guard
against any assumption directly in contradiction to such pro-
perties. By assuming that the earth contained a fluid totally
devoid of viscidity and internal friction, the late Mr. Hopkins
attempted to prove the earth’s entire solidity. He only proved
that it did not contain any of this imaginary fluid; but he by
no means proved the non-existence of a liquid possessing the
properties of viscidity and internal friction common to all
liquids. In the Comptes Rendus of the Academy of Sciences
of Paris for 1871 is a paper in which I have given a résumé of
the arguments against Mr. Hopkins’s conclusions as to the
earth’s complete solidity; and in the subsequent discussions
my priority on this matter seems to have been fairly and
honourably acknowledged{. Ina recent admirable work on
Geology, Pfafi’s Grundriss der Geologie, the author gives a
brief account of the bearing of astronomical and mathematical
investigations on the internal structure of the earth; and he
very justly says that the results of observation compel us to
regard the earth as for the most part fluid, in order to bring
these results into harmony with calculation. . Professor Pfaff
* As having a special connexion with this subject, see a Report by the
Author on Experiments on the influence of the molecular condition of
fluids on their motion when in rotation and in contact with solids (Pro-
ceedings of the Royal Irish Academy, 2nd series, vol. iii. p. 55).
7+ “ Remarques a propos d’une Communication de M. Delaunay sur les
résultats fournis par l’Astronomie concernant l’épaissseur de la crotite
ae du Globe,’ Comptes Rendus de Inst. France, Mars 6, 1871,
p. 250.
matter composing the Interior of the Earth. 265
attributes this conclusion to Hopkins, whereas it is precisely
that which I had long since enunciated, and is entirely opposed
to the views of Mr. Hopkins. More recently Sir William
Thomson and Mr. Darwin have investigated the tidal action of
an internal fluid nucleus upon its containing solid shell. They
have both supposed the liquid to be totally incompressible, and
the containing vessel to be elastic and therefore compressible.
They have thus given the liquid a property which no liquid in
existence possesses, and the solid a property which solids pos-
sess in a much less degree than liquids. Their hypothesis is thus
totally inadmissible as a part of the problem of inquiry into the
earth’s structure. [at once admit thata thin elastic spheroidal
enyelope filled with incompressible liquid and subjected to the
attractions of exterior bodies would present periodical defor-
mations, owing to tidal action far surpassing the tides of the
ocean. But 1 do not admit that such impossible substances
can represent the materials of the earth. My hypothesis is
that the liquid interior matter, instead of being incompressible,
is, like all liquids we observe, relatively far more compressible
than its solid envelope. A highly compressible liquid con-
tained in a very much less-compressible shell would be a hy-
pothesis more in harmony with physical observation. The
tidal phenomena of a compressible fluid, it is easy to see,
would be very different from those of an incompressible fluid.
The work done by the action of certain disturbing bodies in
the strata of compressible fluid would partly result in causing
variations of density, instead of producing tidal waves of great
magnitude. This has been already shown in the Mécanique
Céleste by Laplace, in discussing the tides of the atmosphere.
Theory shows that the atmospheric tides should be nearly in-
sensible, notwithstanding the great depth of the atmospheric
column, because the work done in the atmosphere is very dif-
ferent from what is peformed in the less-compressible water of
the ocean. Observation has fully verified this result.
3. It is admitted that the earth’s density increases from its
surface towards its centre. If its interior is occupied by a
compressible fluid, the law of density of this fluid would result
from the compression of itsown strata; just as the law of density
of the atmosphere is produced by the pressure of the upper
atmospheric layers upon those below. But instead of suppo-
sing the interior of the earth to be filled by a fluid thus con-
forming to the observed properties of fluids, both Sir William
Thomson and Mr. Darwin have applied their great powers as
accomplished mathematicians to the tides of an incompressible
and homogeneous spheroid, such as I admit to have no real
existence whatsoever.
266 On the Matter composing the Interior of the Earth.
4, The labour bestowed on the problem investigated could
scarcely be considered at all necessary or fruitful, except as
atfording an admirable illustration of the results flowing from
the employment of hypotheses framed in direct contradiction
to the fundamental conditions to which every truly philoso-
phical hypothesis must conform. It is scarcely necessary to
add, that the conclusions of Mr. Darwin, as well as those of
Sir William Thomson, cannot be considered as having invali-
dated the carefully framed hypothesis that the earth consists
of a solid crust physically similar to the rocks we are enabled
to cbserve, and a contained spheroid of liquid matter partaking
of the established properties of liquids, and physically similar
to the liquid rock poured out by volcanic openings.
5. It is with much satisfaction that I can trace a gradual
growth of more correct physical views on the questions referred
to in this paper. In ‘ Nature,’ vol. v. p. 288, a paper appeared
in which I ventured to criticise Sir William Thomson’s memoir
on the Rigidity of the Earth, in the ‘ Philosophical Transac-
tions.’ At the Meeting of the British Association in Glasgow,
Sir William Thomson acknowledged the invalidity of many of
his arguments, and requested his audience to draw their pens
through paragraphs from 23 to 31 in his paper. These para-
graphs contain statements and reasonings which J had already
shown to be inconclusive in the paper which has just been
quoted. |
In Mr. Darwin’s paper, recently communicated to the Bri-
tish Association, he admits that in discussing the precessional
and tidal phenomena of a viscous liquid, the supposition of an
elastic spheroid would lead to very different results—-that is to
say, results very different from those deduced by himself and Sir
William Thomson regarding the earth’s structure, and which
the followers of the late Sir Charles Lyell have frequently
assumed to be established. Thus the late Mr. Poulett Scrope
appears to have referred to the bearing of the mathematical
investigations alluded to, on what he calls “the sensational
idea”’ of an internal incandescent fluid beneath the solid crust
of the earth. He forgot that an idea may not be the less true
because it is sensational. The idea of antipodes was at one
time regarded as highly sensational. Those who witness a
great earthquake or a volcanic eruption are usually impressed
with the sensational character of the phenomena.
6. A traveller who was in Portugal more than forty years
since, met a woman over one hundred years of age, and asked
her if she recollected the great earthquake of Lisbon. She
replied, that it was the event of all others in her long life
which she ought to vividly recollect, on account of its impres-
On the Blue Colour of the Sky. 267
sive sensations. History also records the sensational character
of the destruction of Pompeii. If Mr. Scrope’s innuendo re-
garding the internal fluidity of the earth as “a sensational hypo-
thesis’ has any value, we should regard the events referred to
as highly improbable; yet they have been as well authenti-
cated as the most positive facts in science, and no person has
ever expressed the smallest shadow of a doubt as to their oc-
currence.
XXXIV. On the Blue Colour of the Sky. By Arraur Mason
Worrarneton, Trin. Coll. Oxford, M.A., F.R.AS., Head
Master of the Salt Schools, Shipley.
To the Editors of the Philosophical Magazine and Journal.
GENTLEMEN,
N the series of articles which Mr. Norman Lockyer is pub-
lishing in the columns of ‘ Nature,’ entitled “‘ Physical
Science for Artists,’ he broaches an explanation of certain
effects of aerial perspective and sky-colour, which appears to
me inconsistent in itself. It is, moreover, entirely at variance
with the explanation which I believe to be generally accepted
by those who have thought about the matter, and which is
stated without any reserve by Professor Helmholtz in the last
volume of his popular lectures published in 1876, in a lecture
entitled ‘‘ Optisches iiber Malerei.”” Mr. Lockyer writes with
well-deserved authority; and it is, I think, for this very
reason unfortunate that he should set before professedly un-
scientific readers (since he writes for artists) a novel expla-
nation of his own, without at least indicating that there is an
entirely different and generally accepted explanation of the
phenomena of which he is speaking ; for he alludes (p. 156, § 4)
to Dr. Tyndall’s conclusion as somewhat similar to his own.
I wish specially to draw attention to the apparent incon-
sistency of his explanation of the blue colour of the air so fre-
quently seen between the observer and a distant mountain.
In No. 4 of the series (May 30) he explains that gold is
yellow because, out of the white light which enters it, the com-
ponents at each end of the spectrum are absorbed in their trans-
mission into the mass of metal, and so there remain over only
the middle rays,which, if transmitted, appear green, if reflected,
yellow, owing to the greater quantity of the light. Clearly
he regards the colour of gold as green (or yellow), because
the other colours are absorbed. He then quotes from Pro-
fessor Stokes’s admirable South-Kensington Lecture, and
accepts his conclusion, that a poppy is red because out of the
268 Mr. A. M. Worthington on the
white light that enters it and emerges from it to be reflected,
only the red survives absorption ; the rest is absorbed in the
interior of the leaf.
So far, beyond his own explanation of the molecular group-
ings which cause this selective absorption, Mr. Lockyer has
advanced nothing new; he has dealt only with what are called
“natural bodies.”” But in No. 6 of June 6th, he apparently
applies the explanation of the colours of natural bodies to the
colour of the air between the observer and a distant hill; and
here I cannot follow him.
He says, page 155, § 2 :—
“We are in the presence of aqueous vapour competent to
be set in vibration by blue light, and because it vibrates in
this way it appears blue.’’ And in the next paragraph:—
“Tf the stratum of aqueous vapour had had a background
of bright sky, it would have absorbed the blue light of that
sky. By virtue of the principles which I have stated, the sky
would have appeared red in consequence of the abstraction of
blue light.”
Mr. Lockyer here clearly regards the molecules as abstract-
ing the blue rays ; as being set in synchronous vibration by
them, and therefore sending blue light to the eye. He can
hardly mean that the phenomenon is one of selective absorp-
tion and emission, for no vapour emits visible light until its
temperature is very high : indeed there seems no doubt that
he considers the air to appear blue by reflected light; for he
says, speaking of similar water-vapour, on page 156, §§ 2 and
3:— Let us consider, then, the action of those molecules which
absorb the blue light. :
“‘ Now, since these molecules absorb blue light, we know that
they will reflect blue light, and, practically speaking, nothing
else. Here, then, we have the cause for the blue colour of
the sky.”
Why! Mr. Lockyer has himself explained that gold is
yellow beceuse it absorbs the red and blue and reflects the
yellow light; that a poppy is red because it absorbs all but
the red; and now he says that water-vapour is blue because
it absorbs blue.
Apart from the inconsistency of this explanation, I do not
think that, as a matter of fact, Professor Stokes’s explanation
of the colours of “‘ natural bodies ’’ can be applied to the ap-
pearance of a mass of air in which particles of aqueous vapour
are suspended. The following is what Professor Helmholtz
says of the same phenomenon, translated from the lecture I
have mentioned. On page 65, § 3, he says:—“ Under the head
of aerial perspective we understand the optical effect of the
Blue Colour of the Sky. 269
appearance of light proceeding from the illuminated mass of
air lying between the spectator and a distant object. This
appearance of light is due to a slight turbidity, from which
the atmosphere is never quite free. Whenever there are scat-
tered through a transparent medium small transparent particles
whose density and ability to deviate the light are different
from those of the medium, these particles turn aside out of its
direct course any light which falls upon them in traversing
the medium, and, partly by reflection and partly by refraction,
‘ disperse ’ it in all directions, to use an expression of optics.”
After mentioning, as sources of turbidity in the air, dust, smoke,
organic matter, water-vapour on the point of condensation,
and the presence of hot and cold currents of air, he goes on
to say that, as regards the cause of turbidity in the higher
and drier regions of the atmosphere, which produces the blue
light of the sky, whether we have to do here with particles of
foreign matter, or whether the molecules of the air itself act
as a turbidity in the zether, science has no certain information
to give.
PAs regards, however, the colour of the light reflected by the
disturbing particles,” he resumes, “‘this depends practically on
their size. When a log of wood floats on water, and we excite
small wave rings by letting a drop of water fall near it, these
waves are reflected by the floating log as though it were a
fixed wall. But in the long waves of the sea, such a log of
wood would be tossed up and down without the form of the
waves being materially altered in their progress. Now light
also is known to be an undulatory motion transmitted through
the ether that fills space. The red and yellow rays have the
longest waves, the violet and blue the shortest. Very small
bodies disturbing the continuity of the ether will therefore
reflect the latter rays notably more than the former. In fact,
the finer the disturbing particles are, the bluer the light of the
turbid medium; while larger particles reflect more equally
light of every colour, and for this reason cause a whiter tur-
bidity. Of such kind is the blue of the sky, 2. e. of the turbid
atmosphere seen against black space. The purer and more
transparent the air, the bluer the sky. In like manner it
becomes bluer and darker when we ascend a high mountain,
partly because the air high up is freer from turbidity, partly
because there is, of course, less air above our head. But the
same blue which we see before the dark background of space,
appears also before terrestrial objects, e.g. distant mountains
in shadow or wooded, whenever a thick layer of illuminated
air lies between them and us. It is the same ‘air-light’
which makes both sky and mountain blue ; only in the former
270 Lord Rayleigh on Acoustic Repulsion.
case it is pure ; in the latter it is mixed with other light pro-
ceeding from the objects behind, and moreover belongs to the
coarser turbidity of the lower layers of the atmosphere, for
which reason it is whiter. In the drier air of warmer coun-
tries the turbidity is finer, even in the lower strata of the at-
mosphere, and hence the blue seen before distant terrestrial
objects is more like that of the sky. It is to this circumstance
that Italian landscapes owe their clearness and richness of
colour.’’ I fail to detect in this explanation, which was origi-
nally, I believe, due to Dr. Tyndall, the slightest resemblance
to that of Mr. Lockyer.
I am, your obedient servant,
A. M. WortTHINGTON.
XXXV. Note on Acoustic Repulsion.
To the Editors of the Philosophical Magazine and Journal.
GENTLEMEN,
Neo reeont the following explanation of the curious phe- -
nomenon of the repulsion of resonators observed by
Dvorak and Mayer* may be of interest to the readers of the
Philosophical Magazine.
The hydrodynamical equation of pressure for irrotational
motion is (in the usual notation)
_(@?_p_* _itp
a= (Vor 2 ae
If we suppose that there are no impressed forces, R=0. Di-
stinguishing the values of the quantities at two points of space
by suffixes, we may write
d 2
B1—- BD y= 7 (bo— $1) — 3 Uo + 3 Ui. ° = > (2)
This equation holds good at every instant. Integrating it
over a long range of time, we obtain as applicable to every
case of fluid-motion in which the flow between the two points
does not continually increase
Vaydt—Japdt=4\Uidt—3\ Usd. . . . (8)
Let us now apply this equation to the case of a resonator
excited by a source of sound nearly in unison with itself,
taking the first point at a distance from the resonator, where
neither the variation of pressure nor the velocity is sensible,
and for the second a point in the interior of the cavity, where
* Phil. Mag. September 1878, p. 225.
Lord Rayleigh on Acoustic Repulsion. 271
the velocity is negligible, but, on the other hand, the variation
of pressure considerable. It follows that
\(1—a)dt=0, SHIRT eto re cA)
or that the mean value of aw in the interior is the same as at a
distance outside.
The remainder of the investigation depends upon the rela-
tion between p and p._ If the expansions and contractions are
isothermal, p=a’p, and w=a’logp. Thus
flog pidt=log p, . t; Migs spe eye, at Cy
or the mean logarithmic pressure in the interior is the same as
the constant logarithmic pressure at a distance. Hquation (5)
may dlso be written
flog (14 BP) amo, < Scctiecte |, ona GOD)
* Vie ARES
@ Le 7 fe. hat=0; ae i.)
Po Po
whence, if the changes of pressure be relatively small, we see
that the mean value of p;—7p is positive, or, in other words,
that the mean pressure inside the resonator is in excess of the
atmospheric pressure.
If, as in practice, the expansions and contractions are adia-
batic, p xp’, where y=1°4, and (5) is replaced by
or
ten Yet
PAD niba es a Loa, ehh cote ey, (8)
Thus, instead of (7),
\{ G+ 25P)F—1barmo; Hise 3
whence, by the binomial theorem,
ne, el 2
(PP atm (BSP) at are (3)
approximately, showing that here again the mean pressure in
the interior of the cavity exceeds the atmospheric pressure.
Hence, on either supposition, the resonator tends to move as
if impelled by a force acting normally over the area of its aper-
ture and directed inwards.
Iam, Gentlemen,
Your obedient Servant,
RAYLEIGH.
Terling Place, Witham,
September 7, 1878.
[ 272 ]
XXXVI. On certain Phenomena accompanying Rainbows. By
Sirvanvus P. Toomrson, D.Sc.,B.A., F.R.AS., Professor of
Experimental Physics in University College, Bristol*.
he literature of the Rainbow is somewhat extensive; yet
I do not recollect having anywhere seen any record of
certain phenomena, of radial streaks of light, which are occa-
sionally to be seen accompanying rainbows. Iam convinced
that the phenomenon is not rare ; and in the desire of inducing
more observers to watch for its occurrence, I beg to present
the few notes which follow. On the evening of July 8th,
1877, I stood with a friend upon the summit of the Drachen-
fels about an hour before sunset. To the south and south-
east the sky was obscured by dark masses of cloud ; and the
sky above us and to the north and west was covered with
broken clouds: there was no perceptible wind. A fine
rainbow spanned the valley, and extended eastwards toward the
Lowenberg. Both primary and secondary bows were fine ;
and several supernumeraries were noticed. As the bow faded
away a faint streak of light was observed, not unlike the
streak of an aurora, outside the right limb of the secondary
bow, extending up to it, about 12° of arc long by 2° wide,
and making an angle of about 15° with the horizon. It lasted
fully ten minutes, maintaining nearly same position and form.
It was perfectly free from colour. A similar, fainter streak
was observed on the left limb at about 70° to the horizon.
Standing upon the very summit of the Drachenfels, the pro-
file of the hill and our shadows were rudely projected upon
the nearest hillside; it was very easy, therefore, to verify that
these streaks were really radial in direction. Hach of them,
if produced backwards, would have passed through the point
of space exactly opposite the sun.
July 15th, 1877, after a very wet and stormy day, we ob-
served, from the promenade in front of the Schweitzerhof at
Lucerne, a very fine rainbow at sunset. The colours were
unusually brilliant. Seven supernumeraries of the primary
bow were distinctly visible, and one of the secondary. The
clouds behind presented a uniform deep grey tint. A colour-
less streak was visible within the primary bow, radial in posi-
tion and at about 45° to the left. |
July 16th, 1877, about 6.30 p.m., from the high road near
Sarnen, the same observers watched the same phenomenon.
The day was thundery and with frequent showers and gusts
from the north. A very fine and complete bow was seen,
* Communicated by the Author, having been read before Section A of
the British Association, Aug. 19th, 1878.
On certain Phenomena accompanying Rainbows. 273
partly against the sky, partly against the hills which bound
on the south-east the high road from Alpnach. At intervals
several radial streaks were observed both interior and exterior
to the rainbow. They shifted position and magnitude rapidly.
It was noticeable that to each streak corresponded a patch of
sunshine on the hills behind, each streak pointing to a patch
- and moving with it.
Three times in June 1878 I observed at Bristol similar phe-
nomena accompanying rainbows, though not so favourably.
The explanation which is suggested by the observation made
at Sarnen is very simple. These wedge-shaped radial streaks
are “‘beams”’ of sunlight, and become visible by diffuse re-
flexion from particles of matter in their path, just as the appa-
rently divergent beams of sunrise or sunset become visible.
These “beams” being practically parallel to one another,
appear to converge in the point exactly opposite the sun by
perspective ; or, in fact, just as the parallel beams of sunset
appear divergent. Since the rainbow has for its centre the
point opposite the sun, such beams must necessarily have
positions radial with respect to the bow. They resemble,
therefore, the ‘‘ rayons du crépuscule’’ occasionally seen in the
east at sunset, or in the west at sunrise.
Here let me mention one peculiarity of the radial streaks,
in which they appear to differ from the “rayons du cré-
puscule.”’ I have never observed a “ streak ’’ crossing the dusky
_ region between the primary and secondary bows, though I have
seen one and the same streak extend beyond the bows both
outside the secondary and inside the primary. I have never
seen a “streak ’’ of colourless light cross the coloured part of
arainbow. I have noticed a faint bow crossed by a streak ;
where the streak crossed it, the bows (primary, secondary, and
supernumerary) became more vivid. There was more light ;
but it was dispersed in the usual way, and the intermediate
region between the bows was no brighter where the streak
crossed it. I conclude, then, that such a streak is the very
stuff, so to speak, of which rainbows are made; only when
the neighbouring regions are obscured by clouds, the beam of
light which struggles through builds up its own portion of the
arch in its appropriate place.
Two not dissimilar phenomena (quite independent of the
rainbow) appear to confirm this conclusion. Stand in the
sunlight, when the sun is high, so that the shadow of your head
falls upon the surface of a slightly turbid pond or lake, whose
surface is covered with gentle waves, or ripples: you will
see the shadow of your head surrounded by a halo of quivering
radial streaks of light. From the deck of a steamer on the
Phil. Mag. 8. 5. Vol. 6. No. 37. Oct. 1878. T
274 Dr. R. 8. Ball on the principal Screws of Inertia
Thames I have often observed this. The waves or ripples of
the surface cause the sun’s rays to enter the water with
unequal intensities at different points. At certain points the
beams will enter almost without loss by reflexion, and will be
traceable by their illuminating the particles of the turbid
water. These beams will be nearly parallel to one another ;
but as they all retreat from the observer, they will appear to
converge to a point exactly opposite the sun ; toa point within
the shadow of his head, in fact, giving the nimbus effect.
The other analogous phenomenon requires to be explained
by reflexion. If you stand upon a ridge, or a high wall in
the sunlight, so that your shadow falls upon a field of waving
corn, you will notice that the corn-field appears to be illumi-
nated in the region all round the shadow of your head. This
is best seen when travelling by railway, with the sun about
50° above the horizon, from the top of an embankment, so
that the shadow of the train and observer fall upon the corn-
fields below.
University College, Bristol.
July 31, 18
XXXVIT. On the principal Screws of Inertia of a Free or Con-
strained Rigid Body. By RopertsS. Baur, LL.D., FR.S.,
Royal Astronomer of Ireland*.
‘hae the following paper I propose to treat of the effect of an
impulse upon a quiescent rigid body, so far as the initial
movement of the body is concerned. The analytical investiga-
tion of this problem is so well known, that I do not propose to
enter into that subject at present. I believe, however, that
the ordinary method of viewing the question may be supple-
mented by the purely geometrical or physical treatment which
I shall endeavour to sketch. This geometrical aspect of the
problem, as it has presented itself to my mind, has been de-
veloped in the course of certain researches in the dynamics of
a rigid body which I have ventured to call the Theory of
Screws. I shall here indicate the more salient points of this
theory which are necessary for the present question.
The most important feature of the geometrical method of
viewing the subject is its extreme naturalness, as well as the
wide generality with which the problem is grasped. If the
rigid body were perfectly free, the questions presented are
comparatively simple, so much so that there is not a great deal
of interest attached to the investigation. But when we con-
sider the case of a rigid body whose movements are more or
* Communicated by the Author, having been read before the British
Association, Dublin, August 1878.
of a Free or Constrained Rigid Body. 275
less constrained, the problems possess a high degree of geo-
metrical interest. It is also the occasion of some surprise that,
notwithstanding the infinite variety of conceivable constraints
(such as fixed points, axes, contact with fixed surfaces, ar-
rangements of link-work and the like) by which the move-
ments of the rigid body may be hampered, their geometrical
classification is of the utmost simplicity. It will be shown
that there are six fundamental descriptions of constraint,
which include every conceivable arrangement, from leaving the
body absolutely free on the one hand, or absolutely immovable
on the other. With the investigation of these fundamental
forms of constraint we may fitly commence our inquiry.
In the first place, it is to be observed that, as the constraints
limit the movements of a body, we may adequately describe
the nature of those constraints either by pointing out all the
movements of the rigid body which are prohibited, or, on the
other hand, by ascertaining all the movements which are per-
mitted. It is obviously more to the purpose to adopt the latter
method of viewing the subject; and therefore we shall proceed
to indicate the method by which a complete inventory may be
made of the possible movements which a rigid body can
execute. It is also to be continually borne in mind that we
are only considering the initial movements of the body, and that,
consequently, it is only necessary to consider movements which
are of indefimtely small magnitude.
Let it therefore be supposed that the rigid body is submitted
to our examination when it occupies a definite position A. We
are not now going to apply the impulsive forces to it; we are
at present merely making a preliminary trial of a purely geo-
metrical or kinematical character of its capability for displace-
ment. It is at once perceived that the body, not being fixed,
can be moved into many closely adjacent positions. Take any
one of these positions and call it B.
By a celebrated theorem of Chasles it is known that the
displacement of the body from A to B can be produced by
translating the body parallel to a certain line, and at the same
time rotating the body about the same line. We may, for con-
venience, speak of this motion as a twist; and we may term
the angle of rotation the amplitude of the twist. The distance
of the translation is proportional to the amplitude of the twist,
and may be taken to be equal to the product of the amplitude
of the twist and a certain linear magnitude called the pitch.
The axis about which the rotation is made, associated with the
linear magnitude termed the pitch, constitute what is called a
screw. We therefore say that the displacement of the rigid
body from A to B is effected by a twist about a screw.
T 2
276 Dr. R. 8. Ball on the principal Screws of Inertia
It is to be observed that the twist involves two elements,
2.é@. a graphic element (the screw), and a metric element (the
amplitude of the twist). A little reflection will show that the
constraints which permit displacement from A to B must also
admit of any infinitely small twist being made upon the screw
defined by A and B. We may therefore say that the body is
free to twist about the screw (A, B). If we find on exami-
tion that the body cannot be displaced to any position eacept
those which could be attained by twists of suitable amplitude
about the screw (A, B), then we can assert that the body has
only one degree of freedom; and that freedom is perfectly ex-
pressed by the capacity to twist on one definite screw.
It is easy to verify in particular cases the general principle
that, no matter what the constraints be, a body which has but
one degree of freedom can twist about a certain screw and
can have no other movements. For example, a body free to
rotate about an axis, but not to slide along it, can only twist
about a screw of which the pitch is zero, or a body free to
slide along an axis, but not to rotate around it, can only twist
about a screw whose pitch is infinite. A less obvious instance
is presented in the case of a body of which five points are
limited each to a given surface ; but even in this case the body
is still only free to twist about acertain screw. Draw the five
normals to the surfaces, and regard them as the rays of a
linear complex. Then the screw about which the body can
twist is the principal axis of that complex, while the pitch of
the screw is its parameter. These, however, are only illus-
strations; our concern is with the general proportion that when
a body has but one degree of freedom, from whatever cause
arising, it is free to twist about one screw, and only one.
Suppose, however, it were found that the body, besides
being able to twist about a certain screw a, was also able to
twist about a second screw §, then twisting about an in-
finite number of other screws must also be possible. For
the position attained by a twist about a, followed by a twist
about 8, could have been reached by a single twist about some
screw y. Now as the amplitude of the twists about a and 8
are arbitrary, it is obvious that y must be one of a singly in-
finite number of screws which include a and B. _ It follows
that the body must be able to twist about all the screws which
constitute the generators of a certain ruled surface.
This surface is called the cylindroid: it is of the third order,
its equation being
a +y’)—2 may =0.
The cylindroid is already well known to the students of the
linear geometry of Pliicker.
of a Free or Constrained Rigid Body. 277
A body which has two degrees of freedom is therefore able
to twist about all the screws which lie upon acylindroid. This
is true, no matter what be the nature of the constraints. It
is a matter worthy of notice that notwithstanding the infinite
variety of constraints which would permit a body to have two
degrees of freedom, that freedom must still be completely de-
_ fined by a cylindroid, although all cylindroids are similar sur-
faces, and possess no variety except as to absolute size. It
should also be remarked that the pitches of the screws on the
eylindroid are proportional to the inverse squares of the paral-
lel diameters of a certain conic.
If it be found that a body can be twisted about three screws
which do not lie upon the same cylindroid, then the body must
be capable of being twisted about a doubly infinite number of
screws. Of this doubly infinite number three pass through
each point in space, all the screws of given pitch lie upon a
hyperboloid, and all the screws parallel to a plane lie upon a
- eylindroid. The pitch of each screw of the system is propor-
tional to the inverse square of the parallel diameter of a certain
quadric called the pitch-quadric ; and the pitch-quadric is
itself the locus of the screws of zero pitch. The entire sys-
tem is determined when the pitch-quadric is known. These
kinematical theorems are intimately connected with Pliicker’s
geometrical speculations on a system of three linear complexes.
Included in the case of freedom of the third order, we have
the celebrated problem where a body is rotating around a
point. In this case, however, the pitch-quadric assumes an
evanescent form, and the general conception of the capabilities
of a body which has freedom of the third order are very much
degraded.
If a body be able to twist about four screws which do not
all belong to such a system as that we have just been describing,
then the body must he able to twist about a trebly infinite
number of screws. A cone of screws of this system passes
through each point of space ; and the cone may be drawn by
letting fall perpendiculars from the point upon the generators
of a cylindroid. It is remarkable that these cones are of the
second order ; and it can also be shown that the feet of their
perpendiculars upon the generators of the cylindroid are in
the same plane. It is thus to be observed that the capabilities
of motion possessed by a body which has freedom of the fourth
order are completely determined when a certain cylindroid is
given in size and position; for then all the cones are deter-
mined.
In the case where a body can twist about five screws
not belonging to a system such as that we have just been
278 Dr. R. 8. Ball on the principal Screws of Inertia
describing, then the system of screws is quadruply infinite ; in
fact, the body can then twist about one screw of a certain pitch
on every line in space.
Finally, if the body can twist about six screws not belong-
ing to the system just mentioned, then the body has freedom
of the sixth order, and is, in fact, perfectly free.
We thus see that, corresponding to each order of freedom, a
certain group of screws is appropriate ; and we may call such
a group a screw-system for the sake of brevity. Thus, in the
case of freedom of the second order the screw-system is a cylin-
droid ; in the case of freedom of the fourth order the screw-
system consists of all the screws of proper pitch which inter-
sect a generator of a cylindroid at right angles, and so on.
By this preliminary investigation we are enabled to dismiss
entirely all further mention of the constraints. Hvery con-
ceivable form of constraints can only give the body permission
to twist about one of the six types of screw-system. I have
not in this brief summary attempted to give any demonstra-
tions of the different theorems involved. For these, reference
may be made to the ‘ Theory of Screws’ *.
We have now laid the foundation of the first part of the
problem to be discussed in this paper, inasmuch as we have
shown how the body may move; the next question is to ascer-
tain how the body will move when it receives an impulse.
It will, however, be first necessary to consider the most
general form of impulse which the body can receive. Now
it is well known that all the forces acting upon a rigid body
may be reduced to a single force, and a couple in a plane per-
pendicular to that force. The efficiency of the couple is ex-
pressed by its moment; and the moment is the product of a
force and a linear magnitude. It will not be unnatural to as-
sociate this force and couple with the conception of the screw,
already introduced. We may use the expression wrench to
denote a force along a screw and a couple in a plane perpen-
dicular to the screw, the moment of the couple being equal to
the product of the force and the pitch of the screw. Thus,
every system of force acting upon a rigid body constitutes a
wrench upon a screw ; and itis completely determined when the
screw on the one hand, and the force on the other, are both given.
The analogy subsisting between the twist and the wrench,
as implied by their mutual connexion with the abstract geo-
metrical conception of a screw, will be the main source of the
theorems now to be enunciated.
The original problem has now been brought into this con-
dition. On the one hand, we have a body whose freedom is
* Ball’s ‘Theory of Screws :’ Dublin, 1876.
of a Free or Constrained Rigid Body. 279
expressed by a certain screw-system ; and, on the other hand,
we have a group of impulsive forces which constitute a
wrench on what may be called the impulsive screw. Now,
in consequence of this impulse the body will commence to
move; but the only motion it can execute must be to twist
about some screw of its screw-system ; there must therefore
be. in the screw-system a certain instantaneous screw corre-
sponding to each impulsive screw. If the impulsive screw be
given, the instantaneous screw is determined ; but the converse
is not true. In fact, the instantaneous screw is limited to the
screw-system, whereas the impulsive screw may be anywhere
in the universe and with any pitch. It is, however, possible to
clear away this ambiguity in a very satisfactory manner. It
can be shown that, whenever the body is not quite free, there
are a group of impulsive screws corresponding to each instan-
taneous screw. It is not here necessary for us to enter into
the properties of these groups of impulsive screws, further
than to remark that, if a body receive an impulsive wrench
upon any one of the screws belonging to this group, it will
commence to twist about the instantaneous screw to which the
group is correlated. “In each group of impulsive screws there
is one screw which merits most particular attention. It can
be proved that in each of these groups there is always one
screw (but only one) which not only belongs to the group but
also belongs to the screw-system expressing the freedom of the
body. Ittherefore follows that the effect of an impulsive wrench
anywhere in space could have been produced by an impulsive
wrench on a screw suitably chosen from among the members
of the screw-system itself. We need therefore only consider
the effect of impulsive wrenches upon screws which actually
belong to the screw-system.
In this way the ambiguity has been dissipated without any
sacrifice of generality: to each screw of the system regarded
as an instantaneous screw corresponds another screw of the
complex regarded as an impulsive screw, and vice versd.
The study of this system of correspondence between the im-
pulsive screw and the instantaneous screw of the same screw-
complex, leads to many results of considerable interest, not
only on account of their great generality, but also on account
of their geometrical character. It is natural to consider, in
the first place, whether there are any common elements in the
two corresponding systems; and we are thus led to the dis-
covery that when a rigid body has freedom of the uth order, then
n screws can be selected from the screw-system expressing that
freedom such that, if the body receive an impulsive wrench on any
one of these screws, the body will commence to twist about the
same screw. These are called the principal screws of inertia,
280 On the Inertia of a Free or Constrained Rigid Body.
We shall illustrate the existence of these principal screws
of inertia by pointing them out in the particular cases of
freedom of the second and third orders. When the body has
freedom of the second order, the screw-system is a cylindroid.
All the generators of a cylindroid are parallel to a plane ; and
by the anharmonic ratio of four generators is to be understood
the anharmonic ratio of four parallel rays drawn through any
point. Now it can be shown that the anharmonic ratio of four
instantaneous screws on the cylindroid is equal to the anhar-
monic ratio of the four corresponding impulsive screws. When,
therefore, three impulsive screws and the three corresponding
instantaneous screws are known, the instantaneous screw
corresponding to any impulsive screw is at once determined
by geometry. The double rays of the two equianharmonic
systems must of course be parallel to the two principal screws
of inertia on the cylindroid ; and thus the problem of finding
the principal screws of inertia for freedom of the second order
is completely solved. |
In the case of freedom of the third order, the three principal
screws of inertia can also be completely determined by geo-
metry. Tor this purpose it is necessary to construct a certain
ellipsoid, which is defined by the following theorem.
The kinetic energy of a rigid body when twisting with a
given twist velocity about any screw of ascrew-system of the
third order is proportional to the inverse square of the paral-
lel diameter of a certain ellipsoid.
If this ellipsoid be made concentric with the pitch-quadric,
it will be possible to draw a triad of common conjugate dia-
meters to the two surfaces; and the required principal screws of
inertia are the three screws of the complex which are parallel
to these conjugate diameters.
In that special case of freedom of the third order in which
a body is rotating about a fixed point, then the general pro-
perty of the three principal screws of inertia degrades to the
well-known property of the principal axes. It will be ob-
served that the theory here propounded may be considered to
generalize the property of the principal axes into a general
property for freedom of the third order, and then further into
a property for freedom of any order.
We conclude by pointing out the six principal screws of
inertia of a perfectly free rigid body. They are found as
follows :—Draw the three principal axes, A, B, C, through the
centre of gravity, and let a, b, c be the radii of gyration; then
two screws on A with the pitches +a, —a, and two similar
screws on B and on OC, constitute the six principal screws of
inertia.
Dunsink, Co, Dublin, August 1878.
h .Bedi a7
XXXVITI. On the Discharge of Water from Orifices at diffe-
rent Temperatures. By Professor W. C. Unwin, I.1.C.E.*
e) the Journal of the Franklin Institute for May 1878,
there is a paper by Chief-Engineer Isherwood, of the
U.S. Navy, giving an account of some experiments on the
discharge of water from orifices at different temperatures.
Those experiments appear to have been made on a sufficient
scale and with very great care ; and they lead to the conclusion
that temperature has a very marked influence on the discharge.
The author evidently supposes his conclusions to be applicable
to orifices in general ; for he remarks that, “in the various de-
terminations which have been made of the ratio of the actual
to the theoretical discharge of water through orifices, the tem-
perature of the water should have been noted. The experi-
mental ratios are true for only the experimental temperatures,
and need reduction to a standard temperature.”
The experiments were made by noting the time in which
the level of the water in a cylindrical vessel fell from one level
to another, the water being discharged from a given orifice.
The observed results of the experiments are not given. These
results were plotted in a diagram, and a fair curve drawn pass-
ing as evenly as possible through the plotted points. The
results are stated to have been corrected for the dilatation of
the orifice by heat; but it is not stated whether any correction
was made for the dilatation of the volume of the vessel from
which the water flowed, a correction quite as important as the
other. The following short Table gives a few of Mr. Isher-
wood’s results, as measured by him from the curve represent-
ing the observed results :—
Temperature, Relative time Relative velocities
Fahrenheit. of discharge for of discharge for
6 equal volumes. equal volumes.
ee Eee 1°0000 1:0000
ON dos aanecic.« 0:9896 10105
OE Severino x te wie 0-9696 1:0313
£40: vices vevveee 0:9457 1:0577
VS Ot 5... 0c 00d 0°9156 1:0922
1 I CA Oeee 0°8855 1°1293
Thus the velocity of discharge increases 12 per cent. as the
temperature rises from 32° to 212°, and it increases 8 per
cent. as the temperature rises from 60° to 180°.
Now there is this difficulty in accepting the results of Mr.
Isherwood’s experiments,—that the actual velocity of discharge
at ordinary temperatures differs from the whole velocity due
to the head by only from 3 to 6 per cent. for simple orifices.
* Communicated by the Physical Society.
282 Prof. W. C. Unwin on the Discharge of Water
It is not easy to see that any increase of fluidity of the water
or diminution of friction could do more than annul this loss of
from 3 to 6 per cent. Mr. Isherwood’s experiments seem to
imply that the velocity of discharge at high temperatures may
be greater than the velocity due tothe head. It seemed worth
while therefore to repeat the experiment. The means at the
author’s disposal did not permit him to make the experiments
on quite so large a scale as those of Mr. Isherwood; but it
was, he believes, quite large enough to indicate any gain of
velocity of the amount mentioned above.
A cast-iron cistern was used, the interior bored out to a
diameter of 0°4 metre. The first orifice tried was a carefully
formed brass conoidal orifice, formed as nearly as might be to
the shape of the vena contracta, and very approximately 0-01
metre diameter. Three pointed indexes were fixed in the cis-
tern, below the surface of the water; so that, as the level of
the water descended, the instant at which the point broke the
surface could be very exactly observed. Calling the levels of
the three indexes A, B, and C, the time was noted in which
the water-level descended from A to B and from Ato @. A
chronograph-watch was used, the seconds’ hand being started
at the moment the water-level was at A. When the level
reached B, the time elapsed was noted by an observer count-
ing seconds. When the level reached C the hand of the watch
was stopped. This last observation was perhaps more reliable
than the intermediate one at the level B.
For the higher temperatures the water was taken from a
steam-engine boiler; it was somewhat discoloured by iron
and sediment. ‘The same water was used in the experiments
at lower temperatures, but in its ordinary clean condition.
The author does not think that the condition of the water made
any sensible difference in the results of the experiments.
Experiments on a Conoidal Orifice, June 4, 1878.
Time of fall of water-level
Temperature, in seconds.
Fahrenheit. r~ — —
i From A to B. From A to C.
LEST ORS Berea sees 2: 59 89
POG escotes weet ieee 5384 884
LOM, scleticnes teenies O94 90
OU sinh ens meserncess 62 93
BO ttn cpiaiteun opcecoe 614 924
Mean Results.
1 OO Se ee 58°75 88°75
130 I, cee eee BOD 90:00.
OO isiexie Gaseilieh aoe 61°75 92°50
_ from Orijices at diferent Temperatures. 283
These results show a distinct increase of velocity of dis-
charge at the higher temperatures ; but the increase from 60°
to 190° is only 4 per cent., or less than half the increase ob-
served by Mr. Isherwood.
When water issues from an orifice with gradually diminish-
ing head, the relation between the time and volume of dis-
charge is given by the well-known equation
OO SOY Sa
where © = area S water-surface in reservoir,
@ = area of orifice,
hy, hy = heads at beginning and end of experiment above
centre of orifice,
¢ = time of outflow in seconds,
c = coeflicient of discharge.
Let D = diameter of the cylindrical reservoir, and d = dia-
meter of the orifice. Then
O71 Dd?
ne
Hence the equation aes becomes
10% rae a ack
= BA) Wi VIG}:
In these experiments D = 15:7 inches, d = 0°3937 inch.
Reducing these values to feet and introducing them in the
equation,
ai O94: -—
{Viy— V hg }-
The heights of the peeled: above the centre of the ori-
fice were, as nearly as could be measured,
oe) Hale. gine: 7c IA Oe foots
Sane eo bea) 6
Oren Fe ene ye, OOF Gane
Hence, for experiments in which the level fell from A to B,
57895
TS a eT + ee (2)
and for experiments in which the level fell from A to C,
87°748
TitGhics tS oP eee
Neglecting for the present the expansion of the reservoir
and orifice, the coefficients of discharge deduced from aie eX-
periments are as follows :—
284 Prof. W. C. Unwin on the Discharge of Water
Coefficients of Discharge.
Fall of level Fall of level
from A to B. from A to C.
O “9813 "9859
te 9896 ‘9915
TOO? te ae ee "9750
60° "9338 ao
"9414 -9486
Mean Values of c.
19Q° we RE OS
ESOS OLR pues BUMS YO TAD
602" 222 ee aes
The experiments on a conoidal orifice having shown a small
but definite influence of temperature on the discharge, it
seemed desirable to try whether a similar effect would be pro-
duced in the case of a thin-edged orifice. With the conoidal
orifice there is no contraction of the jet, and the discharge is
less than the so-called theoretical discharge by an amount de-
pending only on the friction of the orifice. In the case of
a thin-edged orifice, the jet contracts to an area of about 2
that of the orifice; and the discharge is diminished not only
by the friction, but also to a much greater extent by the con-
traction. ‘The thin-edged orifice was 1 centimetre diameter ;
and the heads were nearly the same as before.
Haperiments on Thin-edged Orifice, 1 centim. in diameter,
June 12, 1878.
Time of discharge Time of discharge
Temperature, of water between of water between
Fahrenheit. A and Bin fifths <A and C in fifths
3 of a second. of asecond.
DO UIE See nn erie) 748
20D Geer ee a0 747
TAO ia? tx Oe 744
Go Wek IGO. Qe B00 746
Od) ae ee ORL OD 740
Glee Bite, Sues Oe 740
’ Mean Values.
62). im dane eo eee 742
TAD ae iets Bad) 144
205. so saunas anodes T4T'5
The times here recorded show that, in the case of a thin-
edged orifice, the temperature has an extremely small influence
rom Orijices at different Temperatures. 285
on the discharge, and that, unless the small differences in the
experiments are errors of observation, the discharge is greater
at low temperatures. Whether this is due to the increase of
temperature increasing the contraction at the same time as it
diminishes the friction, could only be determined by much
more extensive experiments.
For these experiments, when the level fell from A to B,
_, 292-75 -
ee
and when the level fell from A to C,
443°71
Cte aUaM tists guNe iidha tubes Gb)
t being in fifths of a second.
Coefficients of Discharge for Thin-edged Oriyice.
Values of ¢.
Temperature, i oF
Fahrenheit. Fall of level Fall of level
4 from A to B. from A to C.
PME es Ge yi COAL qa ay
Ue a cies ye Oe) "5940
Gee ie LL: "5964.
een aoe ree 2 a OUD "5948
a eR i eine Ge he 1! 000
Meer fs eee OO EE “D996
Mean Values.
Ogee oe ag 5837 5936
| 1213) ah a sale Saas ar 2: | 5964
Be tre BOE 5980
These results seem to show that the temperature has hardly
any sensible influence on the discharge from orifices of this
kind.
It will be seen that the results of these experiments do not
at all agree with those of Mr. Isherwood; and although made
on a smaller scale, the author believes that if the influence of
iemperature had been nearly as great as that stated by Mr.
Isherwood, it could not possibly have escaped detection. Mi-
nute errors in measuring the head or the size of the orifice
would sensibly affect the values of the coefficients obtained ; and
these may possibly be wrong to the extent of 2 or 3 per cent. ;
_ but these errors would not affect the relative values of the
coefficients in any sensible degree, and the author therefore
286 Prof. W. C. Unwin on the Discharge of Water
believes that temperature has a far less influence on the dis-
charge from simple orifices than Mr. Isherwood’s resuits would
imply. It is difficult to explain to what the higher results
obtained by Mr. Isherwood are due ; but the conjecture may be
hazarded that the orifice in his experiments was very excep-
tionally placed. It was at the end of a bell-mouthed tube
some 10 inches long, a great part of which was only # inch
diameter ; and there was a plug-cock immediately above the
orifice, It seems possible that “there was a good deal of fric-
tion in this pipe, and that the diminution of friction in this
part of the apparatus led to the increase of discharge as the
temperature increased *.
Thus far the effect of the temperature on the capacity of
the reservoir and the size of the orifice has been neglected.
It only remains to examine whether the expansion of these
has any material influence on the results.
The effect of temperature on the quantities entering into the
2
equation of flow is twofold. First, the ratio a is altered,
because the mouthpiece was of brass and the reservoir of cast
iron; and the former expands more than the latter. Secondly,
the level marks being attached to the side of the cistern, the
distance between these marks and the centre of the orifice in-
creases as the temperature rises. There is, however, an un-
certainty in applying a correction for the expansion of the
metal, because, its external surface being exposed to the air,
its mean temperature would be less than the temperature of
the water. The following estimate of the correction is there-
fore approximate only.
Let e, be the expansion of brass per unit of length and per
degree ;
€- the expansion of cast iron estimated in the same way ;
= the excess of temperature during the experiment
reckoned from 60°.
* It is impossible to calculate, except roughly, the frictional resistance
of the tube to which, in Mr. Isherwood’s experiments, the orifices were
attached. Taking 4 “inches length of pipe 7 inch in diameter, and neglect-
ing the bell-mouthed part, we get, using D’Arey’s coefficient of friction,
and putting the data in feet :—
For a discharge of DOTS ANS RG 0:0374
» velocity DIO. Qrep wuabete 12:2
5,4, ead Jostan pipe OC 06h ote 0-12
» total head DEO NS Sac ue ene 1:0
So that apparently about 12 per cent. of the head may have been lost in
the friction of the pipe leading to the orifice,
from Orijices at different Temperatures. 287
Then, in consequence of the expansion of the metal, the ratio
DD?
of the areas Pp becomes
(1 +er)? D?
(1+e,7)* ad’
and the true difference of the square roots of the heads is
V1 +e7(V hy—hy).
The formula of flow, allowing for the alteration of the dimen-
sions by rise of temperature, is therefore
mee ea) oo as ue
t= ie Vt er a VS hy— WV hy}.
Let e,=*000006,
e,= "00001,
tT =190°—60°=130;
1+¢,7) OOUES No ee ee
ees V1 +é¢,7= erunis?) / 1:00078 =0°999355.
Hence it is obvious that the effect of the expansion of the
reservoir and orifice is very small for the range of temperature
in these experiments. Allowing for that expansion, we get
for the experiments at 190°,
OO ja Wane oe 2
Sina & {Vh,—V ho}
or slightly smaller values of the coefficient than those given
above.
It is rather curious that it is stated in Mr. Isherwood’s paper
that the results are corrected for the variation of the size of
the orifice as the temperature varied, but no mention is made
of a correction for the size of the reservoir or the expansion of
the vessel to which the index-marks denoting the initial and
final heads were attached. If these latter corrections have
been omitted, though this is difficult to believe, Mr. Isher-
wood’s results should be divided by
(l+e7/PV1+e7,
where e, is the coefficient of expansion of the material of the
reservoir, whatever that was. This would sensibly diminish
the apparent increase of discharge at high temperatures given
in his experiments.
[ 288 ]
XXXIX. Action of Alkaline. Solution of Permanganate of
Potash on certain Gases. By J. A. WANKLYN and W. J.
CooPer*.
N continuation of our work on the oxidizing-power of
strongly alkaline solution of permanganate of potash, we
have made experiments on the common gases, and have arrived
at results of some interest. The solution which we have em-
ployed in these experiments contained 16 grms. of permanga-
nate of potash and 5 grms. of caustic potash dissolved in a
litre of distilled water.
Binoxide of Nitrogen, NO.
This gas was prepared in the usual manner by the action of
diluted nitric acid on metallic copper. On submitting it to
the above-described solution of alkaline permanganate there
was immediate action, the gas being instantly absorbed at
ordinary temperatures, and the solution being instantly deco-
lorized and caused to deposit the brown hydrated binoxide of
manganese.
110 cubic centims. of NO and 30 cubic centims. of the
potash-and-permanganate solution were shaken up together.
Immediately the solution lost its colour and deposited the
brown binoxide of manganese, and 85 cubic centims. of the
gas was absorbed. 7
The reaction is
NO+KMnO,=Mn0,+KNO;,
Protoxide of Nitrogen, N,O.
This gas, prepared in the usual way from nitrate of ammonia,
appears to be quite without action on the alkaline solution of
permanganate of potash. Hven on prolonged heating of the
materials in the water-bath there was no sign whatever of
action, the permanganate preserving its brilliancy, and the
volume of the enclosed gas undergoing no diminution.
Nitrogen Gas.
Experiments published some years ago by one of us show
that this gas is not attacked by the alkaline solution of per-
manganate, even when the temperature is considerably raised.
Carbonic Oxide, CO.
This gas, prepared by the action of excess of sulphuric acid
on ferrocyanide of potassium, is attacked by the alkaline solu-
* Communicated by the Authors.
Prof. E. Edlund on Unipolar Induction. 289
tion of permanganate. The action is not instantaneous, as in
the case of the binoxide of nitrogen, but is comparatively slow.
118 cubic centims. of CO and 30 cubic centims. of the
above solution of potash and permanganate of potash were
sealed up and heated in the water-bath, being frequently
taken out of the bath, cooled, and shaken. Altogether the
heating occupied some three or four hours. On opening the
tube under water it was found that great absorption of gas
had taken place.
Of the 118 cubic centims. of CO taken for experiment,
92 cubic centims. were absorbed,
26 i » _ , residue:
118
The action appears to be
CO+0=CO0,,
regard being had to the amount of KMnO, which had been
reduced during the operation. At ordinary temperatures the
action takes place, but very slowly.
Hydrogen
is also absorbed by the alkaline solution of permanganate. In
an experiment in which 64 cubic centims. of hydrogen were
sealed up with 16 cubic centims. of alkaline permanganate and
heated for some hours in the water-bath, an absorption of 34
cubic centims. of hydrogen was noted.
We are continuing the investigation.
XL. Researches on Unipolar Induction, Atmospheric Electri-
city, and the Aurora Borealis. By H. Epuunp, Professor
of Physics at the Swedish Royal Academy of Sciences*.
[Plate VIII.]
“ Res ardua rebus vetustis novitatem dare, novis auctoritatem, obscuris
lucem, dubiis fidem, omnibus vero naturam et nature suze omnia.”—
Puiny, Hist. Nat. t.1., preefatio.
§ 1. Unipolar Induction.
W* represent to ourselves a steel magnet in a vertical
position, readily set in rotation about its geometric
axis; and we picture it besides surrounded by a metallic muff
in the form of a cylinder, which can likewise turn about the
same axis. If the current of a pile be caused to pass into this
* Translated from a copy, communicated by the Author, of the Kongl.
Svenska Vetenkaps-Akademiens Handlingar, vol. xvi. No. 1.
Phil. Mag. 8. 5. Vol. 6. No. 37. Oct. 1878. U
290 Prof. E. Edlund on Unipolar Induction.
cylinder in such manner that one of the electrodes is in con-
tact with it in the vicinity of the poles of the magnet, and the
second electrode at a point situated between the two poles,
experience shows that the cylinder begins to rotate about the
magnet. The direction of rotation depends on that of the
current in the cylinder, and also on the situation of the poles.
As to the magnet itself, it remains perfectly motionless ; con-
sequently the galvanic current does not exert upon it any ro-
tatory action. It is therefore possible to turn the magnet
mechanically round its axis without the slightest obstacle being
offered by the reciprocal action of the magnet and current ;
the sole resistance to be surmounted in the mechanical rotation
of the magnet is occasioned by the friction in the sockets of
the axis, a a resistance which has nothing to do with the
current. Ina previous memoir* I have demonstrated that,
according to the mechanical theory of heat, every phenomenon
of the sort mentioned will be accompanied by a phenomenon
of unipolar induction. In fact, if the pile be removed and
replaced by a galvanometer inserted between the two above-
mentioned electrodes, and in contact with the cylinder, the
galvanometer indicates the rise of a current as soon as the cy-
linder is mechanically put in rotation. The electromotive
force here consists of the mechanical work necessary to over-
come the reaction of the magnet upon the current in that part
of the circuit which is set rotating. This species of induction
has received the name of “ unipolar induction.” The current
produced is proportional to the velocity of the cylinder. Of
course the simultaneous mechanical rotation of the magnet
produces no augmentation in the current generated by the
rotation of the cylinder, since this augmentation would be
made without the consumption of a corresponding amount of
mechanical work—which would be perfectly absurd. Pliicker
has also proved by experiment that in this case the rotation of
the magnet is incapable of producing a current. Here is an-
other reason :—It has been demonstrated by experiment that,
in the case in question, for the magnet a solenoid can be sub-
stituted, producing the same effectf. I have myself shown,
on a previous occasion}, that the rotation of the solenoid about
its axis cannot produce a unipolar induction current, whether
proceeding from a single fluid or from two fluids in transla-
tory motion. It is therefore, in this case, the rotation of the
cylinder about the magnet that gives rise to the observed uni-
* Ofversigt af kongl. Vetensk.-Akad. Véorh. 1877; Wiedemann’s An-
nalen, vol. ii. p. 347.
tT Ofversigt, April 1877; Pogg. Ann. vol. clx. p. 604.
t Ofversigt, Jan, 1877; Poge. Ann, vol. clx. p. 617.
Prof. E. Edlund on Unipolar Induction. 291
polar induced current ; while the rotation of the magnet about
its axis has nothing to do with the phenomenon, as several phy-
sicists have assumed. Ifthe magnet and cylinder be connected
together so as to form a compact body, the magnet is carried
in the direction of the rotation of the cylinder without any
modification in the induction of the magnet resulting, as we
have seen. The magnet acts in this case on the cylinder as if
the former were immovable and the latter alone rotating. The
opinion expressed by several physicists, that the magnet can-
not produce unipolar induction in a conductor with which it is
intimately united, is therefore not correct. If the radius of
the cylinder be sufficiently reduced for the cylinder to be in
perfect contact with the magnet, this circumstance will not
prevent induction taking place in the cylinder; and since in-
duction will be produced perfectly irrespective of the thickness
of the cylinder, the latter can be entirely removed and the
electrodes of the galvanometer put into immediate contact with
the magnet without causing the induction to cease. The
magnet itself then performs the functions of a conductor, and
the induction does not result from its being put in rotation as
a magnet, but from its rotation as a conductor. We are here
in presence of the phenomenon of unipolar induction first pro-
duced by W. Weber*.
If now we are asked how it is that a current is possible in
this case, we can reply that this must necessarily take place if
our idea of the nature of the galvanic current is correct—
namely, that it consists in the translatory motion of a fluid
going in the positive directiont, or of two fluids following op-
posite directions. To understand the necessity of the produc-
tion of a current in the case in question, one can adopt either
of the above-mentioned opinions. In the memoir cited (p. 3),
I have recalled the known fact that a metal ring surrounding
a magnet and traversed by a galvanic current transports itself,
if movable, along the magnet. It stops in the middle, where
it takes up a position of stable equilibrium if its galvanic cur-
rent follows the same direction as the molecular currents of
which we imagine the magnet to be formed. If, on the con-
trary, the current of the ring follows the opposite direction,
the ring will be in unstable equilibrium at the middle of the
magnet; and if removed from that position, it will continue
moving further from the centre until it passes beyond the
poles of the magnet. This motion of the ring is determined
by the law which regulates the action of a magnetic pole upon
* Poge. Ann. vol. lil. p. 353.
7 « Thcorie des Phénoménes Electriques,” Kongl, Svenska Akad, Hand-
lingar, vol, xii,
U2
292 Prof. E. Edlund on Unipolar Induction.
an element of current, which law, as is known, is formulated
as follows:—A single magnetic pole acts on a current-element
ds with a force directly proportional to the product of the
magnetic moment M of the pole, the intensity 2 of the current,
and the sine of the angle X between the current-element and
the straight line joining the pole of the magnet to the same
element, and inversely proportional to the square of the dis-
tance 7 between these last. ‘The force in question may there-
Mi sin Ads
ae
fore be expressed by The point of application of
the force is situated in the current-element ; and its direction
is perpendicular to the plane which passes through the mag-
netic pole and the current-element. ‘The sense in which the
force acts upon the said direction depends, moreover, on the
direction of the current and the nature of the pole.
When the cylinder is put in rotation about the fixed mag-
net, the electric fluid or the two fluids (if we admit two) put
themselves in rotation in the same direction. They form, then,
currents with a horizontal circulation round the vertical mag-
net ; and their intensity will be proportional to the velocity of
the rotation.
The sole difference between these currents and ordinary
galvanic currents is, that the two fluids (if they are two in
number) follow the same direction, while in ordinary galvanic
currents they take opposite directions. But, according to the
usual ideas, the action of the magnet upon the negative cur-
rent is the same as its action upon a positive current going in
the opposite direction. Now the poles of the magnet act, in
virtue of the law above cited, upon the currents produced by
the rotation of the cylinder ; and the consequence of this will
be that the cylinder will receive an excess of ether (electro-
positive fluid) at its two extremities, and a deficiency of ether
(electronegative fluid) in the centre, or vice versd, according
to the direction of the rotation and the position of the poles.
In a conducting wire, one of the extremities of which is in
contact with the centre, and the other with one of the edges
of the cylinder, there will necessarily arise a galvanic current.
The direction of the current thus produced and the augmen-
tation of its intensity with that of the velocity of rotation are
perfectly like what takes place in experiment.
In opposition to this view the following objection may now
be raised :—If the rise of the unipolar induced current depends
on the electric molecules commencing to move round the
magnet at the same time as the conductor in which they are
present, a similar induced current should also arise if, the con-
ductor and the electric molecules remaining at rest, the mag-
Prof. E. Edlund on Unipolar Induction. 293
net is put in motion round them, seeing that the phenomenon
can only depend on the relative motion between the magnet
and those molecules. If, then, it is proved by the above-
mentioned experiments that the magnet acts on an electric
molecule in rotation about it, it must equally act on the mole-
cule if the latter is at rest while the magnet moves round it.
This certainly ought to be the case, and we shall see examples
of it in the sequel. ;
Let us imagine the cylinder divided into vertical columns,
each presenting a section equal to unity. To determine quanti-
tatively the force of induction produced in the cylinder by
the magnet, it will be sufficient to take one of the columns
into consideration. Let us represent the magnet by ad
(Plate VIII. fig. 1), and name one of the columns de, the dis-
tance of which from the magnet shall be indicated by vr. Let
s designate the south pole, and 7 the north pole, and 2/ the
distance from the one to the other. Suppose that the cylinder,
viewed from above, revolves round the magnet in the opposite
direction to that of the hands of awatch. The excess of ether
(electropositive fluid) will then collect at the extremities of the
column, and the deficiency will make itself sensible in the
centre. If the angular velocity be designated by v, the velo-
city of the column will be equal to rv. The intensity of a
current can be expressed by qav, in which g denotes a constant,
a the section of the conductor, and v the velocity of the elec-
tric fluid. The intensity of the current produced by the rota-
tion in any element dz can then be designated by grvdz, in
which g is a constant, and rv, as we have seen, the velocity of
the before-mentioned element. If straight lines be drawn from
the two poles to the element dz situated in & at the distance z
from the line fe, and if kg and khare perpendicular to the lines
mentioned, the south pole will drive the ether (electropositive
fluid) along kg, while the north pole will lead it along kh.
Designating by M the intensity of the magnetic poles, the
first force will be represented by
+ Mgrvdz
(l=zy +r”
Marvdz ;
(i+2)+r
and the second by
The component of these forces along the column cd will then be
+ Mqr’vdz ve Mgr’vdz
[=z +r}? [Crete y
294 Prof. EH. Edlund on Unipolar Induction.
Supposing the length of the cylinder equal to the distance
between the poles of the magnet, or 2/, by integration we shall
obtain the force conducting the electric fiuid of the evlinder
to its extremities, namely ;
1 1
2Mqvl} ———_, —-————7, |. . . . (A
d meyer eal (9
This last expression constitutes the electromotive force pro-
duced.
We will now see if this expression of the electromotive force
conforms to the exigences of the mechanical theory of heat.
If a current equal to unity be made to pass through the column
from f to d, the column begins to rotate in the opposite direc-
tion to that in which we considered it to move by the action
of the external mechanical force. From the law previously
given, it is easy to calculate the force with which the mag-
net acts upon the current. The squares of the distances of the
two poles from the element dz, situated at the distance z from
the line fe, are (/—z)? +7? and (/+z)?+7”; and sin) is equal,
. r
———___——, and —______,,
Levee, Ae) ee
tively. The force with which the magnet acts upon the cur-
rent in the direction normal to the plane containing the poles
of the magnet and the element dz is therefore
Mrdz iif Mrdz
MG eye lee) aoe
the integral of which, between the limits indicated, is
2M/ J 1
ye [<< Ore Warr ° e e . (B)
rey Gli)
It has been demonstrated in my memoir™ that, according to
the mechanical theory of heat, the electromotive force of in-
duction resulting from the rotation of the cylinder with a
velocity w=rv will be equal to a constant (the value of which
depends on the unit chosen to designate the intensity of the
current) multiplied by the product of the expression (B) and
rv. In fact, by multiplying rv into that expression we find
again the previously given expression (A). 3
We obtain, then, the following result :—If it be admitted
that, in the case in question, ynipolar induction is produced
by the action of the magnet on the currents due to the electric
molecules being carried along in the direction of the rotation
of the cylinder, we shall get for the electromotive force an ex-
* Wiedemann’s Annalen, yol. ii. p. 347.
in the two cases, to respec-
Prof. E. Edlund on Unipolar Induction. 295
pression conformable to the requirements of the mechanical
theory of heat.
We will now treat another case of induction. — sn (fig. 2)
represents a powerful magnet, the south pole of which is in s,
and the north pole inn; and abcd is a circular metal plate
having its centre in the prolongation of the geometrical axis
of the magnet, and its plane perpendicular to the same axis.
If the plate be set in rotation about the axis so, the electric
fluid will be carried in the direction of the rotation, and the
velocity of an electric molecule will be proportional to its dis-
tance from the centre o. Now let us imagine a plane con-
taining the axis of the magnet and an electric element dz
situated in m, at the distance r from the centre of the plate.
Then let the right lines mg and mét be drawn in this plane,
respectively perpendicular to the lines sm and nm. The line
mq is then perpendicular to the plane which passes through
the south pole and the tangent of the orbit of the element dz;
and the line mt is perpendicular to the plane passing through
the same tangent and the north pole. The plate being in ro-
tation in the direction indicated by the arrows, the electric
element is urged by the south pole towards q, and by the north
pole towards ¢. Let / be the distance between the poles, p the
distance from the north pole to the centre of the plate, r the
distance from this last to the point m, and M the force of the
poles ; further, let £ be a constant, and v the velocity of rota-
tion of the plate: the force with which the element dz is urged
by the south pole towards the periphery of the plate (or, which
comes to the same, the component of the action of the same
pole upon dz along the plane of the plate) will be given by
kMor(l+ p)dz
eee COI dal
[G+py +r]?
and the force with which the north pole tends to direct the
same element towards its centre will be expressed by
kMorpdz
(p? +.0?)8
By equating these two expressions we shall obtain the value
of x for which the two forces make equilibrium. We get this
value from the equation
4 2 2 4
m=U+p) p> +U+p) p®.
The circle whose radius has this value may be called the neuter
circle. If, for example, we take =10 and p=5 centims., we
get r=12°7 centims. The electric molecules situated between
the neuter circle and the periphery of the plate are directed by
296 Prof. E. Edlund on Unipolar Induction.
the magnetic force towards that periphery ; and those which
lie between that circle and the centre are driven towards the
latter. As the formula shows, the value of 7 of the neuter
circle increases with / and p. If the plate be touched outside
of the neuter circle with the ends of the electrodes of a galva-
nometer, the galvanometer indicates a current which goes from
the point of contact situated nearest the periphery, through
the galvanometer, to the other point of contact. If, on the
contrary, both points of contact lie between the neuter circle
and the centre of the plate, the current passes from the point
of contact situated nearest the centre, through the galvano-
meter, to the other point of contact. If the neuter circle lies
between the two points of contact, the positions of these latter
can be selected so as to give rise to no current. If the plate
moves in the reverse direction, the electric fluid accumulates
around the neuter circle, and the current consequently changes
its direction. These deductions from theory have been verified
by the observations of M. Felici*.
Pliicker has experimentally investigated the following
case :—Through the centre of a metal disk, ab (fig. 3), passes
an axis, ed, of the same metal, about which the disk can be set
in rotation. Nearer to the circumference of the disk an aper-
ture is pierced, into which a magnet, sn, is fitted so that its
centre is in the plane of the disk, and its axis parallel to the
axis of rotation. Ifthe rotation takes place in the direction
indicated by the arrow, the poles of the magnet having the
position shown in the figure, on uniting by a conducting wire
one of the extremities of the axis of rotation to the circumfe-
rence of the disk we obtain a galvanic current passing from
the former to the latter through the wire. The current con-
sequently follows the same direction as if the disk with its axis
were in rotation about the magnetf.
According to what precedes, the induction at any point of
the conductor depends on its motion relatively to the magnet
regarded as a fixed point. As is known, this relative motion
undergoes no modification if to the magnet as well as to the
point in question equal velocities in the same direction be im-
parted. Thus, in the first place, it is easy to determine the
induction in the axis of rotation itself by proceeding as fol-
lows :—To the rotation-axis and the magnet a velocity is im-
parted equal but opposite to the actual velocity of the magnet,
which therefore comes to rest, while the axis rotates about it
in the direction indicated by the arrow. The induction in the
axis consequently becomes the same as if the magnet were at
* Ann. de Chimie et de Physique, (3) xliv. p. 343.
tT Pogg. Ann. vol. Ixxxvii. p. 352.
Prof. H. Edlund on Unipolar Induction. 297
rest and the axis were revolving round it with the same an-
gular velocity. As regards the induction in the metallic disk,
it can be determined in the following manner :—
Let a (fig. 4) be the point of the disk in which the axis
is fixed, m that in which the disk is traversed by the magnet,
and p the distance between these points. The rotation-velocity
may then be expressed by pv, v denoting the angular velocity,
and this being effected in the direction from mtob. Any
point, g, of the disk, at the distance r from the axis, will then
move with the rotation-velocity rv in the direction gs. In
order to determine the induction at the point g, we now give
to the magnet and to the point g the velocity pv, but in a di-
rection opposite to that previously impressed on the magnet.
This comes to rest, and the point g receives a velocity equal in
quantity and direction to the resultant of the two velocities pu
and rv, represented in the figure by the lines gt and gs. The
ange gsw being equal to the angle a, the value of that resultant
will be
oN 7? +p? —2rp Cos a.
Now V7?+p’—2rp cosa denotes the distance at which g lies
from m, the point at which the magnet is fixed in the disk.
Consequently the point qg receives the same velocity as if it
moved round the fixed magnet. As this applies to any point
whatever, it follows that the induction produced in the disk
during its motion round the axis will be the same as if the
disk moved round the magnet with the same velocity of rota-
tion.
The following case of induction permits the intensity of the
induced current to be compared with the result obtained by
calculation :—In fig. 5, sm represents a magnet having its
south pole in s and its north pole in m. At the centre of the
magnet and near the south pole are two brass bars of equal
length, ab and cd, fixed perpendicular to the axis of the mag-
net. ‘The bar ad is insulated from the magnet, and furnished
at its lower side with a cylinder which is soldered to it, sur-
rounding the magnet without being in contact with it. Upon
this cylinder slides a metal spring connected to the galvano-
meter by the wire /. The other bar, cd, is in metallic contact
with the magnet; it carries at its upper extremity a mercury-
cup, into which dips the second wire, /’, coming from the gal-
vanometer.
The two brass bars are joined together by the cylinders ac
and bd of the same metal. These cylinders can be placed at
different distances from the magnet, either one on each side
or both on the same side of it. If this apparatus be put in
298 Prof. E. Edlund on Unipolar Induction.
rotation about the axis of the magnet so that, viewed from
above, it moves in the opposite direction to the hands of a
watch, an induced current is obtained passing from the mer-
cury-cup, through the galvanometer, to the spring that slides
upon the metal cylinder. We will now calculate the intensity
of this induced current. :
An electric element dr, situated in ¢, at the distance r from
the magnet, has a velocity which may be designated by rv if
v signifies the angular velocity. Upon this element the two
poles exert equal actions, the one along the right line tw, the
other along tw. Taking the component of these forces in the
direction ab, we shall get (2/ signifying the distance between
the poles, M the magnetic moment of the poles, and & a con-
stant)
2kMvlrdr
(2 +7?)2
Integrating this expression between the limits r=0 and
r=7p (this last denoting the distance between the magnet and
the cylinder ac), we get, for the total electromotive force in-
duced in the bar ao,
Sky ee
(P +73)?
The two poles tend to drive in opposite directions an elec-
tric element dz of the bar ac, situated at the distance z from
the point a; but the action of the south pole is the more pow-
erful, because that pole is nearer to dz than the other. The
resultant of their action will be
ior? if 1
Ufa| oo om RS UL © ae Ges Tene
° Laney +72 |2 [(@+2)P?+ =
Integrating between the limits z=0 and z=1, we get, as
the expression of the total of the electromotive force induced
in the cylinder ae,
Q2kMol 2kMol
isan en age (D)
(P+)? (4? +75)?
For the calculation of the electromotive force induced in
the bar es, the north pole will be sufficient to take into consi-
deration, since the south pole, acting perpendicularly to the
length of this bar, does not contribute to the transfer of the
electric molecules. It is moreover evident that the electro-
motive force induced in es acts in a direction opposite to
that of the forces induced in ao and ac. The expression
Prof. E. Edlund on Unipolar Induction. 299
of this force will be
2kMvl
+ kMv— ——_——_.. oe. (es ° ° eae iD
(4P +73)3 o
Subtracting the expression (EH) from the sum of (C) and
(D), we get, for the total electromotive force of the induced
current,
kMv.
This force, then, is independent of the distance between the
bar ac and the magnet, just as it is of their lengths. The
theoretic consideration, moreover, evidently requires that the
force be independent of the section of the conductor, and that
it have the same value, whether the brass cylinders ac and bd
are introduced both at the same time into the apparatus, or
only oneatatime*. In the former case we have two elec-
tromotors ; but they are placed side by side and consequently
do not augment the electromotive force. The same fact pre-
sents itself here as when we connect each to each the po-
sitive poles and the negative poles of two ordinary piles: the
electromotive force is not changed ; but the resistance of the
combined pile is lessened by one half. Now the resistance in
the circuit oacs is extremely slight in comparison with that of
the galvanometer ; therefore the intensity of the current will
remain the same, whether the cylinders ac and 6d be both in-
troduced into the apparatus or only one of them, and the dis-
tance at which they happen to be from the magnet will not
influence the result. This is proved by the following experi-
ments, made with an apparatus of this kind :—
Galvanometer-
deflections.
scale-divisions.
A single cylinder placed at 4:5 centims. f 36-0
distance from the magnet . . . . 37°5
A cylinder on each side of the magnet, ora
placed at 4°5 centims. distance 37:5
A single cylinder placed at 4:5 centims. { 37°3
memineha maoriet: 2.24mi i.) 8. 38°0
The mean of the two first and the two last observations is
37:2; and that of the three middle observations is 37°5.
* Pliicker has inferred from some experiments that the induced elec-
tromotive force of a conductor is proportional to the section of the con-
ductor and dependent on its conductive power (Pogg. Ann. vol. lxxxvii.
p- 368). Examination of his experiments, however, shows that they by
no means authorize this conclusion. ;
300 Prof. E. Edlund on Unipolar Induction.
The induced current is therefore of equal intensity with the
two cylinders as with one only.
Galvanometer-
deflections.
scale-divisions.
One cylinder on each side of the meant 360 ba
at a distance of 8°5 centims. '
36°5
37°0
One cylinder only, at 8-5 centims. from the 33.0 (39.3
magnet UUs eh a a 40-0
The mean of these six observations is 37:5, consequently
nearly the same as before, though the distance from the
magnet has been almost doubled.
A single cylinder at 3 centims. distance Bi 33-0
from the magnet Cite : 39-5
These observations, therefore, have verified the results of
the theory. :
It is unnecessary to say that the above deflections are cleared
of the feeble thermoelectric currents produced by the heating
of the points of contact during the rotation. It is easy to
eliminate these currents, seeing that they are independent of
the direction of the rotation. 3 :
After this I proceeded to the following experiment :—
Two ebonite disks, agbh and ekfm (fig. 6), of equal dimen-
sions, their peripheries encased in a band of brass, were
pierced in the centre and passed over an axis cd, about which
they could be put in rotation. ab and ef represent two brass
rules fixed to the disks and communicating in a and e with
the brass bands, while they are insulated from them in 0 and
fand likewise from the axis cd. sn is a magnet passing
through the two disks without any communication with the
two brass rules. One of the disks is placed at the height of the
south pole, and the other at the centre of the magnet. tu is
a brass bar communicating with the rules ab and ef; this bar
can be placed at different distances on both sides of the axis.
The brass springs p and gq slide over the brass bands that en-
circle the disks, and thus communicate with the rules ad and
ef and the bar tu. These springs are connected with the elec-
trodes of the galvanometer. The rotation of the apparatus
about cd, in the direction indicated by the arrow, gives rise to
an electric current which passes from the spring q, throngh
the galvanometer, to the other spring.
During the rotation the poles of the magnet describe circles
about the rotation-axis the radius of which is equal to 7» ;
Prof. H. Edlund on Unipolar Induction. 301
their velocity may therefore be denoted by mv, if v is the
angular velocity. The velocity of the bar tw is rv, 7, de-
noting its distance from the rotation-axis. The relative velo-
city of the bar with respect to the magnet regarded as im-
movable will therefore be (7) +7 ;)v, as already remarked above.
If the bar passes through the points 2 and y on the same side
of the axis of the rotation as the magnet is placed, and at the
distance 7, from that axis, the relative velocity of the bar with
respect to the magnet will be (7%»—7,)v. Thus the relative
velocity of the bar will in both cases be the same as if the
magnet were regarded as immovable, and the disks as well as
the bar as in rotation about it with the same angular velocity
as that which they have in reality about the axis cd. It is
the same with the brass rules ab and ef.
This being admitted, let us suppose we make two experi-
ments with the same velocity of rotation, but with this dif-
ference—that in the one the bar occupies the place indicated
by the figure, while in the other it is placed in xy. In both
cases the induction will be the same as if the apparatus: were
in rotation about the magnet at rest. In the first case we
have to consider the induction in the circuit atwe as well as in
the two rings surrounding the disks, and in the second case
the induction in aaye as well as in the same rings. Now the
calculation given above has shown that the induction in the
circuit atue is equal to that of the circuit azye. Therefore, if
these deductions are correct, the intensity of the induced
current must be the same, whatever the situation of the bar.
The experiments gave the following deflections, in divisions
of the scale :—
The bar placed on the oppposite The bar on the same side of the
side of the axis to the magnet. axis as the magnet.
,=40 millims, 7,=24 millims. 7,=24millims, 7,=40 millims.
17-0 17:0 15°5 16-0
16-0 EGO)» 17:2 17°3
16-2 15°2 17-0 16-0
Mean 16:4 1671 16°6 16°4
As the numbers can be regarded as equal, it follows, as cal-
culation also shows, that the intensity of the current is inde-
pendent of the position of the bar.
According to the preceding statement, unipolar induction
ought not to be considered a real induction, but an ordinary
electrodynamic phenomenon due to the action of the magnet
upon the electric currents produced by the motion of the
- conductor relatively to it. As for the action of the magnet,
whether the currents on which it acts are produced by spe-
302 Prof. E, Edlund on Unipolar Induction.
cial electromotive forces, or by the electric fluid being carried
along in the direction of motion of the conductor, is quite
immaterial. If we notwithstanding continue to regard the
unipolar phenomena as belonging to those of induction, we
shall be obliged to distinguish the following species of
magnetic induction :—
1. Induction due to the action of the magnet upon the
induced circuit augmenting or diminishing, or in general un-
dergoing a variation. This may take place in the two follow-
ing ways:
(a) The magnetic moment undergoes a change, while the
induced circuit and the magnet remain at rest, and conse-
quently do not alter their relative position ;
(6) The magnet and the induced circuit approach towards
or recede from each other without the magnetic moment under-
going variation.
2. Induction due to the circumstance that the conductor
moves in regard to the magnet without the distance from the
poles of the latter to the different points of the conductor ne-
cessarily varying, and without augmentation or diminution of
the magnetic moment—unipolar induction.
These different species of induction may of course some-
times present themselves in combination, as the following ex-
ample shows. Let sn (fig. 7) be a magnet, and ab a metal
tube the axis of which coincides with the prolongation of the
axis of the magnet. If we increase, or if we diminish the
magnetic moment, there will arise in the tube induced cur-
rents of the species la. If we move the brass tube towards
or away from the magnet without modifying the magnetic
moment, induced currents will result of the species 1b, but
also at the same time those of the species 2. On removing the
tube away from or approaching it to the magnet, the electric
molecules present in the tube are carried in the direction of
the movement, and thus form true electric currents, upon which
the magnet acts according to the known law of action between
a magnet and an electric current. It is easy to perceive
that these two kinds of currents proceed in the same direction;
but those of species 2 are so feeble in comparison with the
others, that they can hardly be observed at the same time with
them. In the last place, if the tube is put in rotation about
its axis, induced currents exclusively of species 2 tend to be
formed ; and they become appreciable if the two ends of the
tube be connected with the electrodes of a galvanometer.
By making the theory which has just been expounded serve
for the explanation of the known cases of unipolar induction,
any one may convince himself that it gives for every case re-
Prof. H. Edlund on Unipolar Induction. 303
sults accordant with the experiment. The principle on which
it rests, that the magnet acts upon the electric currents due to
the rotation of the conductor with respect to the magnet in
the same way as upon ordinary currents, this principle cannot,
as far as I can see, give occasion for any doubt. The only
objection which it would be possible to make to it would be
that, the velocity we are able to impart to the conductor being
relatively slight, these currents become so feeble that the
action of the magnet upon them is in reality inappreciable.
But to this remark it may be replied that the velocity of the
electric molecules in an ordinary galvanic current has never
been measured ; several physicists have assumed, upon good
grounds, that this velocity is in reality not very great; it is
therefore not improbable that the velocity which it is possible
to impart mechanically to a conductor is comparable to that
of the electric molecules in a galvanic current of average in-
tensity. We must here carefully distinguish between the
velocity with which the electric movement is propagated from
place to place and that with which the molecules themselves
move. ‘These two velocities have no relation with each other;
thus, as experiment shows, the former velocity may be ex-
tremely great, although the latter be insignificant *.
As the electric molecules are carried along in the direction
in which the conductor is moved, it might perhaps seem, pre-
vious to mature reflection, that a cylindrical tube set in rota-
tion about its axis must exert an electrodynamie action in the
same manner as a coil through which a galvanic current passes.
Such an inference, however, is any thing but justified. If we
admit two electric fluids, one positive and one negative, it will
be noticed that both fluids are conveyed with the same velocity
and in the same direction during the movement of the con-
ductor; therefore these curents mutually destroy their reci-
procal effects. ven if it be admitted that the electric phe-
nomena proceed from one fluid only, the above conclusion is
premature. But to prove this it is necessary to revert to the
principles of the theory as previously explained by mef.
The phenomena of optics have led to the assumption that
the ether is attracted by ponderable matter. A material body
condenses the zether between its molecules until the attraction
exerted upon an zther molecule situated within the body by
the molecules of the body becomes equal to the repulsion ex-
erted by the already condensed ether upon the same ether
molecule. When this point is reached the material body is no
longer in a position to put in motion the external molecule of
ether. Besides that quantity of ether which may be regarded
* Théorie des Phénomenes Electriques, p. 10. + Ibidem.
304 Prof. E. Edlund on Unipolar Induction,
as connected with the body’s own molecules, there exists free
wether between those molecules ; and the quantity of free sether
contained by the entire body must be equal to the quantity of
wether contained in a volume of vacuous space equal to that
of the body. This is what takes place as long as the body is
at rest. If, on the contrary, the body is put in motion with
the ether which it contains, not only the repulsion of that
ether, but also the attraction of the molecules belonging to
the body upon an exterior ether molecule at rest is modified,
and that in virtue of the established principle that “every
thing» that takes place or is effected in nature requires a certain
time.” But, as I have already pointed out, it does not at all
follow from this principle that the modification which the at-
traction between the material molecules and the exterior zether
molecule undergoes in consequence of the motion must be
equal to the modification of the repulsion between the ether
molecules contained in the body and the same exterior molecule.
On the contrary, I have positively expressed the opinion * that
the action between different kinds of molecules is also different
in this respect. Let us now suppose that d (fig. 8) represents
an element of a circuit containing the quantity m of free esther
and a quantity m,) of condensed ether, and that this element,
with the ether contained in it, moves with the velocity h in
the direction indicated by the arrow. We at the same time
suppose that m, is an exterior ether molecule at rest, that the
angle between the right line which joins d and m, and that of
the direction of velocity is 0, and that the distance between
the molecule m, and the element d is equal tor. The repul-
sion between m and m, is then, according to the memoir cited,
expressed by
—
(1—ah cos 0—3kh? cos? 0+ 4kh?) ;
and the Bade between the condensed ether mp) and m,
will be
ni ar (1—ah cos 0—3kh? cos? 0+ $kh?).
Using a and ky to denote new constants, the attraction
exerted upon m, by the material molecules can be expressed by
(1—aoh cos O— 3k oh? cos? 0+ Shh”).
MoM,
The sum of these three expressions indicates the action of
the whole of the element d upon the ether molecule m.
Nothing is known beforehand about the ratio existing
* Op. Git. Dil,
Prof. HE. Edlund on Unipolar Induction. 305
between a@ and ap, nor of that between & and ky ; they can only
be determined by experiment. There is nevertheless a phy-
sical phenomenon which can make them known; and that is
the development of electricity by friction. In this phenome-
non the ether molecules pass from the rubber to the body
rubbed, or vice versd. This passage of the molecules from one
_ side to the other can hardly have its cause except in the fact
that the repulsion exerted upon them by the body in motion
has been modified in some way by the motion itself. Now
the action of the moving body upon an ether molecule present
in the motionless rubber is given by the sum of the three ex-
pressions above cited. If now we put 2 = 2 Se iinet that
sum will be equal to — or, in other words, we get the
same value for the repulsion as before the body was put in
motion. Therefore, in order that friction may be capable of
ke
7, cannot have precisely the same
producing electricity, = and
value.
What has just been said applies to the case in which the
moving body and the rubber are in contact—that is to say,
when 7 is infinitely little. If the two bodies are at a certain
distance from one another, it is impossible to produce a sen-
sible development of electricity by the movement of one of
them ; consequently a and 2 must be sensibly equal to
Mm+™Mp
My
in motion together with the zther, both free and condensed,
which it contains, its action upon a motionless exterior zther
molecule at a given distance will be nearly as great as if the
body were at rest at the same distance. It can easily be shown
that the case is still the same when the exterior zther mole-
cule is itself in motion, and consequently forms an element of
a true galvanic current. A cylindrical tube put in rotation
about its axis will therefore not exert any electrodynamic
action ; or if it does so, at least the action will be insignificant.
In fact, the action of the currents due to the ether being
carried in the direction of the rotation is neutralized by the
opposite electrodynamic action produced by the motion of the
proper molecules of the body in the same direction*.
* When deducing the formule expressing the reciprocal action of two
galvanic current-elements while the conductors in which the electric fluid
is moving are at rest, we have assumed (op. cvt. p. 12) that a,=a and
Phil. Mag. 8.5. Vol. 6. No. 37. Oct. 1878. Xx
as soon as 7 has a finite value. If, then, we puta body
306 Notices respecting New Books.
M. Lemstrém, however, has succeeded in showing, in a
series of very remarkable experiments, that a rotating eylin-
der is capable of producing a real although excessively feeble
electrodynamic action. On putting a pasteboard cylinder
filled with air in rapid motion round a cylinder of soft iron, he
found that the magnetic condition of the latter was modified
by the rotation. M. Lemstrém has demonstrated that the mo-
dification can hardly be attributed to any other cause than the
electrodynamic action of the pasteboard cylinder. He intends
to continue these researches so interesting and important, es-
pecially from the theoretic point of view.
As is sufficiently apparent from the preceding considera-
tions, the theory above formulated for the phenomenena of
unipolar induction does not rest upon vague and arbitrary
assumptions respecting the properties of the magnet and the
galvanic current. Quite the contrary ; it is based exclusively
on their known properties, discovered by means of experiments
or of investigations of another kind. The theory is indepen-
dent of the admission of one or two electric fiuids, and
gives results in complete accordance with experience and with
the requirements of the mechanical theory of heat. We
therefore believe we can affirm that it furnishes the only ad-
missible and true explanation of the phenomena of unipolar
induction, which, as we shall see in the following section,
play a most important part in nature.
[To be continued. |
XLI. Notices respecting New Books.
Elements of Dynamic; an Introduction to the Study of Motion and
Rest in Solid and Fluid Bodies. By W. K. Cuirrorp, F.RS.,
late Fellow and Assistant Tutor of Trinity College, Cambridge ;
Professor of Applied Mathematics and Mechanies at University
College, London. Part I, Kinematic. London: Macmillan and
Co. 1878. (Crown 8vo, pp. 221).
Pus is the first part of a work the completion of which will be
looked forward to with great interest by all students of Ma-
thematical Physics. Its scope is sufficiently described by its name:
it is a treatise on Kinematics. Change of motion as it occurs in
nature is due to the mutual action of bodies on each other. It is,
however, possible to study and describe the motion of a system
without taking into account the conditions that arise from these
mutual actions. The theory of motion when thus treated is Kine-
k,=k. In this way the same result is arrived at as by assuming that the
ratio between these constants is equal to a, but its deduction be-
0
comes more simple.
Notices respecting New Books. 307
matics; or, in the words of the author “the science which teaches
how to describe motion accurately, and how to compound different
motions together, is called Kinematic (xeynua, motion)” (p. 2).
_ The existence of a distinction between Kinematics and Dynamics
was recognized long ago, perhaps in the first instance by Ampére* ;
but up to the present time it has only been obtaining recognition
gradually in the Mechanical Treatises most commonly in use. The
Kinematical part of Applied Mechanics, it is true, received separate
and systematic treatment long ago in Professor Willis’s ‘ Elements
of Mechanism ;’ and in Professor Rankine’s ‘ Applied Mechanics’
there is a separate Part (III.) on the “ principles of Cinematics, or
_ the comparison of Motions,” in addition to a Part (IV.) on the
“theory of Mechanism.” But long after the publication of the
former of these works the distinction was simply ignored in the
text-books of Theoretical Mechanics commonly in use; or where
that was hardly possible (as in treating the motion of a rigid body
about a fixed point), a few kinematical propositions were introduced
under some such heading as “the Geometrical Nature of a Body’s
Motion about a Fixed Point,” or ‘“‘ the Geometry of the Motion of a
Rigid Body,” &c. In fact the distinction was not worked out com-
pletely until the appearance of the first (and hitherto the alone
published) volume of Thomson and Tait’s ‘ Natural Philosophy.’
When a subject consists of two distinct branches, that alone is a
sufficient reason for their separate treatment; but if a further reason
for the separation were needed, it would be found in the fact that,
in consequence of the customary indirect treatment of Kimematics,
parts of it seem to escape the attention of students. Thus, though in
the course of their Dynamical studies most students obtain indi-
rectly an acquaintance with the geometry of translatory and rota-
tional motion, comparatively few (as we have reason to believe)
have any acquaintance with the geometry of strains.
The work before us will doubtless confirm the existing tendency
towards a separate study of the theory of pure motion; but this
may be regarded as one of its least merits. The most marked pe-
culiarity of the volume is the unusual form in which even the most
elementary parts of the subject are set forth. To all appearance
the author has established for himself a peculiar point of view from
which to regard the whole subject of Dynamics; and consequently
his exposition of the kinematical part follows lines quite wide of the
beaten tracks. This does not indeed appear at first sight; for he
treats it under its most obvious subdivisions of Translations, Rota-
tions, and Strains; but when the details of any one of these sub-
divisions are examined the originality of the treatment becomes at
once apparent. For example, the second chapter of the first book
is headed “Velocities,” and occupies nearly a ‘fourth part of the
volume. Although it treats in great part of matters familiar to
every student of Mathematics, the form in which they appear is
very unlike that in which they are commonly treated, and is appa-
rently the author’s own: ¢. g., instead of introducing the reader
* See Whewell, ‘ Phil. Ind. Sci.’ vol, i. p. 152.
X 2
308 Notices respecting New Books.
directly to such a function as e, our author prefers to start with
the definition “ that a point is said to have logarithmic motion on a
straight line when its distance from a fixed point on the line is
equally multiplied in equal times” (p. 78) ; and then, from the discus-
sion that follows, the function ¢;, as it were, emerges. Itis needless
to add that it is most instructive to see how familiar matters are
regarded by a mind of great acuteness. Other instances might be
given, such as the articles headed ‘“ Exact Definition of Tangent,”
which leads up to another, entitled “ Exact Definition of Velocity.”
However instructive many of these discussions may be, it is never-
theless somewhat difficult to account for the presence of many
things in the volume. For instance, it is hard to see why a trea-—
tise on Kinematics should contain a demonstration of the fact that
the flux of a function of functions is given by the formula
U=LO,U+Y9,u*,
and the more as the demonstration is hardly perfect. What Pro-
fessor Clifford says is this:—w denoting f(#, y), where w and y
are functions of ¢, we find
Dime ES hae’ Pica Y)—F Y,) = Yin See Y.-F Ys) s
t.—t, t,—t, v,—%X, t—t, Y¥,—Y, ‘
‘and when we strike out common factors and omit suffixes in this
last expression, it becomes 70,f+y0,f, where f has been shortly
written instead of fiw, y). Or, substituting w for f, we have” the
above formula (p. 66). We will not urge that the reader might
easily misunderstand the direction to strike out common factors on
the right-hand side of the equation. But we would ask how, in the
case of any function not purely algebraical, does the student know
that there is a common factor to be struck out of the numerator
and denominator of any one of the four fractions concerned? The
fact is, that in all but a few cases the calculation in question can
hardly be performed except by the use of limits or infinitesimals.
The point which has given rise to these remarks by no means stands
alone. We find in different parts of the volume :—accounts of
the elementary properties of quadric curves (pp. 27-31, 38, 39, 91)
and surfaces (pp. 172-176, 177-181); the method of finding the
fluxion of é (p. 55), of finding the area of a parabola (p. 73), of
t
establishing the relation | #dt=d#+1:k+41 (p. 73), and of pro-
0
ving that “ the central projection of a harmonic range is also a har-
monic range” (p.42). These and other things like them fairly suggest
the question, For what class of readers is the book designed? The
* Looking at this well-known relation when thus written, we are
strongly tempted to suspect that in matters of notation there is a good
deal of mere fashion or arbitrary preference. Mr. Clifford’s way of writing
the formula combines two modes of notation, both of which, a few years
ago, would have been considered to have had their day. There is, how-
he a eae why the fluxional notation should not be altogether lost
sight of.
Notices respecting New Books. 309
only answer that occurs to us is, that the writer hopes by inserting
these matters to render his book accessible to readers who bring
nothing with them but a knowledge of the elements of Algebra,
Geometry, and Trigonometry. Our author may perhaps find one
or two readers capable of making out the contents of the volume on
these terms, 7. ¢. capable, while studying a distinct subject, of
picking up incidentally a knowledge of the Geometry of Curves and
Surfaces of the second degree, the principles of the Differential and
Integral Calculus, the properties of the Potential, and some thing
more than the elements of Quaternions. All but a very few find it
necessary to devote their undivided attention to these subjects ; and
even then a great amount of illustration is needed to ensure their
being firmly grasped; and we may add that even the few would
be the better for going through the usual discipline, though they
might possibly do without it. The remarks made by a most com-
petent judge in a somewhat similar case* would, we believe, apply
to this. A retentive memory and great clearness and precision of
thought may (though only in exceptional cases), supersede the ne-
cessity of a progressive training. In other cases, should the student
attempt to dispense with such a training, he will probably rise from
his labours without retaining a single definite conception either of
the propositions or their proofs. |
The Moon, her Motions, Aspect, Scenery, and Physical Condition.
By Ricuarp A. Proctor. Second Hdition. London: Long-
mans and Co. 1878.
The appearance of a Second Edition of this work is strong
evidence of an increasing interest in Selenographical inquiries.
The Moon’s distance, size, and motions, which Mr. Proctor treats
of in his opening Chapters, have long claimed the attention of astro-
nomers; and of all the triumphs yet achieved, the Lunar Theory
stands preeminent. It is of late years that many astronomers have
exhibited no little interest in examining the external characteristics
of members of the Solar System, seeking from them to obtain some
indications of their physical condition ; and those who are interested
in our Satellite are turning their attention especially to the external
configuration of her globe, with a view, first, to ascertain if any
changes occur among the numerous objects diversifying her sur-
face, and, secondly, from the observations obtained to endeavour to
derive some idea of the forces operating in her interior. To this
part of his general subject our author has devoted two chapters—
one on the study of the Moon’s surface, the other on its condition.
These chapters will be read with interest by every student seeking
_ information on the rise, progress, and present state of Selenography.
In many respects this edition is an improvement on the first; and
we wish it all the success which the well-earned popularity of the
author is likely to obtain for it.
* Peacock’s Life of Young, pp: 51, 191.
310 4
XLII. Proceedings of Learned Societies.
GEOLOGICAL SOCIETY.
June 19, 1878.—John Evans, Esq., D.C.L., F.R.S., Vice-President,
in the Chair.
[Continued from p. 285. ]
aS following communications were read :—
2. “ Notes on the Paleontology and some of the Physical Con-
ditions of the Meux’s-Well Deposits.” By Charles Moore, Ksq.,
E.G:S.
The author remarks that the various deep-well borings around
London have abundantly proved the correctness of Mr. Godwin-
Austen’s inference that the Paleozoic axis of the Mendips is con-
tinued beneath the Secondary rocks of the south-eastern counties.
Mr. Moore has himself shown that where these Palaeozoic rocks
finally disappear under the Secondary strata, there are found at the
unconformable junction of the two formations a set of deposits in-
dicating the existence of very peculiar physical conditions, and con-
taining an admixture of fossils from very different geological hori-
zons. Hence he was led to inquire whether any trace of similar
abnormal deposits might be found in the deep-well borings of
London.
With this view he set to work at washing some of the materials
supplied to him from the Meux’s well, and studying the minute and
often microscopic organisms thus obtained.
The Chalk was not particularly examined ; but from a single small
sample of Upper Greensand he obtained numerous Foraminifera and
Entomostraca, including one Cyprid new to science.
The Gault yielded 16 genera and over 30 species of Foraminifera,
and 20 species of Entomostraca, 4 of which are new, together with
many young forms of Gasteropods and Cephalopods.
But the chief interest of Mr. Moore’s investigations centres in the
67 feet of strata intervening between the Gault and Devonian. In
this marly and oolitic-looking deposit he found no less than 85 dif-
ferent kinds of organisms, exhibiting a singular admixture of marine
and lacustrine forms of life. Foraminifera are rare, but Entomostraca
and Polyzoa are very abundant. Some genera are found, such as Car-
penteria, Saccammina, Thecidium, and Zellania, of which the range in
time is greatly extended by these investigations.
The author fully confirms Mr. Etheridge’s reference of the beds
in question to the Neocomian period, widely as they differ in phy-
sical characters from the Lower Greensand strata of the south-east
of England. From a careful study of the nature and condition of
preservation of the minute organisms he concludes that the deposits
which contain them were formed at first in shallow lacustrine hollows
on the surface of the Devonian rocks now lying buried at a depth of
1000 feet below London, and that these lakes were invaded by the
waters of the Neocomian sea, with the deposits of which their sedi-
ments were in part mingled, and under which they were finally buried.
Geological Society. 311
The Chair was then taken by Prof. Prestwich, M.A., F.R.S.,
Vice-President.
3. “On Pelanechinus, a new Genus of Sea-urchin from the Coral
Rag.” By W. Keeping, Esq., B.A. F.G.S., Professor of Geology
in the University College of Wales.
4. “ Remarks on Saurocephalus, and on the Species which have
been referred to that Genus.” By H. Tulley Newton, Esq., F.GS.,
of H.M. Geological Survey.
5. “A Microscopical Study of some Huronian Clay-slates.” By
Dr. Arthur Wichmann.
Although a considerable amount of attention has been devoted
during recent years to the microscopical study of clay-slates and
slate-clays, yet in none of the published researches on this subject
has any account of the structure of the clay-slates of archean age
been given. The author has availed himself of the extensive series
of Huronian clay-slates collected by Major T. V. Brooks in the
country around Lake Superior to supply this deficiency. The suc-
cession and relation of the rocks described have been fully treated
of in the work of Hermann Credner and the publications of the
Geological Survey of Michigan.
The chief object of the author is to discuss the origin of the crys-
talline constituents in clay-slates, and at the outset he describes in
detail the microscopical character of clay-slate, of novaculite or
whetstone, and of carbonaceous shales and slates respectively, dwell-
ing more especially on the crystallized minerals which can be detected
in each of these rocks, and the nature of the isotropic ground-mass
which sometimes surrounds them. He then points out that three
theories have been advanced to account for the presence of these
erystalline constituents in clay-slates. According to the first of
these theories, the crystals in question are regarded as the
product of chemical action in the ocean in which the original
material was deposited ; the second theory attributes the formation
of the erystallme minerals to processes of metamorphism which
haye taken place subsequently to the solidification of the rocks ;
the third theory refers them to aggregative action going on in the
still plastic clay-slate mud prior to its solidification. The first of
these theories has been maintained by G. R. Credner ; but against it
the author adduces numerous arguments, and especially points out
the difficulty of supposing an ocean capable of depositing from its
waters at successive periods minerals of such different chemical
composition as chlorite, actinolite, &c. In opposition to the second
theory, which has received the support of Delesse, the author points
out the existence in the rocks in question of broken crystals which
have been recemented by the surrounding clay-slate substance.
The author is thus led to incline towards the third theory, in favour
of which some striking facts, drawn from the microscopical structure
of the rocks, haye already been adduced by Zirkel. He admits,
however, that later metamorphic actions are not to be excluded in
seeking to account for the origin of the crystalline constituents of
312 Geological Society :—
clay-slates, and points out that four distinct stages must be con-
sidered in the series of changes by which the rocks in question have
acquired their present character :—I1st, the deposition of the mud ;
2nd, the formation of minerals during the plastic state; 3rd, the
separation of materials during solidification ; and 4th, the action of
metamorphic processes.
6. “On a Section through Glazebrook Moss, Lancashire.” By T.
Mellard Reade, Esq., F.G.S.
The section described has been exposed in a cutting made by the
Wigan Junction Railway. The moss rests on an almost perfectly
level floor of Boulder-clay, and is at the deepest part about 18 feet
thick. In the 8 or 4 feet at the base are branches &c. of trees; and
the stools are found resting on and rooted in the Boulder-clay ;
these are of oak or birch. Prostrate trunks were found, one, an
oak, being 46 feet long and 3 in diameter. The surface of the clay
is about 60 feet above O.D. The author thinks the section shows
that the moss originated from the decay of the forest, favoured by
change of climate, and gradually extended itself from the centre
outwards, trees within it at the outer part being much less dis-
coloured than those further in. In the latter part of the paper
some cuttings and borings in the clays and sands are described, and
the asserted occurrence of the trunk of a tree in the Boulder-clay is
noticed.
7. “On the Tertiary Deposits on the Solimées and Javary Rivers
in Brazil.” By C. B. Brown, Esq. With an Appendix by R. Ethe-
ridge, Esq., F.R.S., F.G.S., and communicated by him.
The author in 1874 had the opportunity of examining some beds
on the Solimées, or Upper Amazon, and the Javary, one of its
tributaries, containing fresh- and brackish-water shells similar
to those found in Tertiary deposits at Pebas, still higher up the
river. ‘he author indicates certain errors into which he considers
previous writers to have fallen, and calls attention to the great
extent of these beds, now demonstrated to occupy a tract of country
300 miles in length by 50 miles in breadth, and to the enormous
change in the physical features of the region which must have taken
place since their deposition. When this took place the sea reached
probably 1500 miles west of its present shore-line, covering the
country which is now the valley of the Amazon. The absence of
examples of false-bedding in the deposits leads him to the conclusion
that they were formed in comparatively still water, into which
flowed numerous streams bearing much vegetable matter, which has
served for the formation of lignitic deposits, the whole being pro-
bably the upper beds of a series deposited under similar conditions
to those of deltas in the present day. In an appendix, Mr. Etheridge
notices the fossils collected by the author, which included seeds of
Chara, and species of Mytilus (1 new), Anisothyris (4, 1 new),
Lutraria (1), Thracia (1), Anodon (1), Unio (1), Natica? (1),
Neritina (2 new), Odostomia (1), Hydrobia (1 new), Iscea (1), Dyris
(1), Asstminea (1 new), Fenella (1), Cerithium (2 new), Melania 4(
On the Physical History of the English Lake-District. 318
new), and a new Gasteropod constituting a genus (Alyccodonta)
allied to Alyceus. A single palatal plate of Myliobatis or Zygobatis
(probably derived) was also found.
8. “On the Physical History of the English Lake-district, with
Notes on the possible Subdivision of the Skiddaw Slates.” By J.
Clifton Ward, Esq., Assoc.R.S.M., F.G.S.
The author traces the physical history of the lake-district from
the commencement of the period when the Skiddaw slate was
deposited. To this succeeded the volcanic Borrowdale series, which
is followed after a physical break by the Coniston Limestone.
Between this and the succeeding Silurian deposits there is little, if
any, break. Thus, in the Lake-district, the break between Upper
and Lower Silurian is physically below the Coniston Limestone,
though paleontologically it is above it.
The Old Red Sandstone period was one of denudation, which was
continued into the Carboniferous period ; and perhaps the whole
district was actually covered by the sea during the maximum
depression of the Lower Carboniferous epoch. Since then it has
probably never been submerged, but exposed to continuous subaerial
denudation. The physical significance of the Mell-Fell (Lower
Carboniferous) conglomerates receives special attention.
The author then, from consideration of the amount of deposition
and rate of denudation, attempts to estimate the period which has
elapsed since the commencement of the record, and sets it down as
62,000,000 of years. The author then considers the age of the
Skiddaw slates. From lithological resemblances he is led to cor-
relate the Skiddaw grit with the basement grit in the Welsh Arenig
series, and thus to regard the beds below the grit as the equivalent of
the Tremadoc, and perhaps of part of the Lingula Flags.
The paleontological evidence for the correspondence of the Arenig
series with the whole of the Skiddaw slates rests chiefly on Graptolites
and Trilobites. The author holds that the evidence from the former
is inconclusive, and that from the latter to some extent contradictory,
so that the physical evidence can in no way be overridden by it.
9. ‘On some well-defined Life-zones in the Lower Part of the
Silurian (Sedgw.) of the Lake-district.” By J. E. Marr, Esq.
10. “ On the Upper Part of the Bala Beds and Base of Silurian in
North Wales.” By F. Ruddy, Esq. Communicated by Prof. T.
M‘K. Hughes, M.A., F.G.S.
The author describes a series of sections in the upper part of the
Bala and the succeeding beds, and gives lists of fossils. Details of
the various beds between the Bala and Hirnant Limestone are
given, above which come soft blue shales underlying Tarannon
shales, when fossils cease until the base of the Wenlock is reached.
The author has been able to trace the Hirnant Limestone and grit
considerably beyond the limits of the Hirnant valley. The sections
at Cynwyd (to the west of Corwen) are described. Here occur the
equivalents of the Bala Limestone and beds above this up to the
level (probably) of the Hirnant Grit.
pkey
XLII. Intelligence and Miscellaneous Articles.
A SPECTROMETRIC STUDY OF SOME SOURCES OF LIGHT.
BY A. CROVA.
'IXHE general law of emission of the radiations emitted by a body
raised to an elevated temperature is not completely known.
Dulong and Petit * have given the empirical law of the obscure ra-
diations emanating from a body heated to temperatures below 240°;
and Edm. Beequerelf has demonstrated that the intensity of the
red, green, and blue radiations varies with the temperature of the
body which emits them, according to an exponential law analogous
to that of Dulong and Petit.
The exponentials which represent the law of emission of radia-
tions of different refrangibilities are represented by curves of which
the origin corresponds to the temperature at which the radiation
considered commences to be produced, and rises the more rapidly
as the wave-lengths of the radiations become less. According to
M. Edm. Becquerel, the logarithms of the bases of these exponen-
tials vary in the inverse ratio of the wave-lengths of the radiations.
These considerations may serve as a starting-point to a method
of determination, in a spectrometric way, of the temperature of
incandescent solids or liquids. In fact it follows from the investi-
gations of Mr. Drapert and M. Edm. Becquerel that, when the tem-
perature of an incandescent solid increases in a continuous manner,
the spectrum of the radiations emitted by it lengthens towards the
violet end, and that each of the radiations of this spectrum 1s at the
same time increased in intensity according to an exponential for-
mula. The temperature of the luminous source can therefore be
measured :—(1) by means of the wave-length of the radiation which
limits the spectrum towards the violet; (2) by the position of the
thermal maximum of the spectrum, which approaches nearer to the
violet in proportion as the emission-temperature becomes higher ;
(3) by means of the ratio of the lummous intensity of a determi-
nate radiation A, taken in the spectrum of the source, to the inten-
sity of the same radiation in the spectrum of a source of known
temperature, compared with the ratio of the luminous intensities of
another radiation A’ in the same two spectra.
These last determinations can be easily effected by means of a
spectrophotometer. Several observers have made use of instru-
ments of this kind§. I used that of M. Glahn, which permits
measurements to be made upon homogeneous radiations.
On the other hand, I have measured the thermal intensity of the
simple radiations of the solar spectrum by means of a linear ther-_
moelectric pile and a very sensitive galvanometer, using for the
* Ann. de Chimie et de Physique, 2¢ série, t. vil.
+ Edm. Becquerel, La Lumiere, t. i. pp. 61-67.
{ Phil. Mag. 1847, vol. xxx. p. 340.
§ Govi, Comptes Rendus, t. 1. p. 156 (1860). Trannin, Journal de
Physique, t. v. p. 297. Vierordt, Pogg. Ann. Sth series, vol. xx. Glahn,
Wiedemann’s Annalen, vol. i. (1877).
Intelligence and Miscellaneous Articles. 315
first trials a flint-glass prism and a glass concave mirror silvered
at its surface instead of an achromatic lens. The employment
of a network of lines engraved on the metal instead of the prism
would permit the influence of any elective absorption to be elimi-
nated.
I have made numerous determinations of thermal curves of the
solar spectrum on exceptionally fine days, at different periods in
the years 1877 and 1878. These curves differ in the ratio of their
respective ordinates, but especially in the position of the thermal
maximum, as has been shown by Melloni. These curves were ren-
dered comparable with one another by bringing them to the scale of
the waye-lengths, and reducing, by means of the dispersion-curve of
the prism, the intensities to those which would correspond to the
theoretic case of the normal spectrum—that is, of constant dis-
persion.
The following are, for the luminous part of these spectra, the
means of a number of concordant observations made under excel-
lent atmospheric conditions :—
milliim. millim. millim. millim. millim. millim.
Wayve-lengths ...... 0°000676 0-000605 0-000560 0:000523 0:000486 0-000459
Intensities ......... 1000 820 760 670 540 460
Ihave represented by 1000 the thermal intensity which corresponds
to a red radiation of wave-length 0:000676 millim.; the intensities
measured in the ultra-red cannot find a place in this Table, the cor-
responding waye-lengths not being accurately known.
Now here are the ratios of the luminous intensities of the same
radiations of the spectra of the following sources, compared with
the light of the sun :—
millim. milliim. millim. millim. millim. millim.
Warve-lengths ...... 0-000676 0-000605 0-000560 0:000523 0-000486 0-:000459
Electric light ...... 1000 707 597 506 307 228
Drummond light... 1000 573 490 299 168 73
Moderator lamp... 1000 442 296 166 80 27
The electric ight was from 60 large Bunsen elements, Foucault
regulator, with M. Carré’s carbons in the focus of a metallic con-
cave mirror; the Drummond light, oxygen and illuminating-gas
thrown upon lime; the moderator lamp, fed with colza-oil. I
measured the ratio of the intensity of each of the radiations of these
spectra, corresponding to the wave-lengths of the preceding Table,
to the intensity of the same radiation in the solar spectrum, repre-
senting these latter by the value of their thermal intensities, and
always representing by 1000 the intensity corresponding to the
wave-length 676.
For luminous radiations which have undergone no weakening by
previous transmission, there would be proportionality between the
thermal and luminous intensities of one and the same radiation,
whatever its origin, as MM. Jamin and Masson have demonstrated ;
but the experiments of M. Desains* have shown that, in the con-
* Comptes Rendus, t. \xvii. p. 297.
316 Intelligence anil Miscellaneous Articles.
trary case, rays of the same wave-length, taken from different
spectra, may have notably different properties.
We can, however, already state that, the intensity being the
same in the red for the four spectra, the weakening towards the
violet varies with each source, according to a certain function of
the temperature ; and without being able yet to attempt a measure-
ment of this, we can already arrange them in the order of increasing
temperatures :—moderator lamp; stearine candle; illuminating-
gas, of which I have not given the less-accordant Tables ; Drum-
mond light; electric light, and, lastly, the solar light, which cor-
responds to an emission-temperature much higher than that of the
electric light, in spite of the uncertainty caused by the absorptions
it has undergone from its transmission through the gaseous en-
velopes of the sun and our atmosphere.
It will be possible to make rigorously exact measurement of the
temperatures in the spectrometric way as soon as we know the
precise law of emission for all the radiations and the numerical —
constants for each wave-length. The results contained in this Note
may be regarded as a first essay towards the solution of this im-
portant question.—Comptes Rendus de Académie des Sciences,
August 19, 1878, tome lxxxvil. pp. 8322-325.
ON THE EXCITATION OF ELECTRICITY BY PRESSURE AND
FRICTION. BY H. FRITSCH, OF KONIGSBERG, PRUSSIA.
1. It is well known that many crystalline bodies can be power-
fully electrified by pressure. This, however, takes place in each
case only under a perfectly definite condition. Calc-spar becomes
electric only when pressed against another substance, never when
pressed against another piece of cale-spar. Three pieces of calc-
spar were laid one upon another; a pressure was then exerted upon
the uppermost, which would have made each of the pieces singly di-
stinctly electric: the central piece proved to be quite devoid of
excitation; only the two outer ones possessed the usual quantity
of electricity. If two cale-spars were pressed against one another,
the surfaces which were in contact with the foreign bodies by
which the pressure was exerted. exhibited electricity distinctly ; the
two inner surfaces, where calc-spar had been in contact with cale-
spar, were without excitation. I have not yet succeeded in carry-
ing out the same experiment with other bodies.
2. According to previous observations, a definite substance, on
undergoing friction against another, acquires always a certain in-—
variable electrical excitation independent of the collateral cirecum-
stances, and accordingly the nature of the electricity excited is
constantly the same.- To test the correctness of this position the
following experiments were instituted, in which the collateral
circumstances were varied as much as possible.
a. With a violin-bow J stroked plates of zinc, copper, brass, and
Intelligence and Miscellaneous Articles. 317
four different glasses sothat they vibrated transversally ; they became
only negatively electrified. If the same bow was drawn backwards
and forwards lengthwise along the same part of the plate without
producing a tone, it became only positively electric.
6. Copper plates of 4 and 7 centims. diameter were whipped
with white silk in various ways. If the stroke was delivered
nearly perpendicular to the plate, the latter became strongly posi-
tive ; if it was more nearly grazing, the plate became just as strongly
negative. Whether the plate was fresh cleaned with hydrochloric
acid, or by longer exposure to the air had become tarnished, made
no difference, nor yet the size of the plate. Further, by lightly
rubbing its entire rim (best with a silk or woollen cloth in the
form of cone-cover), the plate is always rendered negative; by
hard rubbing with the same silk on the same place, always
positive. Coarse woollen cloth appeared to excite less powerfully.
Zine gave the same result.
c. With brass the collateral circumstances appeared to have an
influence. A square plate intended for the production of Chladni’s
sound-figures behaved exactly like the copper plate. The shallow
brass scale of a table-balance, however, gave both electricities only
when struck with silk, and -when its surface was well cleaned.
Lastly, an old pound-weight could not be excited in different ways
with silk; this could only be accomplished with a violin-bow, ac-
cording as the bow was applied to its thick main part, or to its
thin neck.
d. A small scale-pan of fine silver gave both electricities only
with silk, with wool it only became negatively electric.
e. A hard-gum plate always became negative when slowly stroked
with a tightly folded lmen cloth—when stroked quickly, in other-
wise like circumstances, positive. The surface of the hand produced
the same effect as linen ; only for the positive excitation the stroking
had to be very rapid.
f. White silk always makes the principal-cleavage-surface of
gypsum positive, but the second, which exhibits a vitreous lustre,
negative; while it makes no difference whether the surfaces of this
second cleavage are already present on the piece of gypsum, or are
artificially produced by roughly scraping a surface of the principal
one.
Many other substances give opposite electric excitation on friction,
according to the circumstances—for instance, mica struck with silk,
hardgum rubbed with copper, hardgum whipped with silk, glass
struck with silk; I have not, however, succeeded in discovering posi-
tive rules for this. The few experiments cited above (from « to f)
even show the impossibility of constructing a series of intensities
for frictional electricity. If two bodies are rubbed against one
another, the electricity excited in each of them may change into
the opposite as the pressure, the velocity, or the direetion of the
rubbing motion, &c. varies—Wiedemann’s Annalen, 1878, No. 9.
318 Intelligence and Miscellaneous ‘Articles.
THE SOLAR ECLIPSE OF JULY 297TH, 1878.
BY PROFESSOR HENRY DRAPER, M.D.
As I have recently been giving attention to the subject of solar
spectroscopy in consequence of my discovery of oxygen in the sun,
it seemed to be desirable to take advantage of the total eclipse of
July 29th, to gain as precise an idea as possible of the nature of
the corona, because the study of that envelope has been regarded
as impossible at other times. The main point to ascertain was
whether the corona was an incandescent gas shining by its own
light, or whether it shone by reflected sunlight.
For this purpose I organized an expedition, and was fortunate
enough to secure the cooperation of my friends Professors Barker
and Morton and Mr. Edison. The scheme of operations was as
follows :—(1) the photographic and photo-spectroscopic work as
well as the eve slitless spectroscope were to be in charge of my
wife and myself; (2) the analyzing slit spectroscope was in charge
of Prof. Barker, with the especial object of ascertaining the pre-
sence of bright lines or else of dark Fraunhofer lines in the corona ;
(3) the polariscopic examinations were confided to Professor Morton,
who was also to spend a few moments in looking for bright or dark
lines with a hand spectroscope; (4) Mr. Edison carried with him
one of his newly invented tasimeters with the batteries, resistance
coils, Thomson’s galvanometer, etc., required to determine whether
the heat of the corona could be measured.
This entire programme was successfully carried out; and good for-
tune attended us inevery particular. The results obtained were :—
1st, the spectrum of the corona was photographed, and shown to
be of the same character as that of the sun, and not due toa special
incandescent gas; 2nd, a fine photograph of the corona was ob-
tained, extending, in some parts, to a height of more than twenty
minutes of are—that is, more than 500,000 miles ; 3rd, the Fraun-
hofer dark lines were observed by both Pepto con: Borken and
Morton in the corona; 4th, the polarization was shown by Pro-
fessor Morton to be such as would answer to reflected solar light ;
5th, Mr. Edison found that the heat of the corona was sufficient to
send the index beam of light entirely off the scale of the galvano-
meter. Some negative results were also reached, the principal
one being that the 1474K, or so-called corona line, was either very
faint or else not present at all in the upper part of the corona,
because it could not be observed with a slitless spectroscope, and
the slit spectroscope only showed it close to the sun.
The general conclusion that follows from these results is, that
on this occasion we have ascertained the true nature of the corona, —
viz. :—it shines by light reflected from the sun by a cloud of
meteors surrounding that luminary, and that on former occasions
it has been infiltrated with materials thrown up from the chromo-
sphere, notably with the 1474 matter and hydrogen. As the chro-
mosphere is now quiescent, this infiltration has taken place to a
scarcely perceptible degree recently. This explanation of the
~
Intelligence and Miscellaneous Articles. 319
nature of the corona reconciles itself so well with many facts that
have been difficult to explain, such as the low pressure at the sur-
face of the sun, that it gains thereby additional strength.
The station occupied by my temporary observatory was Raw-
lins (latitude 41° 48’ 50”, longitude 2" 0™ 44* W. of Washington,
height 6732 feet above the sea), on the line of the Union Pacific
railroad, because, while it was near the central line of totality, it
had also the advantages of being supplied with water from the
granite of the Cherokee Mountain and of having a repair-shop
where mechanical work could be done. I knew by former experience
that the air there was dry and apt to be cloudless: in this parti-
cular our anticipations were more than fulfilled by the event; for
the day of totality was almost without a cloud, and the dew-point
was more than 34° I’. below the temperature.
The instruments we took with us were as follows, and weighed
altogether almost a ton :—(1) An equatorial mounting with spring
governor driving-clock, loaned by Professor Pickering, Director of
Harvard Observatory. (2) A telescope of five and a quarter inches
aperture and seventy-eight inches focal length, furnished with a
lens specially corrected for photography, by Alvan Clark & Sons.
(3) A quadruple achromatic objective of six inches aperture and
twenty-one inches focal length, loaned by Messrs. E. and H. T.
Anthony, of New York; to this lens was attached a Rutherfurd
diffraction grating nearly two inches square, ruled on speculum-
metal. The arrangement, with its plate-holders, etc., will be desig-
nated as a phototelespectroscope. (4) A four-inch achromatic
telescope with Merz direct-vision spectroscope, brought by Professor
Barker from the collection of the University of Pennsylvania.
(5) A four-inch achromatic telescope, also brought by Professor
Barker ; to it was attached Edison’s tasimeter. Besides these there
were polariscopes, a. grating spectroscope, an eye slitless spectro-
scope with two-inch telescope, and, finally, a full set of chemicals
for Anthony’s lightning collodion process, which in my experience
is fully three times quicker than any other process.
The arrangement of the phototelespectroscope requires further
description ; for success in the work it was intended to do, viz.
photographing the diffraction spectrum of the corona, was difficult,
and in the opinion of many of my friends impossible. In order to
have every chance of success, it is necessary to procure a lens of
large aperture and the shortest attainable focal length, and to have
a grating of the largest size adjusted in such a way as to utilize
the beam of light to the best advantage. Moreover the apparatus
must be mounted equatorially and driven by clockwork, so that the
exposure may last. the whole time of totality ; and the photographic
work must be done by the most sensitive wet process. After some
experiments during the summer of 1877 and the spring of 1878,
the following form was adopted.
The lens being of six inches aperture and twenty-one inches focal
length, gave an image of the sun less than one quarter of an inch
in diameter and of extreme brilliancy. Before the beam of light
320 Intelligence and Miscellaneous Articles.
from the lens reached a focus it was intercepted by the Rutherfurd
erating set at an angle of sixty degrees. This threw the beam on
one side and produced there three images—a central one of the sun
and on either side of it a spectrum ; these were received on three
separate sensitive plates. One of these spectra was dispersed
twice as much as the other—that is, gave a photograph twice as
long. This last photograph was actually about two inches long in
the actinic region. If, now, the light of the corona was from in-
candescent gas giving bright lines which lay in the actinic region of
the spectrum, I should have procured ring-shaped images, one ring
for each bright line. On the other hand, if the light of the corona
arose from incandescent solid or liquid bodies, or was reflected light
from the sun, I was certain to obtain a long band in my photo-
graph answering to the actinic region of the spectrum. If the
light was partly from gas and partly from reflected sunlight, a
result partly of rings and partly a band would have appeared.
Immediately after the totality was over and on developing the
photographs, I found that the spectrum-photographs were con-
tinuous bands without the least trace of a ring. I was not sur-
prised at this result, because during the totality I had the oppor-
tunity of studying the corona through a telescope arranged in
substantially the same way as the phototelespectroscope, and saw
no sign of a ring.
The plain photograph of the corona taken with my large equato-
rial on this occasion shows that the corona is not arranged centrally
with regard to the sun. The great mass of the matter lies in the
plane of the ecliptic, but not equally distributed. To the eye it
extended about a degree and a half from the sun towards the west,
while it was scarcely a degree in length towards the east. The
mass of meteors, if such be the construction of the corona, is there-
fore probably arranged in an elliptical form round the sun.—Silli-
man’s American Journal, September 1878.
WATSON’S INTRA-MERCURIAL PLANET.
To the Editors of the Philosophical Magazine and Journal.
Haverford College, Pennsylvania,
GENTLEMEN, September 9, 1878.
Gaillot’s estimated orbit for Watson’s inner planet (C. R. 5 Aott
1878) accords closely with my predictions im 1873 (Proce. Soe. Phil.
Amer. xiii. pp. 238, 472). It appears to be the third of the har-
monically indicated intra-Mercurial planets.
Mean distance. Time.
Gaillot (computed) ........ "164 24-25 days.
Chase (predicted) .......... "165 24:50. ,,
Yours truly,
Puiny EARLE CHASE.
THE
LONDON, EDINBURGH, anp DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FIFTH SERIES.]
NOVEMBER 1878.
XLIV. On the Experimental Determination of Magnetic Mo-
ments in Absolute Measure. By Tuomas Gray*, B.Sce.,
Thomson Experimental Scholar in the University of
Glasgow t.
[ Plate V. ]
SOME experiments on the intensity of the earth’s mag-
netism were made by Gauss, and published, under the
title “Intensitas Vis Magnetice Terrestris ad Mensuram
Absolutam Revocata,” in the Commentationes Societatis Grot-
tingensis, 1832, and in a paper on the General Theory of
Terrestrial Magnetism, an English version of which is given
in the second volume of ‘ Taylor’s Scientific Memoirs.’
The results are given (according to the system the import-
tance of which was first seen, and which was first introduced,
by Gauss himself) in absolute measure. The units of length,
mass, and time employed by him are the millimetre, milli-
gramme, and second. His results, when reduced to C.G.S.
units, show that a steel magnet with which he experimented
had a magnetic moment of 22:2 per gramme mass.
Gauss also calculated (Taylor’s Scientific Memoirs, vol. ii.
p- 225) the mass of steel which would have to be placed in
each cubic metre of non-magnetic matter in order tomake up _
* Now Demonstrator in Physics and Instructor in Telegraphy in the
Imperial College of Engineering, Tokei, Japan. .
- Being the Essay to which the Cleland Gold Medal was awarded .
by the University of Glasgow in the Session 1877-78. Communicated
by Sir W. Thomson to the Philosophical Magazine by permission of the -
enate.
Phil. Mag. 8. 5. Vol. 6. No. 38. Nov. 1878. aie?
322 Mr. T. Gray on the Experimental Determination
a globe of the same magnetic moment as the earth. He
found that this bar must contain 3°55 kilogrammes of the
steel of which his magnets were made.
No experiments, however, have been made and published
hitherto (so far as I know) having for their object the deter-
mination of the magnetic moments of steel magnets of different
tempers and tempered by different methods, or which give
information as to the permanence or non-permanence of the
magnetism of such bars when left undisturbed for any consi-
derable time. ‘The experiments described below were under-
taken with the view of supplying some approximately accurate
information on these points, and also as to whether a hard or
soft quality of steel gave the stronger magnets. They were
performed in the Physical Laboratory of the University of
Glasgow. The experiments on the effect of temper were all
made on small bars cut from a wire of soft.carbon steel.
The apparatus used is shown in the accompanying diagram
(Pl. V.). M represents the magnetometer, which is a reflect-
ing instrument consisting of a small mirror about one centi-
metre in diameter, carrying, cemented to its back, four small
needles about 0°8 centimetre long, and suspended by a single
silk fibre ten centimetres long, which passes down a narrow slit
cut in the frout of a wooden upright fixed to the base. This
slit terminates in a small cell, in which the mirror hangs. The
slit and cell being closed in front bya glass plate, a dead-beat
arrangement is obtained similar to that of Thomson’s reflecting
galvanometer. B B is a bar of wood capable of turning round
the vertical axis R, which, by means of a brass spring S is
made to bear against two brass V’s, one of which is fixed
to the upper and the other to the under side of BB.
A A are two arms of wood (shown in plan at the foot of the
diagram), each of them fixed to BB by means of two thin
wooden strips W. As will be seen from the plan of the arms,
these strips were, in every position in which they were placed,
in a vertical plane passing through the axis R.
The upper side of the bars AA was on a level with the
centre of the mirror; and along the centre of them a small
V-groove was cut, the line of which was arranged to pass
through the centre of the mirror. The axis of a magnet
placed in this groove could evidently, by turning the arms
A A, be caused to make any desired angle with the magnetic
meridian ; and hence the instrument could be used either as a
sine or tangent instrument. I is an ordinary galvanometer-
lamp, and M a scale of half-millimetres placed at a distance of
one metre from the plane of the mirror.
The image of a fine wire, fixed vertically at F, was brought
of Magnetic Moments in Absolute Measure. 323
to a focus on the scale by sliding L to the proper distance from
the mirror, and served as an index by means of which the de-
flection was read. The distance of any point on either of the
arms A A from the mirror was found by referring it to a fine
line marked on the upper surface of each of the arms by a
sharp point attached to a fixed support above in such a
position as just to bear on the upper surface of the arms when
they were turned under it. The distance of this line from the
axis was evidently the same for each of the arms; and _ half
the total distance between the two lines thus drawn gave
the distance of either.
The plane of the magnetometer-needles was made to pass
through the axis by first placing the magnetometer in such
a position on the stand that this condition was approximately
fulfilled, and then adjusting it by means of the levelling-
screws at the base of the instrument until the deflections given
on the scale by a magnet placed in the V-groove on one of the
arms, when the arm was turned so that the magnet was alter-
nately due east and due west of the centre of the mirror, were
equal. In order that the magnetometer might be removed
from the stand when desired, and replaced in exactly the same
position, Sir William Thomson’s geometrical arrangement was
employed. One of the three rounded feet of the instrument
was made to rest in a conical hollow cut in the upper surface
of the stand, another in a V-groove cut with its axis in line
with the centre of the conical hollow, and the remaining foot
on the plane upper surface of the stand.
The mode of experimenting was as follows :—A large
number of cylindrical steel bars were cut from the same bar,
the diameter of which was -097 centimetre, its weight per
metre 5°77 grammes, and its density 7°83.
Before being tempered the bars were carefully filed to a
uniform length of five centimetres. Their lengths were com-
pared with a scale of half-millimetres by means of a lens.
About sixty of these bars, in order that they might be heated as
nearly as possible to the same temperature, were spread on the
bottom of a small thin iron tray, and the whole raised to a bright
red heat in the heart of a glowing fire. To temper the bars glass-
hard, the tray with its contents was quickly removed from the
fire and plunged into water atabout 15° Centigrade. The bars
were then made up into parcels of five each, and placed in a
vessel containing oil. The whole was then heated by means
of a Bunsen lamp, and parcels of the bars removed at each of
the following temperatures—100°, 150°, 200°, 240°, 250°,
260°, 270°, 280°, 300°, 310°. While this process was going
on, the heated oil was taken advantage of to temper a number
324 Mr. T. Gray on the Haperimental Determination
of separate parcels by plunging them, after having been heated
to a bright red heat, into oil of various temperatures. These
bars were not again heated. All the bars were then magnetized
by the current from ten of Thomson’s Tray Daniells, flowing
through a magnetizing coil, of the same length as the bars,
made of insulated copper wire. ‘This coil consisted of four
layers of forty turns each, and had a resistance of ‘065 ohm.
Thus, taking the electromotive force of a Tray Daniell as
10° C.G.S8. units, and its resistance as ‘l ohm or 108 C.G.S8.
units, the current was, in absolute measure, approximately,
— This was distributed over 160 turns of a solenoid five
centimetres long; and therefore the magnetizing force was
iI 160
L065 x re x 4r=377 nearly.
Before the magnetic moments could be calculated, it was of
course necessary to determine the horizontal component of the
earth’s magnetic force at the place where the magnetometer
was to stand during the experiment. This was done by
observing the period of oscillation, under the horizontal com-
ponent of the earth’s force, of five separate magnets, each
suspended by a silk fibre about thirty centimetres long, and
enclosed in a glass case placed on the magnetometer-stand,
The magnetometer was then placed on its stand, and the
deflection of its needle by each of these magnets, placed
with its centre at a distance of twenty centimetres from the
needle, observed. A reading was taken with the magnet
resting in the groove on the arm A, which was placed in an
east-and-west direction. The arm was then turned through
180°, and a reading taken with the magnet in its new position.
The same operations were repeated with the ends of the
magnet reversed, and the arithmetic mean of these four read-
ings taken as the deflection on the scale.
The formulas for deducing the horizontal component and
the magnetic moment are easily obtained, as follows :—
Let H = horizontal component of the earth’s magnetic
force.
T = period of vibration of magnet under H.
# = moment of inertia of magnet round an axis
through its centre at right angles to its length.
y = distance of centre of magnet from centre of
needle.
a = virtual half-length of the magnet (that is, half
the distance beteen its poles).
@ = deflection of needle in degrees.
M = moment of magnet.
of Magnetic Moments in Absolute Measure. 325
Then for equilibrium we have
M 1 vi
ey ees
therefore :
yee (r—a)’ (rte) tan?
— re i
Hence H 2r
we (r—ay’ (r+a)* tan 6°
Again,
T Agr
OEE?
or
Agr
H = 72 VM"
Substituting the value found above for M and squaring,
we get Bar?
= i
T? (r—a) (r+a) tan 0
_ These formulas were used in preference to the approximate
formulas which they become when a is struck out, and which
are generally employed.
The distance between the poles of a magnet, or its virtual
length 2a in the above formulas, may be determined by
observing the deflections 0 and 6’ of the magnetometer-needle
produced by the magnet when placed at distances r and
7’ from the centre of the needle.
For we have the equations
2M (7? =a?) tan 0
12 hat r
_ (r?—a’)? tan OY
y!
from which we obtain by reduction
_ rr tan Of — 1? V7’ tan 6
Vr tan & — V7 tan 0
The average of a number of determinations of a made by
this method agreed almost exactly with the actual half-length
of the magnet ; and as the effect of a slight error in the value
of a does not sensibly affect the value of M, the actual half-
length was used. in all the calculations.
The values found from each of the five magnets are given
in the following Table. These results, as well as all those
which follow, are given in C.G.S. units.
326 Mr. T. Gray on the Experimental Determination
No. of Magnet. Value of H.
"15379
"15412
15422
15405
"15375
Ov HS 09 8
Niden value 25399,
In the determination of the magnetic moments no correc-
tion of the value of H was made for induction.
The magnets were then magnetized a second time by means
of the current from twenty double tray-cells flowing through
a magnetizing coil of the same length as the magnets, con-
sisting of ten layers of wire of seventy turns each, and having a
resistance of 2°15 ohms. By the same method as before, the
magnetizing force is found to be 1100 nearly. For ease of
comparison, the moments of the magnets after the first and
second magnetization are placed side by side in the Tables of
results. They show that the magnetizing force first employed
nearly saturated the bars. A few of these magnets were
placed between the poles of a powerful Ruhmkorff magnet,
when the increase of magnetism was found to be very small.
It will be observed from the Tables of results that one or two
of the magnets showed that their magnetic moment had been
diminished by the second magnetization. This may have
been due to some accident ; but the results have been entered
in the Tables as they were obtained.
To show the relative effects of different magnetizing forces
on bars tempered glass-hard and “blue,” two bars were
brought one to each of these tempers, and were then magne-
tized, first with a very small magnetizing force, which was
increased by small measured amounts, and observations of the
magnetic moments of the bars made at each increase. The
results are shown in the annexed curves (Plate V.), of which
the upper corresponds to the blue-tempered, and the lower to
the glass-hard magnet. The abscissa are proportional to mag-
netizing forces, and the ordinates to magnetic moments. It
will be observed from the curve that for every magnetizing
force the magnetic moment of the blue-tempered magnet is
greater than that of the glass-hard magnet, and that the differ-
ence between them diminishes as the magnetizing force is in-
creased.
As will seen from the appended Tables, the results show
that magnets made of steel which had been previously
heated to a bright red and cooled suddenly in cold water,
were scarcely so strong, after the first magnetization, as those
(made of the same steel) which, after having been so treated,
of Magnetic Moments in Absolute Measure. 327
had been again heated in oil to any temperature up to 310°
Cent., and afterwards allowed to cool slowly in air. By the
second magnetization, however, the difference between the
magnetic moments per gramme of the glass-hard and softer
magnets, though still in favour of the latter, was greatly dimi-
nished, which seemed to indicate that the greater strength of
the softer magnets after the first magnetization was rather
due to their being more easily magnetized to saturation.
Magnets made of steel which had been heated to redness and
then cooled in oil had a comparatively small magnetic moment
when they had been cooled in cold oil; but the magnetic
moments gradually increased as the temperature of the oil was
raised till it reached about 150° Cent., after which the mag-
netic moments were smaller the higher the temperature of the
oil. This result was not altered by the second magnetiza-
tion. The magnetic moments of these bars varied from about
60 to 80 per gramme.
Some magnets supplied to Mr. James White, Glasgow,
to be used as adjusting magnets for Sir William Thomson’s
compass, were found to have, when magnetized by a powerful
Ruhmkorff coil, an average magnetic moment of about 50
per gramme. Hach bar weighed about 170 grammes, and
was 30 centimetres long.
These magnets, when supplied by the maker, were com-
paratively soft; and their magnetic moments were slightly
diminished by tempering them glass-hard and magnetizing
them.
A series of experiments was made with magnets of the
homogeneous iron or steel supplied by Webster and Horsfall
for the sheathing of the 1865 cable. Hach of these magnets
was five centimetres long, and weighed 2°27 grammes.
Their magnetic moments per gramme for the different tem-
pers were as follows :—
CERISS= EC ges. cs sok eOckceede 20:22
eG ccaclesewtneheetes cea 17°18
DELO D mame coe oltastdaiaeada's 1)
EUS SUP PMGCs.. <5. ddeesde once 12:09
This shows a marked difference as to magnetic moment
between magnets made of this steel and the magnets used in
the former experiments.
Thus the glass-hard magnets of the soft steel had a mag-
netic moment of 74:3 per gramme, while the magnetic
moments at the other tempers were a little greater. On the
other hand, as the Table above shows, the magnetic moment of
the glass-hard magnets made of Webster and Horsfall’s steel
328 Mr, T. Gray on the Experimental Determination
was only 20°22, and that of the blue-tempered magnets little
more than half of this amount.
With regard to the permanence of the magnets employed
in the first series of experiments, their magnetic moments
were found to be very little, if at all, changed by lying nine
months undisturbed in the laboratory. When newly magne-
tized, the glass-hard magnets lost about 2 per cent. of their
magnetic moment when allowed to fall three times with true
north pole down from a height of 70 centimetres to a hard
paving-stone. Blue-tempered magnets by the same treatment
lost 10 per cent. After lying nine months, the glass-hard
magnets when allowed to fall three times as just described,
lost 0°5 per cent. of their magnetic moment, blue 2°8 per
cent.
The same magnets were then remagnetized and again
allowed to fall as before. The magnetic moment, which had
been but little increased, was found to be diminished in the
case of those tempered glass-hard by 1°7 per cent., and in the
case of those tempered blue by 4:4 per cent.
First magnetization. | Second magnetization.
Magnetic Magnetic
Description of | No. of
temper. magnet. Total moment Total moment
magnetic per magnetic per
moment. | gramme | moment. | gramme
mass. mass,
a
——_—
Heated to bright \ :
redness, and | 20-496 | 72296 | 21:129 | 74-529
plunged in | 20°551 71857 21-204 74140
sea ta 20551 | 72-235 | 21-199 | 74-296
Wee (Claes 20-291 | 71:322 | 21-185 | 74-464
hard.) gia ) — -20°328 71415 21-073 74-201
ee Oe ee eee
eel ee Sais 20°44 71°82 21°14 74:33
oe Se
6 21-054 | 76566 | 21-304 T477
ate 7. | 20568 | 75897 | 21-054 | 77-660
fe ee 8, | 20869 | 75°887 | 21-258 | 77-275
By ne ean 9, 20:869 75203 21-285 76°670
mies ike 0 20:308 74651 20626 75800
Mean ...... uae hs M2078 75°64 2110 76:98
11. | 20496 | 76107 | 20663 | 76675
Glass-hard, ree} | 19° | 90681 | 76-032 | 21-017 | 77-265
ee ner 13. 21-092 | 76696 | 21-296 | 77-440
ae ane oe 14, 20-253 74-323 20-701 75-962
a 15. 20°421 74834 20°504 75175
MAN inch ee rere 20°59 75°60 20°73 76-50
of Magnetic Moments in Absolute Measure. 329
Table (continued),
First magnetization. | Second magnetization.
is Magnetic Magnetic
Sealy “ ae * Total inmene | Total moment
a eer magnetic per magnetic per
moment. | gramme- | moment. | gramme
mass. mass.
|
Glass-hard, re- ( 17. 20°794 76°029 20°818 76117
heated to 200° + 18. 20-999 76-221 21-352 77-499
C. and cooled | 19. 20°869 75°886 21-072 76°627
16. 20°103 73637 | 20°328 74-461
in air. (| 20. 21-185 | 77-036 | 20756 | 75-476 |
Ll ae 20°79 75°76 20°87 7604 |
21. | 20031 | 74-604
Glass-hard, re { 22, | 21-465 | 78-623 |
ee | 2 | 2b6lk | 77-947
eeuntion) || 2 21-222 | 78-600
eee S| 2, | Sit09 | 77322 |
es SS ea eel SS ES
ae | 21-09 7742 |
Glass-hard, re- (| 26. | 19810 | 73:506 | 20143 | 74-742
heated to 250°|| 27. | 21-465 | 78197 | 21-465 | 78-197
C.andcooledind| 28. | 21-204 | 78243 | 21314 | 78649
air. (Brown-|| 29. 21992 | 77-452 | 21-244 | 77-533
yellow.) 30. | 20-762 | 77-087 | 20818 | 77-251
ae ee 20-89 76-89 21-00 17-27
Gia, (| 5 | 2081 | 799%
aoe to 260 33. | 20557 | 74-889
.and cooledin 34 91-908 79-956
air. (Brown.) | = cae
\| 35. | 20496 | 74-939
ae | 20°78 75°92
Glacs-hard, re-/| 36. | 20346 | 74-664 |
heated to270°}|} 37. | 21595 | 78-243
C.and cooled in 4 38. 21-744 79-358
air. (Purple- | 39. 21:279 77182
brown.) \; 40. 21:285 78508
ES ee epee 21°25 11°59
(| 41. | 20464 | 75-794
Be ocr || 42. | 21-379. | 78-744
ea . {| 43, | 20391 | 74-151
C. and cooledin 44 20-765 76-202
oe (Purple.) { 45. | 20895 | 177-676
| Mean ...... ae Oe el Org: ae |
330 On the Determination of Magnetic Moments.
Table (continued).
First magnetization. | Second magnetization.
Description of | No. of Magnetic Magnetic
temper. magnet. | Total moment Total moment
magnetic per magnetic |~ per
moment. | gramme | moment. | gramme
mass. mass.
Glass-hard, re- (| 46. 20°531 75°757
heated to 290° | 47. 20-291 75713
C. and cooled ¢ 48. 20°254- 74736
in air. (Light | 49. 20°464 79°372
blue.) A Us 20°409 79-146
ean. 82]) tekens 20°39 |—7614
Glass-hard, re- (| 51. | 20464 | 75097 | 21-017 [| 77-125
heated to 300°|| 52. | 21-389 79220 21-504 79644
C. and cooled{| 53. | 22-080 80-732 21-634 79-099
inair, (Full|| 54. | 21595 | 78812 | 21-702 | 79-206
|
blue.) \| 55. | 21519 | 79115 | 21-866 | 80-389
Mica elles 21-41 78:60 21-54 79-09
Glass-hard, re- (| 56. | 20849 | 78-674
heated to 310° | 57. 20-979 79°316
C. and cooled ¢ 58. 21-036 80°014
darktius) (| 60. | 2248 | Foz |
ar ue \ 22 ZA {o°
i | Mean JC)... | aiad | eed 9] = |
Heated to a/| 61. | 17534 | 61-308 | 17-944 | 62-741
bright red heat ( 62. 18:987 66°272 18819 65°686
and cooled in| 63. | 18334 | 63993 | 18-449 | 64394
boiling water. || 64 | 19936 | 65871 | 19930 | 63813
(Glass-hard.) (| 65. | 19025 | 65:605 5 5
Mca aloe | 1876 | 6521 18-95 | 65°85
|| ee. | tress | 63433 | 17986 | 63780
(SSBB Be ( 67. | 17551 | 62127 | 17-615 | 62:354
| brightred heat) 68. [> 97-014 ©| (60216 (Saal iaaeeet
| and cooled in}) ¢9 | 17546 | 62110 | 17-059 | 60385
yeceidies. ' 70. | 17589 | 62151 | 17096 | 60-410
| foie Rewer es Ries eS ee
| Mean -..0[ oo vrs2 | 6201 | 17-47 | 61-86
| (| 71. | 19322 | 70-390 | 19-678 | 71-687
Heated to a}) 49 19594 | 70:64 | 19:993 | 72307
brightredheat)| 73 | 19-826 | 72358 | 19-975 | 72-901
and -eooledian)) |i) 74 19805 | 72281 | 19845 | 72-427
oil at 100°C. || 75, | 19361 | 71-103 | 19-401 | 71-317
7140 | 1978 | 7213
On Multiplication by a Table of Single Entry. 331
Table (continued).
ee ee SS
First magnetization. | Second magnetization.
Description of | No. of Magnetic Magnetic
temper. magnet.| Total moment Total moment
magnetic per magnetic per
moment. | gramme | moment. gramme
mass. mass.
(a idle 21-363 | 76178 | 22096 | 76-990
Heated to 2:1 77. | 21687 | 75064 | 22208 | 77-380
ee aad in t'| | 2e 20-404 | 71-094 | 21-096 73505 |
silat iso°c. || 22: 21-762 | 75826 | 22-263 | 177:°573
Ur 80: 21-484 | 74:857 | 22300 | 177-700
he ere 21°44 74°71 21-99 76°63
___ ee lee eee ee re
|
(| si.. | 1-222 | 74833 | 21349 | 74-778
Be + | 82. 20395 | 73-445 | 21279 | 74-796
ee aa ait |: oo 20-924 73547 21-185 74-464
il at 200° C. 84. 21-147 | 73943 | 21-222 | 74-203
85. 20962 | 73810 | 20924 | 73-676
en 21-08 | 7382 | 2119 | 7438
(| 86. 20369 | 72970 | 20831 | 72:836
Heated ctnenr|| 87 | 20581 | 71988 | 20831 | 73-040
Se eeaadsd in 8. 20-421 "1-778 | 20570 | - 72-302
oil at 250° C. || 89. 20° ne 72444 | 20905 | 72094
(| « 90. 20°7 72282 | 20905 | 72-840
2 eae eee 20-66 72:29 20°81 72°62
a tl) SE | 20887) 73-415) °-20905" | 73-480
right Sedheat ||, 22 21:129 | 74323 | 21-259 | 74195
Sea eaoied G1 |. oo 20794 | 73218 | 21-110 | 74296
oil at 3oocc. || 24 20-745 | 72156 | 20886 | 72-647
bh 395: 21-092 | 73109 | 21-109 | 73-168
Mean ......] ...... Meanie] ne | 2008 | 7824 | 2105 | 7856 20-93 7324 | 2105 | 7356
XLV. On Multiplication by a Table of Single Entry.
By J.W. L. Guaisner, M.A., P.RS.*
§.1. i a the British-Association Report (Bradford, 1873,
pp- 22, 23) I made the following remarks in refer-
ence to multiplication by means of tables of quarter squares :-—
“In 1854, Professor Sylvester, having seen a paper in Ger-
gonne in which the method was referred to, and not being
aware that tables of quarter squares for facilitating multipli-
* Communicated by the Author.
332 Mr. J. W. L. Glaisher on Multiplication
cations had been published, suggested the calculation of such
tables in two papers—‘ Note on a Formula by aid of which, and
ofa table of Single Entry, the continued product of any set of
Numbers .... may be effected by additions and subtractions
only, without the use of Logarithms ’ (Philosophical Magazine,
[IV.] vol. vii. p. 480), and ‘On Multiplication by aid of a
Table of Single Entry’ (Assurance Magazine, vol. iv. p. 236).
Both these papers were probably written together; but
there is added to the former a postscript, in which reference
is made to Voisin and to Shortrede’s manuscript. Professor
Sylvester gives a generalization of the formula for ab as the
difference of two squares, in which the product aaj... a, 1s
expressed as the sum of nth powers of a, d2,... an, connected
by additive or subtractive signs. For the product of three
quantities the formula is
abe=37 {(a+b+c)?—(a+b—c)?—(ec+a—b)?—(b+c—a)*t.
And at the end of the ‘ Philosophical-Magazine’ paper Pro-
fessor Sylvester has added some remarks on how a Table to
give triple products should be arranged.
“ At the end of a memoir, “Sur divers points d’ Analyse,”
Laplace has given a section, , ‘‘ Sur la Réduction des Fonctions
en Tables”? (Journal de l Kcole Polytechnique, cah. xv. t. viii.
pp- 258-265, 1809), in which he has briefly discussed the
question of multiplication by a table of single entry. His
analysis leads him to the method of logarithms, quarter squares,
and also to the formula
sin asin b=3 {cos (a—b)— cos (a+b)},
by which multiplication can be performed by means of a table
of sines and cosines. On this he remarks:—‘ Cette maniére
ingénieuse de faire servir des tables de sinus a la multiplication
des nombres, fnt imaginée et employée un siécle environ avant
Pinvention des logarithmes.’
“It is worth notice that the quarter-square formula is de-
duced at once from
sin asin b=4 {cos (a—b)— cos (a+b)},
by expanding the trigonometrical functions and equating the
terms of two dimensions; similarly from
sin asin bsinc=1 {sin (a+c—b) + sin (a+b—c)
+ sin (b+c—a)—sin(a+b+c)},
by equating the terms of three dimensions we obtain
abe= ay {(at+b+c)?— &e.},
by a Table of Single Entry. 3 333
as written down above, and so on, the general law being easily
seen. We may remark that there is an important distinction be-
tween the trigonometrical formule and the algebraical deduc-
tions from them, viz. that by the latter to multiply two factors
we require a table of squares, to multiply three a table of cubes,
and so on; 1. e. each different number of factors requires a
separate table, while one and the same table of sines and co-
sines will serve to multiply any number of factors. This latter
property is shared by tables of logarithms of numbers, the use
of which is of course in every way preferable ; still it is inter-
esting to note the inferiority that theoretically attaches to the
algebraical compared with the trigonometrical formule.”
The object of this paper is to enter in some detail into the
matters briefly referred to in the above extract.
§ 2. The method of quarter squares depends upon the for-
mula
ab=1(a+b)?—1(a—6)’;
so that, with the aid of a table of quarter squares, in order to
multiply two numbers it is only necessary to enter the table
with their sum and difference as arguments and take the dif-
ference of the tabular results. The first table of quarter
squares was published by Voisin at Paris in 1817, and extends
to 20,000; and the largest that has appeared was published
by the late Mr. 8. L. Laundy, and extends to 100,000.
General Shortrede’s manuscript table, that extended to 200,000,
and so would enable five figures to be multiplied by five
figures, has not been printed. Ludolf, who in 1690 published
a table of squares to 100,000, explains in his introduction how
it can be applied to effect multiplications by means of the
above formula. The title of Voisin’s work is Tables des mul-
tiplications, ou logarithmes des nombres entiers depuis 1 jusqu’a
20,000, aw moyen desquelles on peut multiplier tous les nom-
bres qui nexcedent pas 20,000 par 20,000, et généralement
faire toutes les multiplications dont le produit n’excéde pas
400,000,000... , par Antoine Voisin.... By a logarithm is
here meant a quarter square, viz. Voisin calls a a root, and 4a?
its logarithm. If the sum of the two numbers to be multiplied
exceeds the limits of the table, but each of the numbers is in-
cluded in it, the multiplication is to be effected by means of
the formula
ab=2{1a?+10?—1(a—d)}.
Voisin is thus justified in stating that by means of his table,
any two numbers neither of which exceeds 20,000 may be
multiplied together ; but it is clear that if the sum of the fac-
334 Mr. J. W. L. Glaisher on Multiplication
tors exceeds 20,000 the method loses its advantages, as the
last-written formula requires three entries and a duplication.
An ordinary multiplication table, or Pythagorean table,
giving the product ab for arguments a, b is of double entry, and
so could not be carried to any very considerable extent on account
of the great bulk of the table. Herwart ab Hohenburg’s table
of 1610, referred to in §§ 9-12, extends to 1000 x 1000, as
also is the case with Crelle’s Rechentafeln, which are in general
use; but the Pythagorean table has never been carried beyond
this limit. The question of the reduction of the process of
multiplication to that of addition or subtraction is one that is
interesting both from a practical and historical point of view.
§ 3. In the Philosophical Magazine, [IV.] vol. vii. pp. 431,
432 (1854), Sylvester gave the generalization of the quarter-
square formula for the product of n quantities in the following
form :—
““ Let 0,, 4, 63,...86,, be disjunctively equal tol, 2, 3, ...n;
then |
(2:4.6). \2n)(G; apts san)
= (ag, +49, +49, +...+49,)"—2(—ag +49, +...+49,)”
+2(—ae,—4, +4, +- ee +ag,)” si ieee
4-( "(ap ag —.'s). Gg) =
The first and last terms, the second and last but one, &c., are
identical and may be united, there being one term left over in
the middle if n be even; viz. this becomes
(4.6.8... 2n)(a ay...a,)=(a9, +49, +49, -.-+49,)"
—=(—a9, +49, +49, +++ +46,)"
+. Gels) 2) ye
the last term being
(—)"2i(—a9, = 49. Sard “49, + “6m +1 cul Com+2 zak +ag,)"
if n=2m-+1, and
2\— )"2(— a9, —ag. 22 2—Om ag Aam+1 = Con+e vee t ap,)”
ifn=2m. This last expression is integral, notwithstanding the
factor 4, since each term composing it occurs twice ; as, ex. gr.,
when n=2, the whole term is 3{(a—b)?+(b—a)*}. These
are the formule given by Sylvester on p. 482. The equation
(1) is there proved by showing that the expression on the
right-hand side vanishes when a,=0, and therefore when
~4=0, a=0, &e., so that it =ka,a,...a,, and determining
the numerical factor k by putting a,=a,=...=a,=1.
§ 4. The formule can, however, be proved in the manner
by a Table of Single Entry 335
indicated in § 1, viz. by equating the terms of the nth order in
the equation giving sin a,sina,...sina, as a sum of sines or
cosines. |
Denoting by =,sina the sum of the sines of the angles
+a, +a,...+d,, in which r signs are negative and n—r
positive, viz. denoting by =, sin a the expression which would
be written in Sylvester’s notation,
> sin (—49,—46, we a9 .+ Ban. + Apgprges9 Tr ap,»
and attaching a similar meaning to &, cosa, we have
(—)”"2"~' sin a, sin ag... sina, = sin (a, +a,...+4,)
—>,sina+X;sina...+(—)"2msin a
if n=2m-+1, and
(—)”"2"~' sin a, sin ag... sin a, = cos (a, +ay...+4,)
— >, cosa+ =, cosa...+4(—)”=, cosa
if n=2m. The factor 4 has hefe the same explanation as
before ; viz. each term under the sign 2» occurs twice over,
and the 4 merely causes it to be counted once instead of
twice. The truth of these formule is readily seen by starting
with sinasinb=4{cos (a—b)—cos(a+b)}, multiplying by
sin ¢ and obtaining the expression as a sum of sines, then mul-
tiplying by sin d and so on; the general law then soon becomes
apparent. There is a simple and direct investigation of the
formule by Mr. R. Verdon in the ‘ Messenger of Mathematics,’
vol. vii. pp. 122-124 (1877).
The formule of § 3 in the form (2) foilow at once by equa-
ting terms of the nth order in the expansion of the terms in
these trigonometrical formule, or, what is the same thing, by
writing av,...a,« for a,...a, and equating coeflicients of 2”.
We also see that if in the formule in § 3, the exponent, in-
stead of being equal to n, the number of quantities a,,... an,
be less than n, and differ from it by an even number, the ex-
pressions on the right-hand side of the equations are equal to
zero, and that in general, if we denote
=(—dg, 222g, a a +ag,)?
by 2,a?, then
(ay + Ages. + dn)? —Zya? + >.a? — &c., ° ° (3)
the last term being (—)”"2,,@” if n=2m+1, and 3(—)”3,, a”
if n=2m, is equal to +2”—'p! aya,...a, X the terms of the
(p—n)th order in
2 4 2 2
G-f+ oi —&c.) (1- Ss +&e.), (1- f +é&e.),
336 Mr. J. W. L. Glaisher on Multiplication
where p! denotes 1.2.3...p, and p, nare supposed to be both
even or both uneven. Itis easily seen, by considering separately
the two cases of p even and p uneven, that the terms in the
pane pein are always positive; so that(3) is equal to
2"—-1y1 - dg+.+d,xX the terms of the (p—n)th order in
(1+ 3 stab “+ &e.) (14 ot +&e.). (1+ Bde.) ‘
Thus, for tien let n=3; then
(a+b+c) —(b+c—a) —(c+a—b) —(a+b—c) =0,
(a+b+c)*—(b+c—a)’—(c+ a—b)?—(a+b—c)? =24abe,
(a+b+c)’—(b+ce—a)’—(e+a—b)’—(at+b—c)°
= 80abc(a? +b? +c’),
(a+b+c)'—(b+e—a)'—(ce+a—b)'—(a+b—c)'
a+bht+ct Bet + Ca + ab?
=. 7! abe(— 5" eo
= 5babe(da* + 30* + 3c* + 10b7c? + 10c?a? + 1007b?)
&c. &e.
Let n=4, then
(atbte+a)y
—(—a+b+c+d)?—(a—b+e+d)’—(at+b—c+dp
—(at+b+c—d)P
+(—a—b+c+dy4+(a—b—c+d)’+(a+b—c—dy?
tg — oe
=192abcd if p=4,
=960abcd(a? +b? +c? +d?) if p=6,
= 896abcd(8a* + 3b* + 3c* + 8d* + 10a7b? + 10ac? + 10a7d?
+1067c? + 1067d? + 10d?) if p=8, &e.
§ 5. We can also obtain an expression for the sum of powers
when the exponent p is even and all the terms have the posi-
tive sign. For
2”-1 COS a1 COS Ag... COS In= COS paee see +Gn)
+2, cosa+Z,cosa+...
* Since sintv= sinha, costx = cosh, the trigonometrical formule
become, on writing 7a,,...%d, for a,,...ani—
2"—! sinh a, sinh a,... sinh a,= sinh tate .ee+4,)—5,sinha+€e.
if n=2m-+1, ‘aad
=cosh (a, +a,...+a,)—%, cosha+&c.
if n=2m, leading at once to the theorem in the above form.
by a Table of Single Entry. | 337
the last term being =,,cosa if n=2m+1, and 13,, cosa if
n=2m; and equating the terms of the 2gth order, we find that
(41+ a2... +an)2 + 302+ 20+ &e.,
the last term being ©, if n=2m+1, and 43%a% ifn= 2m, is
equal to 2"~!.2q! x the terms of the 2gth order in
2 4 2 2
1+ t+ + ho)(14 S +hc.).. (14 2 +60.),
(1+ + B+ ho)(1+ F +hc.).(1+ F dbe,
Thus
(at+tb+c)*+(b+c—a)*+(ct+ta—b)*+(a+b—c)*
=4(a* + b* + c*+ 607c? + 6e’a? + 6a7b”) ;sx
and in the case of n quantities @,, da,... Gn,
(a, +a... +a,)*+ Sya* + Zoa*+ ke.
Sa Ol Op ace ae WHO ober Mele CCK.
It may be remarked here, that any trigonometrical identity
in which the arguments are homogeneous functions of the
letters gives rise to a series of algebraical identities by equa-
ting the terms of each order; ex. gr. from
sin (d—b) sin (a—c) + sin (b—c) sin (a—d)
+ sin (c—d) sin (a—b)=0,
we have, by equating terms of the fourth order,
(d—-b)(a—c){(d—b)’ +(a—c)’}
+(b—c)(a—d){(b—c)? + (a—d)’}
+(c—d)(a—b){(ce—d)’ + (a—b)’} =0.
There are a great number of trigonometrical identities of
this kind, such as
sin (b—c) + sin (ec—a) + sin (a—d)
+4 sin $(b—c) sin} (c—a) sing (a—b)=0,
cos (a+b) sin (a—b) + cos (6+¢) sin (b—c)
+ cos (¢+d) sin (e—d) + cos (d+a) sin (d—a) =0, Ke. ;
and some of the algebraical identities thus obtained are of
interest. An identity of this class is referred to in the ‘ Mes-
senger of Mathematics,’ vol. viii. p. 46 (July 1878).
§ 6. In Laplace’s section, ‘Sur la Réduction des Fonc-
tions en Tables,’ he considers the question of multiplica-
tion by means of a Table of single entry. First, assuming
that ay=¢(X+Y), where X is a function of w only, and Y a
Z
Phil. Mag. 8. 5. Vol. 6. No. 38. Nov. 1878.
338 Mr. J. W. L. Glaisher on Multiplication
function of y only, it is found that
e=She — e,
giving the method of logarithms ; and assuming
ry=$(X+¥)—4(X-Y),
it is found that solutions are :—
PX+V)=a(ety)’s
e=sinX, y=snY, o(X+Y)=—tcos(X+Y).
Laplace then shows that the values of f(z, 7) can be calculated
by means of a table of single entry, if the differential equation
obtained by eliminating c from the equation f(z, y)=c be of
the form Sdz+Tdy=0, 8 being a function of # only, and Ta
function of x only.
It is clear that the formula
sin a sin b=}{cos (a—b) —cos (a+b) }
does reduce multiplication to addition or subtraction by means
of a table of sines; and Laplace’s remark that tables of sines
had actually been used in this manner for about a century
before the invention of logarithms led me to search for the
history of this curious method.
§ 7. The method in question was called prosthapheresis,
often written in Greek letters zpooc@adaipecis, and had its
origin in the solution of spherical triangles. A careful exa-
mination of the history of the method is given by Scheibel in
his Einleitung zur mathematischen Bicherkenntniss : siebentes
Stick (Breslau, 1775), pp. 18-20; and there is also an account
in Kastner’s Geschichte der Mathematik, t. i. (1796) pp. 566—
569,in Montucla’s Histoire des Mathématiques, t. 1. pp. 583-585
and 617-619, and in Kliigel’s Wérterbuch (1808), article Pros-
thapheresis. The method consists in the use of the formula
sin asin b= {cos (a—b)— cos (at+b)},
and
by means of which the multiplication of two sines is reduced
to the addition or subtraction of two tabular results taken from
a table of sines; and as such products occur in the solution
of spherical triangles, the method affords the solution of sphe-
rical triangles in certain cases by addition and subtraction
only. It seems to be due to Wittich, of Breslau, who was
assistant for a short time to Tycho Brahe*; and it was used by
* Christmann, in his Theoria Lune, states that the first inventor of the
method was Werner of Nuremberg, who employed it in a treatise De
Triangulis, which was never printed (Montucla, t. i. p. 584). ;
by a Table of Single Entry. 539
them in their calculations in 1582. Wittich in 1584 made
known at Cassel the calculation of one case by this prostha-
pheeresis ; and Justus Byrgius proved it in such a manner that
from his proof the extension to the solution of all triangles
could be deduced. Clavius generalized the method in his
treatise De Astrolabio (1593), lib. i. lemma liii. The lemma
commences as follows :—
“ Questiones omnes, que per sinus, tangentes, atque secantes
absolvi solent, per solam prosthapheresim, id est, per solam ad-~
ditionem, subtractionem, sine laboriosa numerorum multiplica-
tione, divisioneque expedire.
“Hdidit ante tres, quatuorve annos Nicolaus Raymarus
Ursus Dithmarsus libellum quendam, in quo preter alia pro-
ponit inventum sane acutum, et ingeniosum, quo per solam
prosthapheresim pleraque triangula spheerica solvit. Sed
quoniam id solum putat fieri posse, quando sinus in regula
proportionum assumuntur, et sinus totus primum locum ob-
tinet, conabimur nos eam doctrinam magis generalem efficere,
ita ut non solum locum habeat in sinibus, et quando sinus
totus primum locum in regula proportionum obtinet, verum
etiam in tangentibus, secantibus, sinibus versis et aliis nu-
meris, et sive sinus totus sit in principio regule proportionum,
sive in medio, sive denique nullo modo interveniat: que res
nova omnino est, ac jucunditatis et voluptatis plena.”’
The work of Raymarus Ursus, referred to by Clavius, is
his Fundamentum Astronomicum (1588). Longomontanus,
who also assisted Tycho Brahe, in his Astronomia Danica
(1622) gives an account of the method, stating that it is not
to be found in the writings of the Arabs or Regiomontanus.
Scheibel also mentions a manuscript ‘‘ Melchior Jéstelii logis-
tica mpocfadaipecis astronomica”’ (1609).
With the exception of Clavius, | have not examined the
works referred to, but have relied on Scheibel and the
other writers mentioned at the beginning of this section.
Jt did not seem necessary to enter further into the matter, as
there can be no doubt that the method of prosthapheeresis is
that to which Laplace’s remark refers, and that it was used
for performing multiplications, even when the quantities to be
multiplied did not present themselves as sines and cosines. It
need scarcely be remarked that when the method was in use
(previous to the invention of logarithms) the cosine had not
been introduced; so that the rules for the different cases of
sin a sin b, sin a cos b, &. were complicated, it being neces-
sary to frequently pass from the angles to their complements.
In Kliigel’s Wérterbuch it is mentioned that, if other trigono-
metrical functions have to be multiplied besides sines and
Z 2
340 Mr. J. W. L. Glaisher on Multiplication
cosines, or if a sine or cosine is a divisor, the process is more
troublesome—that these multiplications can be effected by the
formula, but that the requisite transformations are more la-
borious than the multiplication itself, which is purely mecha-
nical, while with the prosthapheresis method more care is re-
quired and, in addition, it is more difficult to obtain accuracy
in the result. These remarks seem to be obviously just; and it
is clear that the method could not be a good one for the
ordinary multiplication of numbers not given in the form of
sines of angles, as four entries of the tables would be neces-
sary, besides very troublesome interpolations.
§ 8. Napier published his Canon Mirificus in 1614; and then
the prosthaphzeresis method was at once superseded by Joga-
rithms. The latter process requires only three entries of the
table in order to multiply two numbers, and, even regarded
merely as a multiplication method, is oreatly superior in every
respect to that of prosthapheresis, which requires four entries.
Before the invention of logarithms the object was to arrange
formule, of which numerical values were required, as sums of
sines by prosthapheresis,so that they might admit of calculation
by addition or subtraction ; since the invention of logarithms
the object has always been to throw formule into the form of
products.
Regarded as processes for effecting multiplications, the
methods of (1) prosthapheresis, (2) logarithms, and (3)
quarter squares, may be compared as follows :—The first
theoretically solves the question, but is impracticable as a
general method. The second is the best method, if only a few
figures (viz. 6 or at the most 9 figures) of the product are
wanted : if m numbers are to be multiplied together, only n+ 1
entries are required. The method of quarter squares is the
best if only two numbers are to be multiplied together, and
if all the figures of the product are wanted. Only two entries
are required; and a table from 1 to 200,000 (which would
only occupy a moderate octavo volume) would give the pro-
duct of any two five-figure numbers by two entries and one
subtraction, no interpolations being necessary. A Pytha-
gorean table of this extent would be absolutely impossible, as
it would occupy 100 x 100, or 10,000 volumes similar to Crelle’s
Rechentafeln, which in the new edition occupies one volume
folio (see § 10). The quarter-square method seems not to have
been much used, partly because it has never become generally
known, and partly because no table exceeding 100, 000, and
therefore available for all fiv e-figure numbers, has been ‘pub-
lished. Such tables are also only suitable for the one purpose
of multiplication, while logarithms have a great variety of uses.
by a Table of Single Entry. 341
The connexion between prosthapheresis and quarter squares,
and between the generalization of the prosthapheresis formula,
as given in § 4, and the formula for the product of n quan-
tities as a sum of nth powers, viz. that the algebraical formule
may be obtained by equating terms of the same order in the
expansions of the trigonometrical formula, is noteworthy ; but,
as mentioned in § 1, the trigonometrical formula only requires
one and the same table (a table of sines), however many quan-
tities have to be multiplied together, while the algebraical for-
mula requires a table of squares to multiply two numbers, a
table of cubes to multiply three, and a table of nth powers to
multiply n numbers; and to multiply m numbers, 2”! entries
would be required. We might, however, multiply two numbers
by means of a table of quarter squares, and then multiply their
product by the third number and so on (which would also re-
quire 2”~' entries); but we should only obtain the exact
value of the result if all the products were included within
the limits of the arguments of table, 7. e. if the sum of the
largest multiplier and the product of the other factors be within
these limits. Practically, however, the sine table would only
contain a certain number of decimal places; and if we assume
the sine table to be perfect so as to render any number of multi-
plications possible, we ought at the same time to assume the
quarter-square table to be extended ad libitum; so that the theo-
retical advantage of the trigonometrical formula, as only re-
quiring one table, is more apparent than real, if we admit the
repeated use of the quarter-square table.
As just remarked, a table of sines, like a table of logarithms,
is only available for obtaining results to a certain number of
figures; and the superiority of the quarter-square method,
when only numbers within the range of the table have to be
multiplied together, is very decided.
~ §9. The title of Herwart ab Hohenburg’s multiplication
table is “ Tabule arithmetice tpooagdaipecews universales,
quarum subsidio numerus quilibet, ex multiplicatione produ-
cendus, per solam additionem ; et quotiens quilibet, e divi-
sione eliciendus, per solam subtractionem, sine tediosAa &
lubricA Multiplicationis, atque Divisionis operatione, etiam ab
eo, qui Arithmetices non admodum sit gnarus, exacté, celeriter
& nullo negotio invenitur. BE museo Ioannis Georgii Herwart
ab Hohenburg. .. . Monachii Bavariarum. Anno Christi,
M.pc.x.” The book is a very large and thick folio, containing
a multiplication table up to 1000 x 1000, the thousand mul-
tiples of any one number being given on the same page; and
there is an introduction of seven pages, in which the use of
the table in multiplying numbers containing more than three
342 Mr. J. W. L. Glaisher on Multiplication
figures, and in the solution of spherical triangles, is ex-
plained.
The mathematical bibliographers and historians afford very
little information with regard to the work. Heilbronner (His-
toria Matheseos, 1742, p. 801) gives the title not quite cor-
rectly, and adds, ‘‘ Docet in his tabulis sine abaco multiplica-
tionem atque divisionem perficere.”’ Kistner ( Geschichte der
Mathematik, 1796-1800, t. iii. p. 8) quotes the title from Heil-
bronner and his remark, and adds that Heilbronner could not
have known Herwart’s method, or he would have described it.
He remembers to have read somewhere that the book con-
tained a number of tables of products,.arranged by factors,
like a great multiplication table. Scheibel (Hinleitung zur
mathematischen Biicherkenntniss : eilftes Stiick, 1779, pp. 417-
420) gives the full title of the work, a description of it, and
an example worked out to show how it is to be applied to
multiply numbers of more than three figures. He commences
his account:—“ Der Herausgeber dieses colossalischen Hinmal
Hins ist also kein anderer, als der so beriihmte Staatsmann
und Geschichtschreiber, dessen sehr wichtiges und seltenes
Werk: Ludovicus IV Imperator defensus za Miinchen
1618. 1619. in gr. 4. in der Hamburg. Histor. Bibliothek
Cent. VIII. Art. 97, beschrieben wird;’’ and concludes, “ So
viel von diesem ungeheuren Folianten, den man bloss zur Cu-
riositit und seiner Seltenheit wegen, in einer mathematischen
Biichersammlung aufbewahret.”” Montucla (Histoire des Ma-
thématiques, t. 11. pp. 18, 14) gives a short account of the table
and the mode of using it when the numbers to be multiplied con-
tain more than three figures. This is introduced by the words:—
“Nous terminons cet article, en faisant connoitre un livre
assez obscur, dont l’objet étoit d’abréger les calculs arithme-
tiques, et qui n’auroit pas été inutile, sans invention des lo-
garithmes ;”” and Montucla adds further on, ‘ Tel est l’esprit
de cette invention, qui, sans la decouverte des logarithmes,
auroit pu étre de quelque utilité aux calculateurs, si toutefois
la peine de chercher ces produits, au nombre de 6, 7, 8 ou 9,
dispersés dans un énorme in-folio, n’efit pas paru plus fatigante
et non moins laborieuse que le calcul méme, pour un homme
exercé.” Murhard (Bibl. Math. 1797-1804, t. 1. p. 199)
gives the title correctly, and marks it with an asterisk to show
that he has seen the book itself. Rogg (Bibl. Math. 1830,
p. 142) merely has, “ Hohenburg, Gregor (sic) Herwardt ab,
tabule arithmeticee mpocfadaipecews universales, 1610.”
Neither Weidler (Bibl. Ast. 1755), Deschales (Cur. seu Mund.
Math. 1699), Lalande (Bibl, Ast. 1803), nor Delambre (Hist.
de lV’ Ast. Mod. 1821) mention the work; but there is a refer-
by a Table of Single Entry. 343
ence to it in Leslie’s ‘ Philosophy of Arithmetic’ (2nd edit.
1820, p. 246). In his article on Tables in the English Cyclo-
pedia (1863), De Morgan, referring to this table, wrote :-—
“The table goes up to 1000x1000, each page taking one
multiplier complete. There are then a thousand odd pages ;
and as the paper is thick, the folio is almost unique in thick-
ness. ‘There is a short preface of seven pages, containing ex-
amples of application to spherical triangles. Itis truly remark-
able that while the difficulties of numerical calculation were
stimulating the invention of logarithms, they were giving rise
to this the earliest work of extended tabulated multiplication.
Herwart passes for the author; but nothing indicates more
than that the manuscript was found in his possession.
The book is excessively rare; a copy sold by auction a few
years ago was the only one we ever saw.” Graesse (1'résor
des livres rares, 1859-1867) says that by the book the use of
logarithms was first spread in Germany, which is obviously
erroneous.
§ 10. Crelle’s Rechentafeln,which also extend to 1000 x 1000,
were first published in two octavo volumes in 1820. A second
(stereotype) edition in one volume (folio) was published under
the editorship of the late Dr. Bremiker in 1864. This work
is well known, and is much used. From Crelle’s preface to
his table in 1820, it is clear that he knew nothing of Her-
wart’s work, and was not aware that a table to 1000 x 1000
had ever been published; for he writes, “ Das neueste und
vielleicht bedeutendste Unternehmen von Tafeln, die mit den
gegenwartigen einerlei Idee zum Grunde haben, ist das Werk :
‘ Tables de multiplication, a Vusage de MM. les géometres, de
MM. les ingénieurs vérificateurs du Cadastre etc. Sec. édit.,
Paris, chez Valace, 1812 ;’” and then he states that this work
only extends to 500 x 500, and is therefore the fourth part of
his own table. It is not a little remarkable that the first mul-
tiplication table of any extent published should have reached
the limit beyond which the table has never been carried.
That Herwart’s idea was good and practicable is proved by
the continual use made of Crelle’s tables ; and but for the great
bulk of his ponderous volume, the table would in all probability
have come into use. The invention of logarithms four years
afterwards afforded another means of performing multiplica-
tions, and Herwart’s huge work never became generally known.
It is curious that from 1610 till 1820 no similar table should
have been published, as it seems clear that the work of 1610
was a failure chiefly in consequence of its inconvenient
size. Herwart’s table is rare; but there are copies in the
British Museum, the Bodleian Library, and the Graves
544 Mr. J. W. L. Glaisher on Multiplication
Library at University College, London; the last is not quite
perfect.
§ 11. While I was engaged in preparing the British-Asso-
ciation report, I endeavoured without success to find any thing
relating to the history of the table; but the hope is there ex-
pressed that, considering the attention so large a work must
have received from contemporary mathematicians, some in-
formation might still be gained with regard to the calculator
of the tables, his objects, &c. I afterwards met with a corre-
spondence of six letters between Herwart and Kepler, which
took place at the end of 1608, and throws light upon these
points. The letters are printed in Dr. Frisch’s Joannis Kepleri
Astronomi opera omnia, t. iv. pp. 527-530, 1863. Herwart,
who was Chancellor of the Palatinate of Bavaria, and a man of
mark in his time as a statesman, was a frequent correspondent
of Kepler’s; and many of his letters upon chronology are
printed in Kepler’s Hcloge Chronice. There is a gap in the
correspondence, however, between January 12, 1608, and
December 5, 1608; and Dr. Frisch, in the notes to the Ecloge,
gives the six letters referred to, prefaced by the words “ Kep-
lerus in Kclogis omisit epistolas Herwarti datas d. 13 Sept.
et 5 Noy. 1608, ipsiusque responsionem d. d. 18 Oct., quum
nihil facerent ad Chronologiam, et maxima ex parte spectarent
opus Herwarti arithmeticum, quod edidit Monachii 1610...”
In the first letter,dated September 18, 1608, Herwart writes:—
“Ich hab bisher in Multiplicatione et Divisione sonderbare
geschriebene praxin gebraucht, dadurch ich den numerum ex
quavis multiplicatione productum, per solam additionem, und
den Quotienten ex divisione resultantem per solam subtrac-
tionem (absque teediosa multiplicationum et divisionum ope-
ratione) gefunden.” He states that J. Praetorius and others
who have seen it, recommend him to have it printed; and he
adds that if he had not had this method (diesen modum), on
account of his continual occupations, and because he is not
a good calculator, he should long ago have had to give up all
mathematical matters requiring calculation. He sends a spe-
cimen page of the Table, the use of which he illustrates by the
multiplication 945,678 x 587, and he asks Kepler to give him
his opinion upon the subject.
Kepler replies on October 18, 1608, and remarks that tables
are very useful to the sedentary man, and “ei, qui perpetuo
cum libris cohabitat.”” For 500 or 1000 pages form a large
volume, which cannot always be at hand. As it will facilitate
astronomical calculations he advises that short precepts on the
solution of triangles should be added. Kepler then pro-
ceeds :—‘ Nam multis partibus expeditius est uti hoc tuo
by a Table of Single Entry. 345
volumine, quam mpocbadaipeces Witichiana, que seepissime
inducit in tabulam sinuum, crebro permutat sinus complemen-
tis, arcus rectis, rectas arcubus. Illaque memoriter nunquam
retineo, et tediosum est, toties adire scripta preecepta, pre-
sertim ingenioso, qui nihil sine causz cognitione cupit agere.
Requirit preterea cautiones crebras, ex quibus neglectis
erebra offendicula. Causz operationum etsi ingeniosissime
tamen semper in abstruso sunt inter operandum. At si mul-
tiplicemus et dividamus simpliciter, tunc videmus quid aga-
mus; et possunt varietates triangulorum talibus preeceptis
comprehendi, que memoria retineri facile possunt.’”? Then
follows a synopsis of the different cases of the solution of sphe-
rical right-angled triangles. Herwart writes on November 5,
and says he had found that triangles could be solved better
and more quickly by means of his table than by prostha-
pheresis, so that Kepler was quite right. He proceeds :—
“Darunter ich aber Vitichium nit gesehen. Dieser abacus
ist universalis. Weil man pflegt den Biichern ein splendidum
titulum zu geben, ut reddantur venales, wollt ich gern dessen
Gutachten vernehmen, ob es nit thunlich ungefihr so: Nova
exacta, certa et omnium facillima ratio Arithmetices, per quam
numerus ex multiplicatione productus sine operatione multi-
plicationis per solam additionem, et quotiens ex divisione re-
sultans absque operosis ambagibus divisionis per solam sub
tractionem cujuscunque, etiam maximze summe, etiam ab eo,
qui arithmetices non admodum sit gnarus, citius quam ulla alia
ratione invenitur.”” He then asks Kepler for his advice as to
how the book should be entitled in Latin and German, and
prays him to write soon.
Not receiving an answer, on December 2 he sends a short
letter to Kepler, again asking for a reply, and suggesting that
perhaps it was not prudent “so speciosum titulum tantillee rei
zu prefigiren.”” Butimmediately after, Kepler’s reply [ which
is lost | was received; and writing on December 5, Herwart
explains that he does not expect an answer to his last letter, and
that he understands that Kepler has no suggestion to make
with regard to the title, but thinks it should be shortened. He
cannot understand the meaning of Kepler’s advice, “ Graeca
compositio imploranda, sed exercito,” and asks for an expla-
nation.
In the last letter of the correspondence, dated December 12,
1608, Kepler explains that, as the title seemed long, he had
advised that it should be shortened by the composition of two
Greek words, as in épuvovtredas, piwoxivovvos, &e., and con-
tinues:—“ Mihi quidem cum non occurreret quidquam hujus-
modi, quod ad nostram rem faceret, consului opem imploran-
346 Mr. J. W. L. Glaisher on Multiplication
dam alicujus exercitati in Greeca lingua. Quid si occurrerit
quod placet? LescayPera apiOuntixyn. Nosti enim, ypewv
atoxovras sic dici. Inest vocabulo et emphasis et proprietas
et similitudinis gratia, quia me Hercule novas tabulas introdu-
cis, et uno ictu liberas computatores debitis multiplicandi et
dividendi inextricabilibus. Sed facile est exercitato, copiam
afferre similium compositorum, ut ex lis aptius aliquod eliga-
tur. Mihi jam plura non occurrunt.”” He then refers to the
Tabula Tetragonica [ Venice, 1592] of Maginus, and adds in
a postscript “ Titulus igitur talis: Zecayeva sive Nove
Tabule, quibus Arithmetici debitis inextricabilibus multipli-
candi et dividendi liberantur, ingenio, tempori viribusque ra-
tiocinantis consulitur.”’
§ 12. It thus appears that the table was printed from a
manuscript that Herwart used himself, and which very likely
he had had made. As for the word prosthapheresis which
occurs on the title, it is shown by the correspondence that
Herwart used the table for multiplications in general, and that
it was Kepler who pointed out that by means of it spherical
triangles could be solved more easily than by the prosthaphe-
resis of Wittich, and suggested the addition of the precepts
for the solution of triangles, which actually occur in the pre-
face to the work. The title suggested by Kepler was not
adopted, nor was his advice about shortening it; but it must
be acknowledged that Herwart succeeded. in obtaining a
‘“‘ splendid title,’’ which also contained a Greek word. De
Morgan explained the use of the word “ prosthapheeresis ’’ upon
the title-page of Herwart’s table, thus: ‘‘ Prosthapheeresis is a
word compounded of prosthesis and apheresis, and means addi-
tion and subtraction. Astronomical corrections, sometimes ad-
ditive and sometimes subtractive, were called prosthapheereses.
The constant necessity for multiplication in forming propor-
tional parts for the corrections, gave rise to this table, which
therefore had the name of its application on the title-page.”
The correspondence, however, shows that the table derived
its title not from its general use in the calculation of astrono-
mical prosthapheereses, but from the special prosthapheresis
of Wittich for the solution of triangles. In a paper on Her-
wart’s Table read before the Cambridge Philosophical Society*
on October 25, 1875, which contained the greater part of the
contents of §§ 9 and 11 of the present paper, I remarked that
the prosthapheresis referred to seemed to be most likely a
method of solving spherical triangles, in which the product of
* “On Herwart ab Hohenburg’s Tabule Arithmetice rpoo Oapaipecews
universales, Munich, 1610.” Proceedings of the Cambridge Philosophical
Society, vol. ii. pp. 886-392 (part xvi.).
by a Table of Single Entry. 347
two sines, or a sine and cosine, was avoided by the use of a
formula such as sin asin b=4{cos (a—b)—cos (a+b)}, adding
that Laplace referred to such a method. This inference is
shown to have been correct by the contents of § 7. Wittich
does not appear to have published the method himself, though -
from the writings mentioned in § 7, and from Kepler’s letters,
it is clear that it was generally attributed to him: he ought,
I suppose, to be considered the discoverer of the formule
sin a sin b=4{cos (a—6)—cos (a+6)}, &e., which are really
the prosthapheretical formule. Kepler’s remarks upon the
difficulty of using the prosthapheresis for spherical angles, on
account of the confusion between sides and angles and their
complements, is interesting; and it is for this reason that I
have quoted so much of the letter of October 18. The word
prosthapheeresis often means the difference between the true
and mean places of a body in longitude or latitude; but it
seems to have been vaguely used, very much as “ correc-
tion’ is now, to denote small quantities to be added or sub-
tracted to quantities obtained by theory, or by a first approxi-
mation, &c. ; so that without a context its signification is not
precise; but | have not examined this point. In Kliigel the
word is derived from mpécGev and adaipesis; but, at all events,
as far as the mathematical and astronomical use of the word
is concerned, De Morgan’s derivation from mpoc@eous and
adatpects seems to be certainly the true one.
As it happened, Herwart’s employment of the word zpo-
clagaipecews upon his title-page was not fortunate ; for only
four years after the publication of his table logarithms were
invented, all the processes of calculation were changed, and
Wittich’s prosthapheresis passed out of notice.
Kepler, as is well known, greatly admired Napier’s inyen-
tion, and in 1624 published himself a table of Napierian loga-
rithms.
It will have been noticed that Herwart describes his table
as enabling multiplications to be performed “ per solam addi-
tionem,’ and division “ per solam subtractionem.” These
words would immediately suggest to a writer of the last or
present century the method of logarithms ; and it is for this
reason, no doubt, that not unfrequently the methods of pros-
thapheeresis and quarter squares have been confounded with
applications of logarithms. Voisin, as mentioned in § 2, actu-
ally called his quarter squares logarithms; and this has added
to the confusion.
Trinity College, Cambridge.
July 12th, 1878.
[Gade]
XLVI. Magnetic Figures illustrating Electrodynamic Relations.
By Strvanus P. Toompson, D.Sc., B.A., F.R.A.S., Pro-
fessor of Experimental Physics in University College, Bristol*.
[Plates VI. and VII. |
q> a preliminary communication to the Physical Society in
February of the present year, the author announced a
method of studying and illustrating the known laws of the
mutual attractions or repulsions of conductors traversed by
electric currents. The present paper is a complete statement
of the facts obtained in the experimental research which formed
the basis of that communication.
While preparing a set of magnetic currents to illustrate the
mutual actions of magnet-poles, it occurred to the writer that
the mutual attractions and repulsion of currents might be il-
lustrated in a similar manner by the figures formed with iron
filings. He was awarej at that time that the lines of force of
a straight conductor carrying a current were a series of con-
centric circles lying in a plane to which the conductor was
normal. ‘The series of figures now published originates, there-
fore, with the discovery of Faraday that the seat of the mutual
actions of currents and of magnets must be sought in the sur-
rounding medium. Since the communication of the prelimi-
nary notice, the writer has learned that one or two of the figures
had been previously and independently observed by Professor
F. Guthrie, but not published. Two others, Nos. 4 and 5 of
the present series, are imperfectly given by Faraday in figures
18 and 19 of plate iii. in the third volume of his ‘ Experimental
Researches’ (Series Twenty-ninth){,and without reference to
the conclusions to be derived from their forms, which Faraday
apparently overlooked §.
The method employed for preserving the figures has been
uniform throughout the series. Plates of glass, 34 inches long
by 3% inches broad, were coated with a solution of gum-arabic
and gelatine, and were then carefully dried. When the ar-
* Communicated by the Physical Society.
t See Faraday, ‘Experimental Researches in Electricity,’ vol. ii. p.
400, § 8239, and plate i. fig. 17; Guthrie, ‘ Magnetism and Electricity,
Pp: 254, fig. 225 ; Clerk-Maxwell, ‘Electricity and Magnetism,’ vol. i.
art. 47 7.
{ And ‘Phil. Trans. 1862, p. 137.
§ The attention of the writer has also been drawn to a statement in the
American Journal of Science for 1872, p. 263, by Professor A. M. Mayer,
that he has obiained magnetic “spectra ” from electric currents in a manner
somewhat similar to thatnow described. The figures have, however, re-
mained unpublished and undescribed, so that the writer has no means of
learning how far the substance of the present communication may have
been anticipated.
Magnetic Figures illustrating Electrodynamic Relations. 349
rangement of magnets or of conducting-wires had been made
for the particular case of the experiment, and the plate been
laid in a horizontal position, fine filings of wrought iron pre-
viously sifted were dusted over the plate through muslin, and
the plate was tapped lightly with vertical blows from a piece
of thin glass rod. When the filings had arranged themselves,
and the plate was still in situ, a gentle current of steam was
allowed to play upon the plate, condensing upon the surface of
the gum and softening it, and thus allowing the filings to
embed themselves where they lay. After the gum had again
become hard, the prepared face was covered by a protecting
plate of glass, on which in certain cases were drawn the posi-
tions of the wires or magnets employed. The figures fixed in
this manner are suitable for projection with the lantern upon
the screen. They can be readily photographed for transpa-
rencies, or for paper prints; specimens cf each of these
methods of photographic reproduction are exhibited to the
Society.
Figure 1 represents the condition of the magnetic field sur-
rounding the current in a straight conducting-wire, which was
carried vertically through a hole drilled in the plate. The
wire employed throughout the series was a silver one of about
*8 millim. in diameter. The battery power employed for this
experiment was that of 20 Grove’s cells arranged in two series
of ten each. In some of the succeeding experiments a less
current was found sufficient.
But for the imperfections of the method of experiment, these
curves would be perfect circles, and the distances between
two successive lines of force would be proportional to the
square of the distance from the central point. The equipoten-
tial magnetic surfaces, being always normal to the magnetic
lines of force, would be represented by a system of radial lines
forming equal angles with one another. There appears to be
no recognized name for the closed curves traced out by the
lines of force around conductors carrying currents. With
great diffidence I therefore beg to speak of them as isodynamie
lines. They are theoretically disposed about a single straight
conductor in a perfectly concentric manner, and at such dis-
tances apart as would be defined by the requirement that a
parallel conductor, carrying a like current of unit strength,
would do unit work in passing from one isodynamic line to the
next. The absolute value of an isodynamic line would of course
he determined (like magnetic and electrostatic potential) by
the work done by a like element of current in passing to any
point in that line from an infinite distance. No work is done
in moving an element of a parallel current along an isodyna-
350 Prof. 8. P. Thompson on Magnetic Figures
mic line, just as no work is done in moving a magnet-pole
along in an equipotential surface. The isodynamic lines
occupy, therefore, exactly the same relation to the element of
the circuit, as do the equipotential surfaces to a magnet-pole
or to an electrified point.
Figure 2 represents the field above a horizontal wire carry-
ing a current, and separated from the filings by the thickness
of the glass (about 1-7 millim.). The lines cross the wire at
right angles, and are really the projections of a series of such
circles as exist in figure 1.
Figure 3 exhibits the form assumed by the filings when the
wire beneath the plate was coiled into a simple loop, a small
piece of mica being inserted to prevent contact where it re-
crossed its path. The lines of the field within the loop run
longitudinally ; and their projections on the surface are mere
points, as the filings show.
In figures 4 and 5, two wires pass vertically through the
plane of the figur es, carrying parallel currrents, which in
figure 4 are in the same direction, in figure 5 in opposite
directions. Ampere’s well-known law of the attraction in the
former case, and of the repulsion in the latter, is well illus-
trated by the forms of the magnetic curves. In the former,
where the parallel currents attract, the outer isodynamic lines
are closed curves embracing both centres, the inner are dis-
torted ovals about each centre—the whole forming a system of
lemniscates, as would necessarily be the case, since the at-
traction at any point in the plate varies inversely as the square
of the distance from each current*.
In figure 5, where the parallel currents repel each other,
the lines of force due to either current in no case enter or
coalesce with those of the other current. They form two series
of ovals of a peculiar form, flattened on the sides presented
towards the opposing series.
The conception of Faraday, “that the lines of magnetic
force tend to shorten themselves, and that they repel each other
when placed side by side,” has been shown by Clerk-Maxwell,
who thus concisely states it, to be perfectly consistent with the
theory that explains electromagnetic force as the result of a
state of stress in the medium filling the surrounding spacef.
Faraday also observes that “ unlike magnetic lines, when end
on, repel each other, as when similar poles are face to face,”’
and that “ like magnetic lines of force,’’ when end on to each
other, coalesce. The terms “like”? and “ unlike,’’ as applied
* See Thomson and Tait, ‘ Natural Philosophy,’ art. 508, vol. 1. p. 382.
t Clerk-Maxwell, ‘ Electricity and Magnetism,’ vol. i. art. 645; Fara-
day, ‘ Experimental Researches,’ 38266, 8267, 8268,
illustrating Electrodynamic Relations. 3d1
to magnetic lines of force, refer, of course, to the two cases of
similarly or oppositely directed lines, the positive direction of
a line of force being reckoned as the direction in which a
north-seeking pole on it would tend to move*. The mutual
coalescence or repulsion exerted between the lines of force of
unlike or like magnetic poles is familiarly employed in the
experimental illustration of magnetic phenomena, so well known
since the researches of Professor Robison and Dr. Roget on
the magnetic curves, and appears to have been recognized long
beforet. It is believed that the present is the first distinct
attempt to apply similar considerations to the illustration of
electrodynamic relations between systems of conductors car-
rying currents, and between conductors of currents and mag-
net-poles.
_ The isodynamic lines, which are lines of magnetic force,
tend to shorten themselves. A very hasty inspection of fig. 4
will show that if any one of the system of lemniscates were to
“ shorten itself,’’ it would tend to bring the two centres nearer
together. Consider each isodynamic line as a ring of some
elastic material (as, for example, an indiarubber ring) stretched
around a bundle of smooth wires, the cross section of the bundle
having a perimeter corresponding in form to the isodynamic
line under consideration. The maximum shortening of such
an elastic ring would take place when the enclosed area was
made a circle. In other words, the lemniscate-form isodyna-
mics tend to become circles, and the two like parallel currents
are mutually urged towards each other.
In figure 5 the shortening of the isodynamic lines, and their
approach to the truly circular form, could only be accomplished
by the wider separation of the two conductors from each other.
Hence the mutual repulsion of two parallel conductors carry-
ing oppositely directed currents.
Figures 6 and 7 show the lines of force above the parallel
currents when these pass horizontally below the glass. In the
cease of like currents the lines coalesce. In the case of unlike
currents they repel each other, and pass between the two wires
in a direction vertical to the plane of the glass, where their
characteristic form, as lines, is lost. The observation that the
filings adherent to wires carrying like parallel currents are
mutually attractive appears to have been first made by Davy.
Figure 8 illustrates the law of currents crossing one another
at a point. In the two quadrants in which the currents both
* See Clerk-Maxwell, ‘ Electricity and Magnetism,’ art. 489; L. Cum-
ming, ‘ Theory of Electricity,’ p. 194.
T See Musschenbroek, Dissertatio Physica Experimentalis de Mugnete,
cap. iv. exp. cxvii., and tab. iv. figs. 4 & 5.
352 Prof. 8. P. Thompson on Magnetic Figures
run to or from the central point, the lines of force tend to
coalesce. In the alternate quadrants they mutually repel each
other; and the angle of these quadrants tends to increase.
In figure 9 one current is carried horizontally below the glass,
the other traverses the plane of the figure normally. The dis-
symmetry of the resultant distribution of the lines reveals the
dissymmetrical nature of the force which tends to bring the
currents into parallelism. Any shortening of the isodynamic
lines would tend to move the vertical current from that qua-
drant over which the lines are unbroken. Figures have also
been obtained with two currents crossing the plate in a vertical
plane of incidence, but each at 45° to the normal. With some
distortion, these -figures bear a general resemblance to figs. 4
and 5 in the two cases of the currents passing through the
plate in similar or in opposed directions. In the former case
their angular separation tends to diminish, in the latter to in-
crease. °
Figures 10,11, and 12 introduce the action of a vertical cur-
rent upon a small magnetic needle lying on the glass plate.
In the first case the needle lies in stable equilibrium almost
tangentially to the isodynamic lines ; in the third its position
is reversed and unstable ; in the second case it is set at right
angles to the directive action of the current. The dissymme-
trical action of the forces on its poles produces a couple tend-
ing to turn it about its centre, as would be inferred from an
inspection of the lines of force of the figure.
Figures 13 and 14 illustrate a deduction from the theory of
the magnetic shell. A conductor carrying a current is acted
upon by a force urging it forward so as to make the number
of like lines of force included within it a maximum” ; that
is to say, a north-seeking pole is attracted into a circuit
on the side from which the positive current appears to circu-
late in a right-handed cyclical order (or in the same direction
as the hands of a clock). Similarly the circuit is urged back-
wards from a contrary pole, and tends to make the number of
unlike lines of force included within it a minimum. In the
figures a current ascends through the plane of the figure on
the left, and descends through it on the right, in a right-handed
cyclical order as seen from the magnet. Hence a north-
seeking pole is attracted, and asouth-seeking pole repelled.
Figure 15 results from the action of two magnet-poles upon a
vertical conductor, which in this case is attracted between the
oles.
: Figure 16 illustrates the mutual tendency to rotation between
a magnet-pole and a conductor carrying a current parallel to
* Clerk-Maxwell, ‘ Electricity and Magnetism,’ art. 490.
illustrating Electrodynamic Relations. 3093
the axis of the magnet. In the figure, where the vertical cur-
rent passes upwards through the glass, the neighbouring south-
seeking pole (marked in position by a square dot) is urged -
round the current with a couple tending in a right-handed
cyclical rotation. The couple is reversed, and acts in a left-
handed order, if either the current or the magnet-pole be
reversed. The contrasted dissymmetry so produced is very
curious, and the mutual displacement of the radial lines of
force of the pole and of the circular lines of the current is very
significant.
Figures 17 and 18 show lines of force arranged spirally in
the field. In these a current passes upwards through the glass,
while the pole of a magnet is placed vertically beneath: the
current, in fact, passes through the magnet. The form of the
lines of force is remarkable. No work would be done on or
by an element of a vertical current in bringing it up to the
centre along one of the spiral lines; for the work done by it
in bringing it in the spiral path across the successive circular
isodynamic lines of the current would be equal to that done
upon it in carrying it across the successive radial lines of force :
of the magnet-pole. The equipotential surfaces of this field
are consequently another series of spirals of an opposite cy-
clical order. In figure 17 the current running up through a
south-seeking pole produced a right-handed spiral; in figure
18, with a north-seeking pole the spiral is of the opposite order.
Since the magnetic potential decreases from a magnet-pole
with the inverse square of the distance, and since the inductive
action of the current on a point in the plane of the figure also
decreases according to the inverse square of the distance from
the current, each branch of the spirals would be described by a
moving point whose angular displacement from the arbitrary
zero is simply proportional to the distance from the central
point. The results of actual measurement ofthe spirals at
successive distances of whole millimetres from the centre show
as near an agreement with this supposition as the roughness
of the method of procuring the curves permits. The number
of branches of the spiral will clearly be proportional to the
strength of the magnet pole. The obvious result of a “ short-
ening” of the spiral lines would be to produce a rotational
movement, such as we know to be produced on a free-magnet
pole under the influence of a current traversing it longitudi-
nally.
= indebted to Mr. Robert Gillo, of Bridgwater, for the
admirable photographic copies of the various figures.
June 19, 1878.
Phil. Mag. 8.5. Vol. 6. No. 38. Nov. 1878. 2A
Fic Bo aa
XLVI. On the Applicability of Lagrange’s Lquations in cer-
tain Cases of Fluid-Motion. By JouNn Purser, M.A., Pro-
fessor of Mathematics in the Queen’s College, Belfast”.
eee ordinary condition for the applicability of Lagrange’s
equations to the motion of a system is that the position
of all its parts be determined as a function of the generalized
coordinates or parameters which enter into these equations.
When such is not the case, even though the kinetic energy
may be expressible in terms of these coordinates and their dif-
ferential coefficients with respect to the time, the Lagrangian
equations of motion are known not to be in general valid.
A familiar illustration of this is afforded by the motion of a
rigid body rolling on a plane so rough as to prevent sliding.
Here it is evident that the kinetic energy can be expressed in
terms of three coordinates defining the angular position of the
body and their differential coefficients. It is not, however,
possible to express the position of all the points of the body in
terms of these coordinates only ; and accordingly the use of
Lagrange’s equations in terms of these coordinates is known
to lead to erroneous results. It becomes, therefore, a matter
of considerable interest to inquire into the grounds which
justify recent important applications of these equations to
sundry problems of hydrokinetics, relating to the motion of
rigid bodies in an incompressible frictionless fluid.
This case, in fact, is in so far similar to that of the rolling
body already alluded to, that while the kinetic energy of the
system can be expressed (in virtue of Green’s theorem) in
terms of the limited number of parameters which define the
position of the rigid bodies, it is clear from the smallest con-
sideration that these parameters do not determine the position
of the particles of the fluid. It would certainly seem, then,
that we are not entitled primd facie to assume the validity of
Lagrange’s equations when applied to such problems, and that,
if their use be here justifiable, it must be in virtue of special
reasons. ‘To endeavour to supply the proof which is thus seen
to be requisite is the object of the present communication.
Given a number of rigid bodies moving in a frictionless in-
compressible fluid, whether infinitely extended or enclosed in
a rigid envelope ; given also that the motion at one epoch is
irrotational, and therefore always so,—then by D’Alembert’s
principle,
Ldm{xbe+ yoy +262} +8V=0, «. . (A)
* Communicated by the Author, having been read before the British
Association at Dublin, August 1878.
On Lagrange’s Equations applied to Fluid-Motion. 355
where V denotes the potential energy due to the applied forces
which act on the bodies. a, dy, 6z, as far as they apply to
the particles of the bodies, can, of course, be expressed in terms
of 541, ¢2, &e., the sare age of the generalized coordinates
determining the position of the bodies. And the same holds
true for the particles of the fluid, provided we suppose the
displacements irrotational. The above equation may therefore
be written
dV dV |
Qidqn + Qala - + 7 Og + gana ° =:
and the equations of motion are
Q+ 5 =0, G+ 5 =0, be
To obtain Q,, suppose
6q2=0, 693=0, &e.,
then
Ldin(#bx + ydy + 262)
= Sdn © (#82 + G8y + 382)
d
Edm (of a tla Sytee 7 8):
Now if
ox =a,5q1, by = b1841, Oz = 891; &e.,
when a, b;, c, are functions of the q’s and the coordinates
2, y, 2, then
L=MhH, y=hin, EET &e.;
eee ay as
Ot r= doy’ i dqy’ &e.
. Chi
dz dy aT
=§ aa ih es ida pa Me
mdm 5, hae neiags TF _ on 7 ab
If now we are justified in assuming that
ne eyo d )
Edm (ez, deta 7 by +2 5,02
=Zdm(#de+ “Sy +28"),
2A 2
356 Prof. J. Purser on the Applicability of Lagrange’s
then, since this latter expression = $9, a we get at once
Lagrange’s equation,
df CEN ue Lee wa ¥,
Ha.) ~ ae t=O
It remains only to consider why the above assumption is
legitimate. As far as the integral applies to the particles of
the rigid bodies, since . =) = for each particle, the trans-
formation is obviously justified. or the fluid, on the other
hand, it is evident that, for an individual particle, ~ dz is not
= 5 ~ (This may be seen at once by considering the case
of the motion of a flat piece of cardboard in a fluid, and sup-
posing the time displacement perpendicular to its plane and
the arbitrary displacement in its plane.)
To examine the meaning of the differences = 52—68 = dt,
&c., let us suppose that the generalized coordinates are so
taken that one only of the coordinates, say go, alters with the
time, so that the actual time displacement may be treated in
the same way as a possible displacement 845.
The above may accordingly be written 6,6,2—6,6,7, where
5,, 6, correspond to the variations 691, 69>.
Consider any point of the fluid A. =
Suppose the dispacement 6g, fol-
lowed by the displacement dq, and c
let the answering positions of A be D
Band C. Again, suppose the dis-
placement 6g, followed by 69;, and
let the answering positions of A “
be Dand E. E will not coincide
with C, but the displacement is that 4
which has for its projections the expressions above.
For, projection of HC=projection of DE—projection of AB
—(projection of BC—projection of AD)
= 05012 = 01052.
The bodies, however, after these two compound displacements
are in identical positions ; and consequently the displacements
of the fluid (6,6,—6,6,)z, &c., correspond to irrotational dis-
placements of the fluid compatible with a position of the
Equations in certain Cases of Fluid-Motion. 307
bodies momentarily fixed. We have then to show that, for
such a displacement,
dm «6x2 + yoy + 26z)=0.
This is evident ; for the work done by the momenta of the
particles of the system must for any possible displacement be
equal to that done by the impulse ; and the latter in this case
vanishes, as the bodies remain fixed.
The same thing may be shown analytically thus:—
Ld (aba + yby + zdz)
= dp. dbs , dd )
= OTH o 6a + a by + Te oz
= |Jas.p..m :
ii ((f Fae 4 CS dBy -*).
The first term vanishes, since the motion is the fluid in con-
tact with the bodies is tangential; the second, since the fluid is
incompressible.
Addendum.
Sir William Thomson has shown, in his paper on Vortex-
Motion (Trans. R. 8S. H. vol. xxv.), that if one or more solid
bodies are moving in an infinitely extended frictionless incom-
pressible fluid, the motion of the fluid being supposed at one
instant and therefore always irrotational, the impulse (1. e. the
system of forces which would at any instant, if applied to the
solids, generate the motion of the system of solids and fluids)
would, if applied to a rigid body, represent a constant motive. It
may be interesting to show that this conclusion follows directly
from the Lagrangian equations.
First, let there be only one rigid body. Take two systems
of coordinate axes—the first (OX, OY, OZ) fixed in space,
the second (O'X’, O’Y’, O’Z’) attached to the body.
Let wu, v, w be the components of the velocity of O/ esti-
mated along the moving axes ;
p,q, 7 the rotations of the body round these axes ; ;
$,, 9 the usual angles denoting the position of the
moving axes with respect to the fixed axes ;
2, y, 2 the coordinates of O’ with respect to the fixed
axes.
Then, taking as generalized coordinates 2, y, 2,6, W, 0, we
858 Prof. J. Purser on the Applicability of Lagrange’s
should have, were continuous forces applied to the body,
4 Re cine i pater nent of fi
at dz eet ponent of forces,
d-.al «Wt
a ram Ger moment of forces round bg page
O’Z, being a parallel through O/ to OZ.
It follows, integrating through the short interval of time
during which the instantaneous impulse would act, that
a = component of impulse along OX,
at
dy — 3 bb) ONG
dT
ie = ” ” OZ,
e = component of moment of impulse round O’Z,.
In the actual motion
ad tal ok Kal
di de de
.., since T does not depend on 2, y, z,
z-component of impulse = = constant,
and similarly for the y-component and the “compen ae
Let us now proceed to find the physical meaning foes aa : i
and interpret the equation
@ a at
dt dp dp
It is clear from Green’s theorem that T can be expressed as a
quadratic function of p, q, 7, u, v, w with constant coefficients ;
Lat ae dpe. diag ~a dr
TA OR A id a
dT dt du dt da
Ee pe ay! do Ge
When p, q, 7 are expressed in terms of ¢, W, @, their coeffi-
cients do not involve the precessional angle y. Therefore the
first three terms vanish.
Equations in certain Cases of Fluid-Motion. 309
Again
; qv dT aT
du’ dv’ dw
are the force-components of the impulse with respect to OX’,
ory’, OWA ;
du, do dw
dy dw db
correspond to the displacement of a vector u,v, w fixed in
space with respect to the moving axes, owing to the motion dw
of the latter ;
| vector u, v, w
eat 25 component along R of relative displacement of
oe 5 ia dy
= — moment of a force R applied at end of vector
u, v, w round axis O/Z, ;
.. Lagrange’s equation
i ot at
means that
a
a (moment of impulse round O/Z,)
+ moment of force of impulse applied at end of vector
u,v, w round the same line =0.
The left-hand member is obviously
=" (moment of impulse round OZ) ;
.. this last moment is constant, and the moments round OX
and OY are also constant. _
Secondly, let there be more rigid bodies than one. We
can now assume as the generalized coordinates the same as
we have just taken which have reference to one of the bodies,
together with other coordinates depending entirely upon the
relative position of the rigid bodies amongst themselves ; then
= and. 7 are evidently the force-components along the axis
wu -
OX and the moment round the axis O’Z, of the whole impulse,
and the reasoning runs as before.
Pin@boang
XLVIII. Researches on Unipolar Induction, Atmospheric Elec-
tricity, and the Aurora Borealis. By KH. EpiLunp, Professor
of Physics at the Swedish Royal Academy of Sciences.
[Continued from p. 306. |
§ 2. Atmospheric Electricity and the Aurora Borealis.
T is known that the earth may be regarded asa relatively
-L- good conductor of electricity ; while, on the other hand,
the atmospheric air, in the dry state and under the pressure
to which it is subject at the surface of the earth, is a very
bad conductor. Its conductivity, which depends almost ex-
clusively upon the relative quantity of humidity which it con-
tains, is consequently subject to incessant variations from the
double point of view of time and space. When the density
of the air diminishes, its conductivity increases; consequently
there must exist at a considerable altitude above the terres-
trial surface a stratum of air the conducting-power of which
is better, yet without being particularly good. The terres-
trial surface, both solid and liquid, is therefore immediately
surrounded by a stratum of air endowed with feeble conducti-
vity and subject to incessant variations. To this stratum suc-
ceeds another, the conductivity of which is greater and, as
far as we know, sensibly invariable. The upper limit of
the atmosphere has been fixed by astronomic methods at an
altitude of between 70 and 80 kilometres. Truly speaking,
these determinations signify only that the atmosphere up to
that limit possesses sufficient density for its presence to be in-
dicated by the ordinary methods of determination. That the
atmosphere, though excessively rarefied, extends to a still
greater elevation is most evidently proved by the fact that
shooting stars have been observed at nearly 900 kilometres
above the surface of the earth. ‘These small bodies evidently
can only become bright in consequence of a portion of their
vis viva, transformed into heat by the friction of the air, aug-
menting their temperature to such a degree that they begin
to shine. Now we can only perceive the falling body from
the moment when it becomes luminous ; and it is clear that
at that momentit will have already traversed a certain length
of path in the rarefied atmosphere before attaining so high a
‘temperature. Therefore the upper boundary of the atmosphere
must be situated at a much’ greater distance from the earth
than has hitherto been admitted.
The magnetic action of the earth cannot be explained en-
tirely and in detail by the assumption that its magnetic force
is due to a magnet of iron or steel situated in the earth, and
On Atmospheric Electricity and the Aurora Borealis. 361
making a certain angle with the axis of rotation. The said
action is too irregular for such an explanation to be admissible.
Nevertheless the total intensity of the magnetic force is ascer-
tained to increase in a sufficiently regular manner as we re-
cede from the magnetic equator towards the magnetic poles.
If we join the points of the terrestrial surface where the mag-
netic dip has the same value, we obtain curves which, though
not forming true circles encompassing the earth and parallel
to one another, may yet be regarded as parallel circles drawn
at the surface of the earth, and having their centres on the
right line which joins the earth’s magnetic poles. If from
the equator we proceed continually in the direction indicated
by the declination-needle (not in such a direction that the
angle of declination remains constantly the same), we obtain
magnetic meridians converging towards the magnetic poles ;
these meridians are not great circles, but yet beara certain re-
semblance to them*. In general, and on a large scale, it is
therefore permissible to regard the earth as a magnet the axis
of which makes a certain angle with the terrestrial axis of ro-
tation. ‘There is no need of amore exact idea of the magnetic
condition of the earth for the exposition which follows.
Let abcd (fig. 9) be a section passing through the axis of
rotation of the earth (which we will suppose to constitute a
perfect sphere); ac is its rotation-axis, bd its equator, and o its
centre. ‘To simplify the question, we will at first suppose that
the two magnetic poles are on the rotation-axis, the south pole
in s, and the north pole inn. abod will consequently repre-
sent the northern hemisphere; and we will designate by
a’b’c'd’ the upper limit of the atmosphere. While the earth
is turning from west to east about its axis, an electric mole-
cule situated in m describes in the same direction a circle pa-
rallel to the equator, and therefore forms a current which is
acted upon by the two poles of the magnet. If now we pass
planes through the circuit-element situated in m and through
the two poles of the magnet, these planes will cut the figure
along the right lines sm and nm; and if in the same planes we
draw the right lines mp and mq respectively perpendicular to
ms and mn, we shall get the directions in which the magnetic
poles tend to direct the positive electric molecule (the ether).
Let r denote the distance from the centre of the earth to m,
p the distance from each of the poles of the magnet to the
same centre, and / the latitude of the point m. We remark
at starting that the magnetic phenomena presented by the
earth indicate that at least p cannot exceed in length the half
of the earth’s radius ; and, in consequence, we assume that p
* Becquerel, Tracté complet du Magnétisme (Paris, 1846), p. 428.
362 Prof. HK. Edlund on Atmospheric Electricity
is at most equal to the half of that radius. The squares of
the distances of the two poles from the point m will therefore
be respectively
7+ p°—2rpsin/ and r+ p?+2rp sin Ll.
The intensity of the current is proportional to the velocity
with which the molecule m moves in its parallel circle ; and
that velocity is, in its turn, proportional to the distance from
the rotation-axis, consequently to rcosl. Designating the
intensity of the magnetic poles by M, and by & a constant, we
shall have, for the force with which the south pole tends to
direct the molecule along mp, the expression
kMr cos 1
r+ p*—2rp sin L’
and, for the action of the north pole upon the same molecule
along the line mg,
kMr cos 1
7 + p*+2rp sin [
Taking the sum of the components of these forces along the
earth’s radius drawn through the point m, we get
kMrp cos? 1 #. kM rp cos? 1 ee
(7 +p?—2rpsinl)? (°+p?+2rp sin 1)?
This sum, which we will name the vertical component, de-
notes the force with which the magnet tends to direct the
eether (the electropositive fluid) upward in a vertical direction.
(If we assume also an electronegative fluid, this will be urged
by the same force in the opposite direction.)
If now we consider an electric molecule which is situated
in the atmosphere or at the surface of the earth, for which,
therefore, 7 is >2p, we see that formula (A) will be equal to
zero at the polar point, and will possess a relatively minimal
value in the vicinity of that point. Consequently the force
tending to carry the electric molecule vertically upwards is
nil at the pole, anda minimum in the polar region. It follows
of course, and is besides proved by the formula, that the sum
is equal for the same latitudes in both hemispheres.
Taking the component of these forces in a direction making
a right angle with the earth’s radius (the tangential compo-_
nent), we obtain the force with which the electric molecules
are urged along the tangent of the circle the radius of which
is 7. We have thus :—
kMr(r—psinl)cosl _ kMr(r+psin/) cosl (B)
(7? + p?—2rp sin 1)2 (7? +p’ +2rp sin 1)2
and the Aurora Borealis. 363
In the equatorial plane this force becomes =0. The electric
molecules situated in that plane move therefore vertically up-
ward, seeing that the component of the force A is the only
one which acts upon them. At the terrestrial poles (/=90)
B and A are alike equal to nil; therefore the molecules si-
tuated in the parts themselves undergo no action from the
magnet. For all the other molecules, the distance r of which
from the centre of the earth is above or equal to 2p, the first
term of the expression (B) will be always positive. For the
molecules of the northern hemisphere (that is to say, for the
positive values of the latitude) the first term will be numeri-
cally higher than the second, and consequently the total ex-
pression will be positive; for the southern hemisphere (that
is, for the negative values of /) the first term will be numeri-
cally lower than the second, and consequently the entire ex-
pression will be negative. or the same value ofr, and at an
equal latitude, the expression (B) will have the same numeri-
eal value in both hemispheres ; but this value will be positive
in the northern, negative in the southern hemisphere. It
appears, then, from the expression (B) of the tangential com-
ponent of the force, that the electric molecules situated in the
terrestrial atmosphere or at the surface of the earth endeavour,
in the northern hemisphere, to approach the north pole, and
those situated in the southern hemisphere the south pole. The
vertical component (A) tends in the same way in both hemi-
spheres to move the molecules always further from the centre
of the earth in their course toward the terrestrial poles.
We will now see what is the influence which these forces
are capable of exerting upon the electric state of the earth and
the atmosphere. The lower stratum of the air is a relatively
bad conductor ; and we assume at first the ideal case that its
conductivity is everywhere equal. The vertical component of _
the magnetic force in question then tends to direct the ether
(positive electricity) from the earth to the air, the lower strata
of which consequently become charged with that fluid, while
the earth itself, which is a good conductor, incurs a deficit of
eether (that is, becomes electronegative). The magnetic force
being always in equally intense activity, and the earth rota-
ting with a constant velocity, a portion of the electric fluid is
soon conducted into the upper regions of the atmosphere,
where the conductivity is better. Arrived there, the electric
fluid is impelled towards the poles by the tangential component
of the magnetic force. The ether (positive electricity) in this
way accumulates in the atmesphere, while the earth itself suf-
fers a deficit of electricity (becomes electronegative). This
continues until the electric tension of the atmosphere is suffi-
364 Prof. E. Edlund on Atmospheric Electricity
ciently great to induce a discharge towards the earth. This,
as is the case in the ordinary experiments of the laboratory,
may take place in two ways—that is, either by an instanta-
neous discharge, or by a more or less continuous current.
This difference of discharge depends on the following circum-
stances :— .
The action of a magnetic pole p upon another magnetic
pole g takes effect along the right line which joins p and gq ;
but the action of the magnetic pole p upon a current-element
situated at the same point as g, on the contrary, operates in a
plane normal to the said right line. The component along
this right line of the action of the pole p upon a current-ele-
ment is consequently equal to nil. What has just been said
may be applied also to the case of two magnets acting upon
each other. If, for instance, a magnet sn (fig. 10) acts upon
another magnet s‘n’, and the latter is movable so as to be able
to take any position whatever in relation to sn, the magnet
s‘n’ will place itself in the direction of the resultant of the
action exerted upon it by the magnet sn. The action of sn
upon a current-element situated at the point m, or in the same
place as s’n’, on the contrary, will take place in a plane nor-
mal to the same resultant; the component, then, along this
resultant of the action of sn upon the current-element is equal
to nil. If the circle abed represents a section of the earth, the
magnet s’n’ shows the direction of the dipping needle at the
point m, since we suppose s‘n’ to be in the direction of the re-
sultant of the action exerted upon it by the earth’s magnetism.
Therefore the action of terrestrial magnetism upon a current-
element situated in the atmosphere has zero for its component in
the direction of the dipping needle.
At the equator the dipping needle takes a horizontal posi-
tion. The action of the earth’s magnetism takes effect here,
as the above formulz show, in a vertical direction upward.
If then, the electric fluid of the atmosphere can precipitate
itself vertically into the earth, the force which produces this
effect mnst be sufficiently great to overcome not only the
electric resistance of the subjacent strata of air, but also the
action of tle earth’s magnetism upon the electric fluid of the
atmosphere ; or, in other words, the force must exceed the sum
of the two obstacles to the motion of the electric fluid. We
must further observe that the action of the earth’s magnetism
in the vertical direction upon a current-element situated in
the atmosphere is, according to formula (A), greater at the
equator than to the south or north of that circle.
At higher latitudes the dipping needle has not a horizontal
position, but makes a greater or less angle with the plane of
and the Aurora Borealis. 365
the horizon. Here, then, it is possible for the electric fluid of
the atmosphere to descend into the earth without the terres-
trial magnetism opposing to it an obstacle directly, provided
it follows the direction of the dipping needle ; but in follow-
ing that direction the electricity has a longer path to travel
to reach the surface of the earth, and consequently suffers a
greater resistance than if it could descend vertically. At the
magnetic pole the dipping needle takes a vertical position, in
consequence of which the resistance opposed by terrestrial
magnetism to the propagation of the electricity in the vertical
direction is here equal to nil. From all this it follows that,
all other circumstances being equal, the resistance to the flow of
the electric fluid from the atmosphere to the surface of the earth
is greater at the equator and in the equatorial regions than at a
certain distance from that circle, and that the resistance dimi-
nishes as the dip of the magnetic needle to the earth increases.
It is here that, in my opinion, we must seek the chief cause
of the fact that in the equatorial regions the electric fluid of
the atmosphere descends to the earth by strong disruptive dis-
charges, and in high latitudes chiefly by slow and feeble flow-
ings, forming more or less continuous electric currents. If
we continue to charge with opposite electricities two insulated
bodies at a suitable distance from each other, the electricity at
last traverses the intervening space, producing sparks, and
the two bodies are discharged. That the discharge thus
effected may be powerful and instantaneous, it is necessary
that the bodies be good conductors, and the resistance of the
intervening space great. If the resistance is slight, the dis-
charge commences while the charge is yet feeble. In propor-
tion as the resistance grows weaker, the discharge takes on
more and more the form of a continuous current. In the
equatorial regions, or in general in lower latitudes, the force
of terrestrial magnetic induction acts with very great inten-
sity in rendering the atmosphere electropositive, and, accord-
ing to what has just been said, the resistance to a discharge is
also very great. When the aqueous vapour of the air con-
denses so as to form cloud, this becomes charged with the
electric fluid accumulated in the airin the locality. The cloud,
which is a good conductor, therefore takes an electropositive
charge. It is unnecessary to say that negative clouds may
also in turn be formed under the inductive influence of posi-
tive clouds produced in this way. If now the clouds have
become sufficiently electric, the electric fluid may escape to
the earth by means of an instantaneous discharge. These
discharges, or thunder-claps, then, take place when clouds are
formed and when the electric resistance between them and the
366 Prof. E. Edlund on Atmospheric Electricity
earth is as great as is required. Outside of the equatorial
regions this resistance is less, as has been said, and violent
tempests are more rare. Finally, at a still higher latitude the
resistance is so slight that the discharges are transformed into
slow and continuous currents, giving rise to the phenomenon
called the awrora borealis,
That portion of the electric fluid which does not descend
into the earth by disruptive discharges in the equatorial re-
gions is carried by the tangential component of the force of
induction towards higher latitudes, while its distance from
the terrestrial surface is augmented by the vertical component
of that force. These currents of electric fluid receive accessions
everywhere during their journey towards the poles through
the inductive force of the earth’s magnetism incessantly im-
pelling into the atmosphere fresh quantities of that fluid from
the subjacent terrestrial surface. In proportion as the dis-
tance to the poles diminishes, the vertical component of the
induction-force also diminishes, and the dipping needle conti-
nually approaches nearer to the vertical; and in consequence
the resistance opposed by the force of magnetic induction of
the earth to the flow of the electropositive fluid to the earth
grows less with the diminution of the distance to the poles.
When the difference of electric tension between the atmosphere
and the earth has become sufficiently great to overcome the
resistance opposed by the induction-force of the earth and
the subjacent strata of air, the electric fluid flows from the
atmosphere to the earth. The places where this phenomenon
takes place evidently form a circle around the pole. This
circle is characterized by the circumstance that in every point
of its circumference the vertical component of the force of
terrestrial induction must have nearly the same value. In
the vicinity of the poles the atmosphere receives only a feeble
charge of electricity, the vertical component of the induction-
force being there but very small (as indicated by formula A),
and the tangential component directing towards those regions
only an insignificant quantity of the electric fluid which enters
the atmosphere in lower latitudes.
The electric fiuid impelled into the atmosphere by the ter-
restrial force of magnetic induction descends again therefore
in two ways to the earth—either by powerful disruptive dis-
charges, or by more or less continuous feeble currents. The
former mode of discharge takes place chiefly in the equatorial
regions, the latter especially in high latitudes. The fluid
which is not discharged disruptively in the equatorial regions
is conducted by the induction-force towards higher latitudes,
where the discharge takes place by means of continuous cur-
and the Aurora Borealis. 367
rents. From this it follows that, the less complete the dis-
ruptive discharge in the first-mentioned regions, the more
numerous and intense will be the currents in the second.
We assumed above that the terrestrial magnet coincided
with the rotation-axis of the earth, and that the earth was
everywhere homogeneous and endowed with the same electric
conductivity. Now the magnetic poles of the earth are not
situated on the axis of rotation ; or, in other words, the right
line connecting the magnetic poles does not coincide with that
axis, but makes with it an angle determined by observations
to be about 17°. Moreover the conductivity of the air varies
with the time and place. Yet these circumstances necessitate
only nonessential modifications in what has been said. The
circle abcd (fig. 11) represents a section passing through the
rotation-axis of the earth and through the right line which
joins the magnetic poles. This line makes with the axis the
angle a (= about 17°). The distance of the magnetic poles
from the axis will therefore be p sin a—an expression in which,
as already said, p cannot exceed the half of the earth’s radius.
We will now suppose another plane passing through the
axis, and forming the angle v with the preceding plane; and
we will consider the action of the magnetic poles upon an
electric molecule m situated in this plane. During the rota-
tion of the earth the magnetic poles describe circles the radius
of which is psina. The radius of the circle described in the
same time by the molecule m will be rcos/, r denoting the
distance of the molecule from the centre of the earth, and 7 its
latitude. The relative velocity of the molecule m with respect
to the magnetic pole s will be obtained, according to what
precedes, by giving the same velocity to m and to s, but in the
opposite direction to that of the already existing velocity of
the magnetic pole. If the time of rotation of the earth be
taken as unit, that velocity will be denoted by 27psina. The
magnetic pole will in this way be brought to rest, and the
molecule m will move with the velocity
2a V 7? cos” 1+ p* sin? a—2rp cos /sin «cos v.
The relative velocity of the molecule with respect to the other
magnetic pole will be
2a V 7° cos’ 1+ p” sin? « + 27p cosl sin « cos v.
Now it is obyious that these square roots denote the distance
of the molecule m from the right line drawn through each pole
parallel to the earth’s rotation-axis. Hence it follows that the
magnetic pole acts upon an electric molecule in the same way
as if the pole were at rest and the molecule in rotation about
368 Prof. E. Edlund on Atmospheric Electricity
the right line drawn through the magnetic pole parallel to the
earth’s axis. The squares of the distances between the mole-
cule m and the magnetic poles will be respectively
r+ p?—2rp (cos 1 sin e cos v+ sin J cos «)
and
7” +p? +2rp (cosl sine cosv+ sin! cos@).
The forces with which the magnetic poles s and n act upon
the molecule are therefore expressed by
kM V 7” cos? 1+ p” sin” «—2rp cos / sin @ cos v
7” + p?—2rp(cos/ sin a cos v+ sin /cos 2)
and
kM V1? cos” [+ p* sin? «+ 2rp cos /sin‘a cos v.
7” +p? + 2rp (cos/sin acos v+ sin /cos «)
The former of these forces acts in the plane which passes
through the molecule m and the right line drawn through the
magnetic pole s parallel to the axis of the earth, and the latter
in the plane passing through m and the right line drawn,
parallel to the same axis, through the magnetic pole n. It
will suffice for our purpose to seek the expression of the com-
ponents of these forccs in the cases in which v is equal to 90°
and to 0°. This calculation will show that the electric mole-
cule is moved further from the centre of the earth and carried
from lower to higher latitudes, that it is situated in the plane
represented by fig. 11 or in a plane making a right angle with
it. As this must evidently take place whatever the plane in
which the electric molecule is situated, the result obtained is
that the electric molecules are driven vertically upward and
at the same time from lower to higher latitudes. For the
highest latitudes, where cos / isa minimum, both forces, as also
their horizontal and vertical components, become very small ;
the electric density of the polar atmosphere cannot, therefore,
be great. ‘Thus, although the position of the magnetic poles
is eccentric, the upper regions of the atmosphere from which
the electric fluid is precipitated upon the earth in continuous
currents must describe a closed annular zone about the pole.
But, as we shall demonstrate, this zone is not closed around
the astronomic pole as its centre.
We suppose the molecule m situated in the plane passing
through the terrestrial axis and through the line joining the
poles of the magnet. By making v=0 in the preceding for-
mulz we get the following expressions for the two forces :—
kM(r cos /—p sin «)
7? + p?—2rp sin (/+ «)
and the Aurora Borealis. 369
and
kM(rcosl+psine
r?+p?+2rpsin (l+a)’
Both these forces act in the plane in question—the one
along mp, and the other along mq (fig. 11). The cosines of
the angles formed by them with the terrestrial radius will be
pcos (J+)
/ 7? + p> —2rp sin (+a)
and
pcos (+a)
V7? +p? +2rp sin (l+a)
Therefore the sum of the vertical forces will be
kM(r cos /—p sin «)p cos (J+-@)
[7? + p?—2rp sin (1+) |]?
kM<r cos/+p sin e)p cos (1+ a) (6)
[7? +p? + 2rp sin (+a) ]?
On the other hand, the sum of the tangential forces will be
kM(r cos /—p sin e)|r—p sin (/+2) |
[7? + p?—2rp sin (I+«) ]?
_ kM(rcos/+psina)[r+p sin (7+e) ] as (iD)
[o? +p? + 2rp sin (1+) |?
If =90°—za (or the latitude of the magnetic pole) be intro-
duced into formula (C), the sum of the vertical forces will be
=(. Therefore the electric molecules in the atmosphere ver-
tically over the magnetic poles are not raised in the vertical
direction by the terrestrial magnet.
In the vicinity of the magnetic pole the vertical and tan-
gential components of the induction-force are very small; and
consequently there the electricity of the air must be inconsider-
able, just as it was around the ustronomic pole when we supposed
the coincidence of the two aves. If into formula (D) the same
value of / be introduced, this formula takes a positive value;
or, in other terms, the tangential component tends to bring
the electric molecules thither from the axis of rotation of the
earth. On the contrary, the same formula, when /=90° is
introduced into it, acquires a negative value—which signifies
that the tangential force-component drives toward the mag-
netic pole the electric molecules which are in the atmosphere
over the astronomic pole. It is therefore between these two
points that the point must be situated at which the tangential
Phil. Mag. 8. 5. Vol. 6. No. 38. Nov. 1878. 2B
370 On Atmospheric Electricity and the Aurora Borealis.
force is =0. While the vertical component of the earth’s
induction-force diminishes in general as the latitude increases,
the electric tension of the upper strata of the atmosphere, on
the contrary, is augmented with the increase of latitude until
the tension becomes strong enough to occasion the downflow
of the electric fluid into the earth. The annular space of the
atmosphere where the electric fluid descends to the earth is
evidently closed around the magnetic pole; it is characterized
by the circumstance that in it the vertical component of the
earth’s induction-force has everywhere the same magnitude.
Formula (C) gives an idea of its situation.
As we have seen aboye, the electric fluid flows from the
said space to the earth in the direction of the dipping needle
(of the inclination or dip of terrestrial magnetism). These
electric currents in the rarefied air produce the aurora borealis.
It is evident that this phenomenon ought chiefly to be seen in
the vicinity of the annular space in question. According to
the researches of Mr. Loomis, most of the aurore boreales
appear, in North America, between the latitudes of 50° and
62°, their frequency becoming less at still higher latitudes.
The central line of the space in question lies consequently at
56° latitude—that is, at 34° from the astronomic and at 17°
from the magnetic pole. ‘This central line is denoted by the
point ¢ in fig. 11. We have now to ascertain under what
degree of latitude the annular space must be situated at 180°
of longitude from there, or, in other terms, between what de-
grees of latitude aurore boreales will be most frequent in
Hurope and Asia.
If in formula (C) we make /= 90°—34°=56°, we shall have
kM(r sin 84—p sin 17)p sin 17
(7? + p?—2rp cos 17)?
kM(v sin 34+ sin 17)p sin 17 (B)
(P+p?+2rpcos17)z
This expression designates the intensity of the vertical com-
ponent of the induction-force in North America at 56° latitude.
If in formula (C) we make /=90°, we shall have the ex-
pression of the same component at the astronomic pole, viz. —
kMp? sin? 17 kMp’ sin? 17 (F)
(7+ p?—2rp cos 17)2 (72 +p? +. 2p cos 17)?
By r is meant the distance from the centre of the earth to
the electric molecule under consideration, situated in the atmo-
sphere ; p, being (as already observed) less than the earth’s
semiradius, is consequently also less than 37. Regard being
Mr. J. J. Hood on the Laws of Chemical Change. 371
had to this circumstance, formula (H) obtains a higher nu-
merical value than (F). From this it follows that the vertical
component of the induction-force at the astronomic pole is less
than at the point for which formula (4) holds good. If in
formula (C) we make /=90 +34, we obtain the sought force
for a point ¢’ situated at 56° latitude counted from d. For-
mula (C) is in this way transformed into the following :—
kM(r sin 34° + p sin 17°)p sin 51°
(rv? + p?—2rp cos 51°)?
ms kM(r sin 84°—p sin 17° )p sin 51° (G)
(7? + p? + 2r7p cos 51°)?
Formula (G) having a higher numerical value than (K), the
point at which the vertical component of the induction-force
will be the same as at the point ¢ must be at a higher latitude
than?’. From this it follows that the aforesaid annular zone
will cut the plane in question at a point ¢” situated between
the astronomic pole and ¢’, Thus the zone presenting the
greatest frequency of aurorz boreales must be at a higher lati-
tude in Europe and Asia than in North America.
[To be continued. |
XLIX. On the Laws of Chemical Change.—Part I.
By Joun J. Hoon, Hsq.*
HILE studying chemistry under Prof. Mills, I was
much struck by the want of knowledge concerning
the laws regulating the amount of change which chemically
active bodies undergo in a given time, and in what manner
the rate of change is influenced by heat, electricity, &. Many
cases of change have been investigated and represented gra-
phically ; but, as far as | am aware, no theory has been
given confirmed by experiment whereby, the temperature and
amount of active bodies undergoing change being known,
the amount of remaining energy at any time can be calcu-
lated. The nearest approach to such a theory was given by
Messrs. Harcourt and Hsson in the ‘ Phil. Trans.’ for 1867,
where they showed that for the case of hydric peroxide re-
acting on hydric iodide,
H, 0.4 2HI=2H,0+K,
the amount of change was proportional to the amount of
acting substance, considering hydric peroxide as the active
body.
* Communicated by the Author.
2B 2
372 Mr. J. J. Hood on the Laws of Chemical Change.
A thorough investigation on this point might lead to many
interesting facts in science, and a clearer insight might be
gained into molecular action.
For instance, by a comparison of the rates of change at
different temperatures, all other conditions being the same,
the necessary data could be obtained to deduce the law of
temperature, and so find the point at which no action could
take place; or, again, if analogous compounds, such as the
sulphates, nitrates, chlorides, &c., have an accelerating or re-
tarding effect on the change, their “ equivalence ” might be
determined or compared—that is to say, whether K, SQ,, or
174 parts by weight of potassic sulphate, can perform the
same amount of work as Na,SQ,, or 142 parts of sodic
sulphate.
The cases of chemical change selected for investigation
would require to be under complete control, to allow of the
determination of the amount of change up to any period of
time, as it might so happen that the intervals of time between
two observations would require to be equal in order to calcu-
late the necessary constants required by theory.
The methods of determining the remaining energy should
be accurate and speedy.
When two bodies A and B undergo change and produce a
third, C, which does not take an active part in the change, it
will doubtless, by its mere presence, if not removed from the
sphere of action, either accelerate or more probably retard the
change taking place; and if this effect be great, supposing C
not capable of being removed immediately it is formed, a
mathematical statement of the change would not be possible,
as the influence of C could not be determined. If, however,
the rate of change is so little influenced by the presence of C
that it may be neglected, a theory of the action can easily be
formed as a guide to the experimentalist.
The experiments detailed in this paper were made merely to
see how far the following theory of chemical energy is cor-
rect, neglecting all retarding or accelerating effects of the
compounds produced during the action. By an inspection of
the results, it will be evident that this influence cannot be
very large.
Suppose two bodies in solution which are capable of react-
ing on each other to form new inactive compounds, and the
action taking place be expressed by an equation in terms of
the time and the amounts of remaining active bodies at that
time, on the hypothesis that the amount of change in an inde-
finitely small space of time is proportional to the product of
the remaining active bedies at that time. Let A and B be
Mr. J. J. Hood on the Laws of Chemical Change. 373
the initial values of the bodies, a and @ the amounts of A and
B that have already undergone change up to time't, and let
da be the amount of A acted on in time 6¢; then, by the above
hypothesis,
6a=K(A—a)(B—B)dt. 7.
Suppose, further, that the amounts of A and B are chemi-
cally equivalent (that is to say, they are just sufficient to
render each other inactive), then the ratio
sapeeteg
13 pial o1
call this - , and equation (1) becomes
CoG COL nie a ing 2)
Replacing A—« by y, the amount of A that remains un-
acted on at the time ¢,
d
a = Ky, ag ane a be Tame ta
which, on integrating, gives
1
ona,
or, writing it in the more convenient form,
SO (Cte) Ma Sons ton Oi he ren Rie ©)
being the equation to an equilateral hyperbola with axis ¢ for
asymptote.
The influence of temperature and the non-equivalence of A
and B I will consider further on, after I show how far expe-
riment agrees with this theory.
Experiments.—In the first experiments made, not knowing
how the rate of change was influenced by heat, I took ever
care to keep the temperature of the water-bath perfectly
constant ; but in spite of every attention, the fluctuations
were about +:1°C. This, I afterwards found, could not in-
troduce any considerable error. The flasks containing the
experimental solutions were submerged in the bath, and were
never removed during the experiment. The solutions were
freely exposed to the air, as it was found, after repeated trials,
that atmospheric oxygen had not any perceptible influence on
them during the time the experiments lasted.
The active bodies used were (1) a solution of ferrous sul-
phate containing an indefinite amount of hydric sulphate,
and (2) a solution of potassic chlorate, the strengths of which
were accurately known.
374 Mr. J.J. Hood on the Laws of Chemical Change.
For the determination of the iron, a dilute solution of po-
tassic permanganate was employed, the absolute strength of
which was never determined, as the experiments were wholly
relative. For the experiments made to find the influence of
temperature on the rate of change it was necessary to express
the different solutions of permanganate in terms of-one stan-
dard, this being equivalent to using the same solution for all
the experiments.
For measuring the solutions, 10-cubic-centim. and 50-
cubic-centim. burettes were employed; the errors of calibra-
tion were so small that they were in every case neglected.
Experiment 1.—There were taken 100 cubic centims. ferrous
sulphate solution containing *5772 gram ferrous iron with an
indefinite amount of hydric sulphate, 10 cubic centims. po-
tassic chlorate containing ‘2104 grm., and 200 cubic centims.
water: total volume 310 cubic centims.
‘5772 grm. iron is equivalent to 2105 grm. KCIQO;3, by
the equation
KCIO; == 6 FeO ==. Ui == a Fe, O:.
All the solutions were immersed in the water-bath until
they had acquired the necessary temperature before mixing,
the iron solution being first run into the water, then the
potassic chlorate, and the whole well shaken.
After standing in the bath five minutes, 10 cubic centims.
were withdrawn as rapidly as possible, run into a small flask
containing about 20 cubic centims. of water, to partially stop
the action going on by the dilution, and the remaining iron
determined by means of the permanganate, the whole opera-
tion occupying less than one minute. The time was always
noted just when the iron solution withdrawn had run out the
pipette.
As an excess of permanganate had always to be added to
see the tint, ‘02 cubic centim. was deducted from the reading
of the burette for the coloration ; but in many cases no such
deduction was made. When the iron to be determined was
small, 20 or 30 cubic centims. were withdrawn for titration.
The following Table contains the results of this experiment :
the numbers under “ permanganate calculated ”’ are calculated
by theory from the observed times, and those under “ time
calculated”’ from the permanganate found—the permanganate
found, or y, being the number of cubic centims. required for
10 cubic centims. of the experimental solution.
Taking the first two observations to calculate the constants
oe yat+t)=b,
we get a=133°84, b=1338°4,
~ Mr. J. J. Hood on the Laws of Chemical Change. 375
Temperature 16° C. -
Permanganate, in cubic
: Time, in minutes.
centims.
Found. | Calculated. Found. Calculated.
SS
10 0
8-70 | : 20
7-67 7-69 40 40-7
6-80 | 6-79 63 3
oF al al is ae 106 106-4 |
4:87 | 4-84 142-4 141 |
443 | 4-40 170 168-3
382 | 381 217 2165 |
3°50 3°50 248-5 248-6
3-26 3-24 279 276-7
3-01 3-02 309'5 310-8
2-84 2-81 349 337-4
2-49 2-47 406 | 403-7
2-06 2-04 520° HES 4
1:80 1-75 628 609-7
1-77 1-73 639 622-3
Experiment 2.—The solutions employed were 50 cubic
centims. ferrous sulphate (equal to ‘9847 grm. Fe), 10 cubic
centims. potassic chlorate containing ‘3593 grm. KCI1Os, and
400 cubic centims. water: total volume 460 cubic centims.
The following Table contains the results of this experiment.
Taking the second and third observations for the constants a
and b, the equation is
y(222°8 + t) =2512-1.
Temperature 18° C.
Permanganate, in cubic ; 3 e
Spall. Time, in minutes.
centims,
Found. Calculated. Found, Calculated.
11-21 11:27 0 13
SAU: Sti Wee 35
BEM NY erases! 33
8-48 8-52 72 73:3
7°56 7°59 108 109°5
6-76 6-72 151 148°8
6-54 654 16] 1613
5-96 5-95 199-3 198-7
5-68 5°65 222 223-4
5-32 5:30 251 249-4
4-98 4-96 283 281-6 |
468 4°68 315 314
434 433 | 357 356
4-12 4-1] 388 386-9
3-95 3-92 418 413-1
3°76 3:70 455 445°3
3°69 3°67 46] 458
3-42 3°40 515 511-7
3:22 321 | 560 5574
303 | 2:99 | 617 606-3
| 294 2-92 638 631-6
| 263 2-61 739 732°4
B84 2:30 869 851
BB 2:10 972 957
3876 Mr. J. J. Hood on the Laws of Chemical Change.
Experiments 3 and 4.—Both these experiments were made
at the same time and under ‘similar conditions ; each stood
five minutes before an observation was made. The solution
consisted of 25 cubic centims. ferrous sulphate (equal to
‘4923 orm. iron), 5 cubic centims. potassic chlorate, or *1796
erm., and 200 cubic centims. water.
Taking the second and third observations for the constants
for No. 5.
y(1038°1 + ¢) = 967°23,
and No. 4,
y(104°5 +¢) =976°1.
The results are tabulated below.
Temperature 20° C. No. 3.
Permanganate, in cubic : ; ;
eee Time, in minutes.
centims.
Found. Calculated. Found. Calculated.
9-34 9°38 0 ‘4
Si60: piesa) A ap Che 9°4
Cd SW ee 39°'8
5:60 5°58 70 «69-6
4:70 4°68 103°5 102-7
3°92 3°87 146°5 143°6
3°36 3°26 193-6 190
2°73 2-70 254°5 251-2
2-34 | 316 310-2
2°04 2-02 377 371
1:69 1:66 479 469-2
153 1:52 532 529
1-28 1-26 661 652-2
No. 4.
Permanganate, in cubic lea, fay ante
centims.
Found. Calculated. Found. Calculated.
9°30 9°34 0 “4
roid eo | unin a 1 ar een - ei aS PE
G:6d) oe eS eee AD EL he ere
5°46 5°45 74:5 74:2
4°59 4-58 108-5 108:1
3°84 3°83 150 149-6
3°24 3°23 1975 196-7
2°67 2-69 259 261
2°33 2°31 318 314-4
2:00 1:97 390 383°5
1-67 1:66 483 480
1:50 1-51 542 546:2
1:25 1:26 668 676-3
Mr. J. J. Hood on the Laws of Chemical Change. 377
As acriterion of the probability of the supposed law, I have
calculated the areas enclosed between the curve y(a+t)=),
axis y, and asymptote ¢, with the limits for time of last obser-
vation and zero, on the supposition that the law holds good
between the two observations selected to determine a and 6.
Thus
T
area =| ydt
0
Ah
=) ome (1 + =)
or
b log. 10 logio (1 + =)
taking log. 10 =2°3026.
The areas were also calculated from the experimental num-
bers by the formula
area => G) (tnt1—tn),
which is approximately true, independently ofany law. The
results are given below with the percentage differences of
“found” from theory. As the curve is convex to axis ¢, it is
evident that the areas calculated by the latter formula should
be slightly greater than theory.
Areas.
Percentage
Theory. Found. airs oie.
ING SD ancctes. 2346°8 2362°4 66
Bak v odideei © 4219 4239-9 50
BF PO sca denss 1937°3 1962°5 1-24
ie eee 1952-6 1964:°7 62
_ The question now arises, What will be the form of the equa-
tion representing the change when there is an excess of either
of the active bodies present? ‘Taking equation (1),
da
dt _(A—a)(B—B),
and supposing there is an excess of B sufficient to act on 2
times the amount of A present, then, as before, B=ynA, and
also 8=ve. Since the amount of B rendered inactive is pro-
portional to that of A up to any time, the above equation
becomes
da
Tp MA a) (nA a), . . . ° ° (5)
878 Mr. J.J. Hood on the Laws of Chemical Change.
Since A and nA are the values of the active bodies before
the action begins, they cannot be taken as the initial values
when ¢=0, as the equation only applies when the change is
actually going on, and the solutions require to stand a few
minutes after mixing to allow the action to get into a normal
state before the first observation can be made, when ¢ is to be
taken as =0. Putting y=A—ae, or amount remaining at
time ¢, the equation becomes
d
a = —Kvy((n—1)A+y), « Mere
the solution of which is
if 1 Yy
(n—1)A °8 (n—1)A+y
Let a be the value of y when ¢=0,
1 a :
Oe GD Ane (ney eee
and inserting this value, the final equation becomes
== 0 lose) (c= (EY) }
where
= C—xvt. a)
;__ _ log. 10
~ Kv(n—1)A
This equation is established on the same supposition as (4),
and that the compounds formed during the action have little
influence on the change either as retarding or accelerating
agents, as indeed the experiments indicate.
Experiments.—As yet I have not been able to try very ex-
treme values for n; in the experiments made it only ranged
from ‘5 to 5; above this latter value the action proceeded so
rapidly that large errors occurred, rendering the results worth-
less: still | think the following experiments may be of in-
terest as showing the truth of the formula.
The method of making the experiments was exactly the
same as for those given in the first part of this paper.
Experiment («).—The solutions employed were 25 cubic
centims. ferrous sulphate (equal to ‘4923 grm. iron), 10 cubic
centims. potassic chlorate containing *3593 grm., and 260
cubic centims. water—total volume 295 cubic centims,—this
quantity of potassic chlorate being able to oxidize twice the
amount of iron present, or »=2. The number of cubic cen-
tims. of permanganate required for 10 cubic centims. of this
solution before the action commenced, or the value of A, was
Mr. J. J. Hood on the Laws of Chemical Change. 379
determined by making a solution of iron containing °4923
germ. Fe in 295 cubic centims. water and titrating 10 cubic
centims. with the permanganate used in the experiment; its
value was found to be 10°36 cubic centims., the values of y
being, as before, the number of cubic centims. of permanga-
nate required for 10 cubic centims. of the experimental solu-
tion.
The first observation, at t=0, gave y=9°45 cubic centims. ;
and when ¢=380-°5 units, y=7:30 cubic centims. Taking
equation (8),
—t=C’ logy0 ' Cues) (yh,
and inserting those values, using the second observation to
find C’, we get
OO y ) )
i=490:2 log 05 10°36 9-45. .
The values of ¢ are calculated from this equation (in
minutes), using the observed values of y, and are compared
with those observed. The close agreement between theory
and experiment is very striking.
Temperature 18°C. n=2.
Permanganate, in
i i Time, in minutes,
cubic centims. e, utes
Found. Found. Calculated.
9°45 0
7°30 30°5
5°98 55 56-4
4°74 89 89-1
4:06 112-2 112-6
3°30 143-2 144:'8
2-63 180°5 182°5
2-30 206°8 205°5
1-93 237°5 236°5
1:58 272 273
1:14 336°3 334°4
98 360 3637
Experiment (8).—Hyery thing the same as before, except the
ratio of the iron to the potassic chlorate, viz. 1:3, or n=8, and
total volume 300 cubic centims. The value for A was found
to be 10°18 cubic centims. ; and taking the first two observa-
tions for a and OC’, we get
F 30°11
—{=257°4 logo (S530) SD )}
The results are given below.
380 Mr. J. J. Hood on the Laws of Chemical Change.
Temperature 18°C. n=83.,
Permanganate, in
: : Time in minutes.
cubie centims. A
Found. Found. Calculated.
9:75 0
7:20 24
5:23 50:3 51-4
3°73 81:8 82:5
2:86 106 108:1
2-06 139'3 140°8
1-46 172°8 172°6
115 199-5 201°3
*85 231 233°5
‘61 264 269-4
Experiment (y).—The ratio of the potassic chlorate to the
iron was as 4:1, orn=4; and A was found by experiment to
be 9°78 cubic centims. Using the first and third observation
for a and CO’, we get
banshee y aaa)
alae login Gee Ee
Temperature 17°°8 C. n=4.
Permanganate in
: ; Time, in minutes.
cubic centims.
Found. Found. Calculated.
9-56 0
8°36 25°7 23°8
7:26 49°7
6:38 75:1 74
5°56 104 100°5
4:86 128°3 127
4°32 152-5 - 150-7
3°86 175 173°6
3:07 217°5 221-1
2°68 249 249-8
2:22 293°5 290-2
1:98 317°5 315
1-71 346°5 346°9
1-35 402 399:1
1:30 410°5 407°4
11 447°5 444:°7
"85 508 502°6
Experiment (6).—In this case there was an excess of iron
present, which alters the form of the equation on account
of n being less than unity, the ratio of iron to potassic c.lo-
rate being as 1:°8, orn=*8; A was found to be 9°40 cubic
centims. Taking the second and third observations for C,
Mr. J. J. Hood on the Laws of Chemical Change. 381
and not the first for a, on account of its being faulty, we get
t—25°6=2275°7 log (= ag 1 <2)( sax) } '
Temperature 17°38 C. n=°8.
Permanganate, in
: : Time, in minutes.
cubic centims.
Found. Found. Calculated.
Sg: 0 13
8:38 25°6
‘eit h 48:3
7°20 74°6 735
6°68 102°8 101-1
6:30 126°8 124°8
596 151 149°1
5°70 173 170-1
5°26 216°5 211-6
4:95 248-5 246°8
4°64 292 288
4-48 315°5 312°2
4:26 345 349-2
3°98 401°5 406°4
3°88 438 429°5
3°57 508 513°6
The criterion of areas applied to those experiments gives
very close results. The approximately true areas are given by
the formula |
S (a) Cie ire te) 3
and the real areas are found by assuming the curve to be
at
— C’ logio aoe
which gives for the area between the curve and axes, taking
the limits for y of first and last experiment,
b+
area =bC’ logy, aS 7 ay
using the constants found by experiment.
Areas,
| Theory Bound Percentage
i ‘ difference.
| a ey |
A 1230-4 1229-6 |
(ee $23°4 819 53
ee. 2. 1725 1744 11k
ae 2716 2716°2
382 Mr. J.J. Hood on the Laws of Chemical Change.
In all the experiments given in this paper there is one
special point to which I wish to draw attention; and that
is that only two observations are taken to find the neces-
sary constants ; if these had been calculated for each pair of
observations and the means taken, better agreement with theory
would doubtless have been obtained ; but such a procedure
is apt to throw doubts on a theory, as to which, if it were true,
one observation should be as good as another for determining
the constants, unless large errors were suspected.
Before selecting those observations which were to be taken
for the constants, the first few were laid off graphically, and
those which seemed to be the most regular were chosen.
Influence of Temperature.—Chemical decompositions are all
more or less influenced by heat, the effect being an accelera-
tion of the rate of change ; but it is very probable there is a
point at or below which temperature no change can take
place, as in the many cases where an acid has not action on a
body at the ordinary temperature, while on heating to about
100° C. change goes on briskly.
The relation of the rate of change to the temperature and
the point of zero action are possible to be discovered by the
foregoing experiments in a simple manner.
It has been shown that the rate of change is expressed by
the equation
LY nine 2
ape BY >
and if it be proportional to an unknown function of the tem-
perature /(@), @ being degrees Centigrade above the zero-
point, so that
dy _ a 2
aE uf@)y’,
integrating,
oe ( C ig t);
pf)? \ pf)" °7?
writing it in the usual form,
b=y(a+t),
b and a being determined experimentally. If for a second expe-
riment under exactly the same conditions, but temperature
differing by n° C., the equation is found to be
’=y(a' +t),
we get at once the relation
b _f(O+n).
BE ee
Prof. 8. P. Thompson on Binaural Audition. 383
but it does not follow that “ is also equal to this ratio, unless
the value for 7 when ¢=0 is the same in each case.
A number of experiments were made to determine f(@); but
as the temperatures ranged only from 18° to 22° C., and they
are rather incomplete, I refrain from giving them fully ; the
results, however, seemed to indicate that /(@)=6", or that the
rate of change varies as the square of the temperature from
the zero-point ; and on this hypothesis the point of no action
was found to range from +2° C. to —2° C., or about the
temperature at which the solution would become ice.
In conclusion, I may state that the following experiments
were made. An increase inthe amount of H, SO, accelerates
the change, still obeying the law. Ferrous chloride, in pre-
sence of HCl, is oxidized by KCIO3, at 18° C., approximately
according to the law y(a+¢t)=0b, the discrepancies in this
case being caused by the difficulty of accurately determining
the iron by permanganate in presence of free hydric chloride.
Ferrous sulphate in hydric sulphate is only very slowly acted
on by potassic nitrate in the cold, probably being too near
the zero-point.
I hope soon to give the results of some experiments on the
rates of change for the various chlorates, as potassic against
sodic chlorate, and possibly get some relation between the
dynamical equivalences of those salts.
Glasgow, August 1878,
L. Phenomena of Binaural Audition —Part Il. By Strvanus
P. Tuompson, D.Sc., B.A., Professor of Experimental
Physics in University College, Bristol*.
1, ae a paper read before Section A of the British Associa-
tion last year (1877) on Binaural Auditionf, the author
communicated the discovery of two phenomena: first, the exist-
ence of an interference in the perception of sound ; secondly,
an apparent localization of simple sounds at the back of the
head when led to the two ears in sucha manner that the vibra-
tions reached the ears simultaneously in opposite phases. The
present paper recapitulates the former experiments, and gives
some further account of the phenomena and of new methods
of experimentation.
2. The existence of an interference in the perception of
* Communicated by the Author.
+ Rep. Brit. Assoc. Plymouth, 1877, p. 37; Phil. Mag. October 1877,
p- 274.
384 Prof. 8. P. Thompson on Binaural Audition.
sounds was demonstrated by leading separately to the ears |
with india-rubber pipes the sounds of two tuning-forks struck
in separate apartments, and tuned so as to ‘ beat’’ with one
another—the ‘beats’? being very distinctly marked in the
resultant sensation, although the two sounds had had no op-
portunity of mingling externally, or of acting jointly on any
portion of the air-columns along which the sound travelled.
The experiment succeeded even with vibrations of so little in-
tensity as to be singly inaudible.
3. The apparent localization at the back of the head of
sounds whose vibrations reach the ears in opposite phases
being a subjective phenomenon, was announced by the author
as the result of the concurrent testimony of several indepen-
dent witnesses. Its existence was demonstrated by leading
separately to the two ears the sound of two unison tuning-
forks, one of which was slightly loaded to make its phase change
slowly relatively to the other. The “ beats” were described
as being not “silences,” as ordinarily observed when the dif-
ference of phase is half a complete vibration, yet as being
“most distinctly heard, and seeming to be taking place within
the cerebellum.”” Referring to this attempt to ascertain the
effect of bringing to the two ears waves of equal pitch and
intensity, but differing in phase, the author stated that a fuller
series of experiments was in course of completion. The sequel
of the present paper records with what result those experiments
have been made.
4. The telephone of Graham Bell, introduced into this
country at the Meeting at Plymouth, where the former paper
was read, furnishes a new instrument peculiarly adapted for
researches of this nature. Both the phenomena recapitulated
above have been reobserved by a considerable number of inde-
pendent experimenters, confirming the results announced by
the author. Thus it was announced by Professor Graham Bell,
in a lecture before the Society of Arts, November 28, 1877*,
that these two phenomena had been discovered by Sir William
Thomson when experimenting at Glasgow with the telephone.
One important advantage of the Bell telephone as an instru-
ment of research is that the phase of vibration can be inverted
at will, by reversing the connexions of the receiving-instru-
ment, so that the currents traverse the coil in a reversed direc-
tion, the motion of the vibrating disk being consequently also
executed in a reverse sense. Using two systems of telephones
to bring to the ears two sounds capable of yielding interference-
beats, interference in the resulting perception of the sounds is
* Vide Journal of the Society of Arts, vol. xxvi. No. 1806, p. 22
(Novy. 30, 1877).
-Prof. 8. P. Thompson on Binaural Audition. 385
very clearly recognized. I have not been able hitherto, how-
ever, to devise any crucial experiment to decide whether the
interference is an interference of the sensations, or whether
it is to be attributed to the physical conveyance of the sounds
through the bones of the skull, and their mechanical inter-
ference.
5. Phenomena of Localization —Almost all persons who
have experimented with the Bell telephone, when using a pair
of instruments to receive the sounds, one applied to each ear,
have at some time or other noticed the apparent localization
of the sounds of the telephone at the back of the head. Few,
howeyer, seemed to be aware that this was the result of either
reversed order in the connexion of the terminals of the instru-
ment with the circuit, or reversed order in the polarity of the
magnet of one of the receiving-instruments. When the two
vibrating disks execute similar vibrations, both advancing or
both receding at once, the sound is heard as usual in the ears ;
but if the action of one instrument be reversed, so that when
one disk advances the other recedes, and the vibrations have
_ opposite phases, the sound apparently changes its place from
the interior of the ear, and is heard as if proceeding from the
back of the head, or, as I would say, from the top of the cere-
bellum. So distinctly marked is the apparent localization, that
it has been regularly employed, I am informed, by Professor
D. H. Hughes to ascertain whether a pair of receiving-tele-
phones are rightly adjusted or not.
6. My recent experiments have been directed to determining
how this apparent localization is affected by variations of the
sounds in respect of (a) pitch, (>) phase, (¢) intensity, (d) qua-
lity, and whether it is to be accounted as a physical, physio-
logical, or psychological phenomenon. I have made, finally,
a few experiments on the binaural estimation of combinational
tones.
(a) After employing the simple sounds of tuning-forks of
various pitches, and conveying their vibrations to the two ears
in opposite phases by three distinct methods, I find the appa-
rent locality of the sound (the acoustic “image’’) to occupy
an invariable position near the top of the cerebellum. These
three methods are:—/%rst, employing two india-rubber tubes
of equal length, armed with either glass funnels or box reso-
nators, in front of which two tuning-forks are held, differ-
ence of phase being obtained by rotating one fork round on
its axis, or by loading it to obtain a continuously varying
phase. Secondly, by employing one tuning-fork, but having
a branching tube to the ears, and making ‘the lengths of the
two branches differ by half a wave-length. Thirdl, y, by em-
Phil. Mag. 8. 5. Vol. 6. No. 88. Nov. 1878. 2C
386 Prof. 8. P. Thompson on Binaural Audition.
proying a system of telephones, the two receiving-telephones
eing reversed in action.
For simple tones, then, the acoustic “image” does not vary
in position with pitch, ifthe difference of phase remains always
a maximum. Tor compound tones the first and second of
these methods of experiment are impossible ; but when using
the two telephones, I obtain the localization in the same posi-
tion for sounds of all pitches and kinds. Indeed the observa-
tion of articulate speech appearing to come from a spot at the
back of the head proves the phenomenon to be independent of
the pitch—that is to say, of the wave-length of the component
tones.
I arranged a Hughes’s microphone with two cells of Fuller’s
battery and two Bell telephones, one of them having a com-
mutator under my control. Placing the telephones to my ears,
I requested my assistant to tap on the wooden support of the
microphone. ‘The result was deafening. I felt as if simulta-
neous blows had been given to the tympana of my ears. But
on reversing the current through one telephone, I experienced
a sensation only to be described as of some one tapping with ©
a nammer on the back of the skull from the inside.
7. The relation of the acoustic ‘“‘image”’ to the difference
of phase (b) between the two separate sounds isa more difficult
matter to deal with. The method of the telephone here be-
comes inapplicable, as it provides no means of partially chan-
ging the phase of one of the two sounds. The two sounds
must be either exactly coincident or exactly opposed in phase.
With simple tones, as of the tuning-fork, any desired differ-
ence of phase can be obtained by adjusting to the appropriate
amount the difference in length between the two conveying
tubes; or by loading one of the two forks so as to make its
vibrations lose gradually on those of the other fork, and so
establish a regularly changing difference of phase. Both these
methods agree in showing, as far as accurate observation of
the subjective phenomenon is possible, that when the difference
of phase is partial, the sound is heard partly in the ears and
partiy at the back of the head, the former partial sound dying
out and giving place to the latter as the difference of phase
approaches a maximum, and vice versd.
A variation of this experiment may be of interest to record.
A stout copper wire about 3 feet long had its ends bent round
into smooth loops, and the whole was curved so that the two
loops could be inserted into the two auditory meatus of the
ears. An UT; (c’=256) tuning-fork was then struck; and its
stem was pressed against the middle point of the copper wire,
the vibrations having thus to travel equal lengths of the wire
Prof. 8. P. Thompson on Binaural Audition. 387
before reaching the ears. The sound appeared to come from
‘the ends of the wire in the ears. The stem of the fork was
now slid along the wire. At about an inch and a third from
its former position the difference of path of the two sounds
had been sufficient to produce complete difference of phase,
and the sound appeared to come, not from the two ends of the
wire, but from the back of the head. In intermediate positions
the effect was of a mixed character: part of the sound was
heard as in the ears, part at the back of the head. With
forks of various pitches, a similar result was found, with ap-
propriate differences in the lengths of path.
8. The next experiments concern the relative intensities (c)
of the two sounds. When two simple tones in unison and
agreeing in phase are led to the ears, one tone being louder
than the other, the simple result of experience is that the sound
is heard in one ear more than in the other. It is as if the
sounds were loud, but as if one ear were partly deaf. But if
the two simple sounds differ by exactly half a vibration, and
one is louder than the other, the result is wholly different.
The sound no longer seems to be in the ears. There is an
acoustic ‘image ”’ localized at the back of the head. Instead,
however, of this image appearing to exist at the centre of the
back of the head as it does when the sounds are equal in in-
tensity, it appears to be on one side, nearer the ear in which
the sound is louder. If two unison tones reach the two ears
separately, with complete difference of phase and equal inten-
sity, and then the intensity of one sound be gradually reduced
down to nothing, the acoustic image, which at first occupies
a position behind the middle of the top of the cerebellum, gra-
dually moves round the back of the head apparently just
within the skull, to the ear in which the sound arrives with
full intensity. I have verified this result with tuning-forks
and tubes, and also with the microphone and two Bell tele-
phones, in one of which the intensity of the vibration could
be regulated by adjusting the position of the magnet.
9. The effect of the quality (d) of a compound sound on the
localization of an acoustic image in binaural audition is very
complicated. The action of the telephone in reversing the
phase of all vibrations independent of their quality has already
been noted in § 6.
A case, however, occurred, of some independent interest.
Suppose a simple tone and its octave to be combined together,
so yielding a compound wave of definite form. Suppose now
the octave note to be simply reversed, and in this condition
compounded with the original fundamental tone. The form
of the second compound wave will exactly resemble that of
2C 2
388 Prof. S. P. Thompson on Binaural Audition.
the first, except that it is (so to speak) inverted end for end.
The two associated wave-forms might be, for example, the
two (A and B) subjoined. The question arises, Can we dis-
A
Aye
tinguish between the two compound tones corresponding to
these forms by leading them separately to the two ears—that
is, by listening to them binaurally? We have shown that in
binaural audition we have a perception of a difference of phase
for single tones. Can we go further, and demonstrate the ex-
istence of a perception of phase-difference in the components
of a compound sound ?
Helmholtz*, after a very careful consideration of the sub-
ject, comes to the conclusion that in ordinary hearing “ the
guality of the musical portion of a compound tone depends
solely on the number and relative strength of its partial simple
tones, and in no respect on their difference of phase.” Mr.
Sedley Taylor? repeats the statement in a more emphatic form:
“The ear being deaf to differences of phase in partial-tones,
perceives no distinction between such modes of vibration....
but merely resolves them into the same single pair of partial-
tones.”
To put the matter to the test of binaural hearing, the follow-
ing experiment was arranged :—Two similar glass funnels
were attached to equal tubes leading to the two ears: their
mouths were placed facing one point, but at right angles to
one another. Ifa vibrating tuning-fork be held at the point
toward which the funnels face, it can be so held that the vibra-
tions imparted by the two tubes shall be either alike or opposite
in phase. Jor if the ends of the prongs be held towards one
funnel so that the axis of the fork coincides with the axis of
* Sensations of Tone (Ellis’s translation), p. 184.
+ Sound and Music, p. 146.
Prof. 8. P. Thompson on Binaural Audition. 389
the funnel, and then the fork be slowly rotated round its axis,
the vibrations transmitted down the other funnel will alter-
nately agree with or differ from those transmitted down the
first funnel, according to the aspect of the fork. Two forks
were chosen for the experiment, UT; and UT, (c’=256 and
e’=512). Both were set vibrating at the point whence their
vibrations could enter each funnel ; and they were placed at
first so that the vibrations of each fork reached the ears in
similar phases. The compound tone was heard “ in the ears.’’
Then the UT, fork was rotated a quarter round on its axis,
so that it sent opposite vibrations to the two ears. The two
compound waves transmitted by the two tubes differed there-
fore like those of the diagram above. The sound of the UT, fork
moved its position to the back of the head; the sound of the UT3
fork remained localized in the ears. When the UT; fork alone
was turned round a quarter, its sound alone was localized at
the back of the head. When both were turned one quarter,
both notes appeared to sound at the back of the head. Here
is a case, then, in which by listening with the two ears we can
detect a difference of phase between the component partial
tones of a compound tone. And when we reflect that, except
for sounds whose origin is in the plane coinciding with the
median plane of the skull, the lengths of the paths by which a
sound reaches the two ears are unequal, so that the phases of
the vibrations received simultaneously by the two ears cannot
be alike for all wave-lengths, we must admit that this binaural
perception of a difference of phase cannot but be of importance
in the appreciation by the ear of the quality of compound
sounds such as those of musical instruments (in which every
fundamental tone is accompanied by a certain characteristic
series of upper partials), and of the sounds of the vowels.
10. As to the cause of the singular localization discussed in
the preceding paragraphs, whether it be physical, physiological,
or psychological (that is to say, purely associative ), I hesitate to
give an opinion without further evidence. Insearching for a true
explanation we must not lose sight of the other phenomenon
of the interference in the perception of sounds, though it is
by no means certain that both phenomena can be referred to
the same cause. There is no decussation of the auditory
nerves, like that of the optic nerves, to account for a blending
of the sensations. The portio mollis of the right does not in-
tersect or have any commissure with the portio mollis of the
left after leaving the fourth ventricle of the brain, from which
they originate. This point deserves the attention of anato-
mists and physiologists. .
It may be possible to explain the phenomenon of localiza-
390 Prof. 8. P. Thompson on Binaural Audition.
tion upon a hypothesis of a pure association of previous sen-
sations; but such cannot be framed until the physiological
points involved are more distinctly recognized.
11. The Binaural Estimation of Combinational Tones—In
my paper of last year | remarked that I had been unable to ob-
serve the existence of combinational (differential) tones when
two simple tones ordinarily capable of yielding such tones
were led separately to the two ears. Thus the forks e’ and g/
(MI; and SOL;) when struck together give a differential tone
of 64 vibrations, or C,(= UT,), which is perfectly recognizable;
but when led separately to the ears no such tone is to be heard.
But if the two tones be allowed to mingle and their joint sound
be led to the two ears by a Hughes’s transmitter and two tele-
phones arranged to yield opposite vibrations, then the differ-
ential tone of 64 vibrations is heard accompanying the two
simple tones, and is localized with them at the back of the
head.
Other experiments with forks of higher pitch have convinced
me that the absence of differential tones is general when the
two separate simple sounds do not mingle before reaching the
ears. During a recent visit to the workshop of Dr. R. Konig of
Paris, I had the opportunity of hastily repeating this experi-
ment upon forks of shrill tones belonging to a series purposely
constructed for observations upon the combinational tones;
and the result fully confirmed previous observations.
My paper of last year mentioned a case which seemed to
indicate the presence of summational tones. The difficulty of
observing these is ordinarily much greater than that of obser-
ving the differential tone, and in binaural experiments is still
greater. Further observations are still wanting on this point.
It was remarked in my former paper that in binaural audition
dissonances are excessively disagreeable, and the ordinary
consonant intervals harsh. No subsequent experiments have
been made upon this matter, which is probably connected with
the absence of the differential tones.
12. One other phenomenon, as yet only partially investi-
gated, remains to be recorded. Let a small tuning-fork, such
as that used by pianoforte-tuners or violin-players, be struck,
and its stem pressed against any portion of the back of the
head. If the fork be pressed against the parietal or occipital
regions of the head on the right of the median line, its sound
appears to be heard in the left ear; if held against a region of
the head on the left, it appears to be heard in the right ear.
If, however, the fork be pressed against the region immedi-
ately above either temporal bone, its sound is heard in the ear
of the same side.
Notices respecting New Books. 391
2
. Lecapitulation.
(a) There is an interference in the perception of sound; for
two simple tones capable of interfering are still heard to inter~
fere when conducted separately to the two ears. !
(6) When two simple tones in unison reach the ears 1n op-
_ posite phases, the sensation of the sound is localized at the
back of the head.
(c) The localization of this acoustic “ image”’ is independent
of the pitch of the sounds. wih
(d) When the difference of phase is partial, the sensation 1s
localized partly in the ears and partly at the back of the head.
(e) If the difference of phase be complete but the intensities
unequal, the acoustic “‘image,’’ instead of being at the middle
of the back of the head, is nearer that ear in which the sound
is louder.
(f) It is possible to discern the difference between two
compound tones which differ only in the phase but not in the
pitch or intensity of their component partialtones. For when
two such compound tones are separately brought to the ears
so that the vibrations of any partial tone present reach the ears
in opposite phases, that particular partial tone is singled out
and localized at the back of the head.
(g) When two simple tones are led singly to the ears no
differential tone is heard; there is some evidence that summa-
tional tones are heard.
(h) To binaural audition dissonances are excessively dis-
agreeable, and ordinary consonances harsh.
(t) Vibrations mechanically conveyed to a point of the
parietal or occipital region of the skull, at one side, are appa-
rently heard in the ear of the other side of the head.
University College, Bristol,
July 30, 1878.
LI. Notices respecting New Books.
A Treatise on Dynamics of a Particle, with numerous Examples. By
Perer Gurarie Tair, W.A., formerly Fellow of St. Peter’s College,
Cambridge, Professor of Natural Philosophy in the University of
Edinburgh, and the late W1LLIAM JOHN STEELE, B.A., Fellow of
St. Peter's College, Cambridge. Fourth Edition, carefully revised.
London: Macmillan and Co. 1878. (Crown 8vo, pp. 407.)
HIS work has been long before the world, and its merits as a
comprehensive handbook of the subject are well known. In fact
it contains an account of the Motion of a particle under various cir-
cumstances amply sufficient for the requirements -of the most ad-
392 Notices respecting New Books.
vanced student. After two introductory chapters (one kinematical,
the other physical), there are chapters devoted-to rectilinear and to
parabolic motion, to central orbits, to constrained motion and to
motion in a resisting medium; then follow a chapter of “ General
Theorems,” one on impact, and, finally, a chapter on the motion of
two or more particles. The last of these subjects is treated under
the two divisions of free motion and constrained motion. In the
second division no more than the case of two particles is considered.
The methods employed ‘are applicable to more complicated cases,
when more particles than two are involved; but nothing would be
gained by such a proceeding, as D’Alembert’s Principle supplies us
with a far simpler mode of investigating the motions of any system
of free or connected particles” (p.370). In fact the only case dis-
cussed in detail is that in which two particles of unequal masses
“are attached to different points of an inextensible string, one of
whose extremities is fixed.” The solution of this question is ob-
tained for small vibrations, in which case the integrations can be
effected in finite terms. There is added a discussion of the case in
which the mass of one particle is much greater than that of the
other, and the strings are not approximately equal. This appendix
is taken from a paper by Sir W. Thomson, “ On the rate of a Clock
or Chronometer as influenced by the mode of Suspension.” To each
chapter numerous examples are appended, which have been taken
for the most part from Cambridge Examination Papers; many of
them would require for their solution an amount of ingenuity such
as but few students possess.
Professor Tait gives by way of introduction a short history of the
book, from which it appears that Mr. Steele’s share in the compo-
sition of the First Edition was not very large, and, in fact, that he
died before its final arrangement and revision. The Second Edition
was thoroughly revised and, indeed, recast by Professor Tait, who
thus appears to be the sole responsible author. The Third Edition
was revised by W. D. Niven, Esq., of Trinity. ‘The present
Edition has been thoroughly revised by Professor Greenhill, who
has not only at great labour verified and (where necessary) cor-
rected the examples, but has endeavoured to adapt the book to the
present requirement of the Tripos by the free introduction of Ellip-
tic Functions, &c., which, in my Cambridge days, were under the
ban of the Board of Mathematical Studies.” In short, it will be
seen that no pains have been spared to render the work as complete
and trustworthy as possible. And yet the author does not seem
very well satisfied with his work. The fact is that the book was
written with a view to the requirements of the Mathematical
Tripos; and this circumstance seems to have imposed restraints at
which Professor Tait chafes. Thus we find him writing as fol-
lows :—Several of the examples “have defied all attempts at im-
provement, and now stand in their unintelligibility as a warning, to
che Candidate for Mathematical Honours, of the ordeal he may
have to pass through.” Again, the text of the work is to a great
Intelligence and Miscellaneous Articles. 393.
_ extent broken up into detached propositions, yet he states that in his:
opinion ‘this is not the form in which such a treatise ought to be
written” (pp. vi, vii). And with reference to the chapter of
‘General Theorems,” he says that several of the results proved in
it “‘ have already occurred as immediate deductions from the laws
of motion; but to maintain the special character of the work we
give more formal analytical demonstrations, though these are cer-
tainly superfluous” (p. 259). We cannot help thinking that the
unintelligible examples should have been omitted, and that the book
should haye been written in the form that seemed best to the writer.
But if this could not be, and he were in any sense writing to order
and so obliged to compromise, surely it is somewhat ungracious to
proclaim his dissent, from what is after all his own act and deed,
upon the house-teps. The fact is, if we may venture to hint at a
fault, the Professor’s individuality is a little too pronounced. If he
thought it best, on the whole, not to act upon his private opinion,
it would have been better to have kept silence. Occasionally the
fault takes another form, and he indulges in some thing that might
almost be called autobiography. A very curious instance of this is
to be found in the confession that, when he wrote the second
chapter as it stood in the First Edition, he had net so much as read
** Newton’s admirable introduction to the Principia.”
LIL. Intelligence and Miscellaneous Articles.
A CONSIDERATION REGARDING THE PROPER MOTION OF THE SUN
IN SPACE. BY §. TOLVER PRESTON.
ie is a known fact that a wave emitted in a medium does not
partake of the motion of the body emitting it; for when once
the wave has left the body, the wave depends solely on the mediam
for its propagation. Hence it would follow that, owing to the
sun’s proper motion in space, the waves emitted by the sun must
be situated excentrically about it, the degree of excentricity marking
exactly the direction and velocity of the sun’s proper motion in
space (or in the xther which fills all space). It thereby becomes
possible (in imagination at least) to refer the proper motions of the
sun and stars to one common standard, viz. to the universally dif-
fused ether: or it may be said that the direction and velocity of
the sun’s proper motion (and that of every star) is physically
marked in the ether of space—each stellar sun marking the direc-
tion and velocity of its motion with geometrical accuracy by means
of the relative situation to one another of the spherical waves suc-
cessively emitted, each of which remains immovable or unalterable
in position (in regard to its own centre). In short the centre of a
spherical wave may be said to represent indestructible position, in
the sense that the centre of the spherical wave is an immovably
fixed point, such that the intersection of the normals to two tangent
planes situated anywhere on the contour of the spherical wave
394 Intelligence and Miscellaneous Articles.
always marks the same indestructible locality (which is entirely un-
affected by any subsequent motion of the body which emitted the
wave). In this sense it may be said to be theor etically true that the
locus or origin of any disturbance in a medium is for ever defined
in that medium.
If we imagine a boat sailing in a smooth lake, and drop periodi-
cally stones into the water, circular waves will spread each time
from the centre of disturbance, and the degree of excentricity of
these waves to the moving boat (or to each other) will mark geome-
trically the direction and velocity of the boat’s motion. So the
degree of excentricity of the waves about the moving sun (set up by
the disturbing impulses of its molecules) marks geometrically the
direction and velocity of the sun’s proper motion.
The following point in connexion with this subject may perhaps
be worth a passing notice. It has been computed (according to an
estimate of Sir William Thomson, based on the observations of
Herschel and Pouillet), that the energy of the waves given off by
the sun amounts (in round numbers) to 7000 horse-power per
square foot of surface; or, otherwise, about 1700 foot-tons of energy
are thrown off per second from every square foot of the sun’s sur-
face into the ether of space. It would seem incredible (whatever
the constitution of the ether might be imagined to be) that all this
energy could be given off to a material medium in a particular direc-
tion (2. é. in a direction from the sun) without any reaction in the
opposite direction: or would it be supposed that, if the sun were
emitting all this energy from one side only, there would be no reac-
tion in the opposite direction? Admitting that there would be a
certain reaction in this assumed case, then it would be reasonable
to conclude that, as the case actually stands, the reaction would
not be perfectly balanced, owing to accidental irregularities in the
distribution of the differently radiating materials of the sun’s sur-
face. If this be admitted as possible, then we should have in the
unbalanced reaction a true physical cause for producing (or influ-
encing) the proper motion of the sun.
London, October, 1878.
ON THE DISSOCIATION OF THE OXIDES OF THE PLATINUM GROUP.
BY H. SAINTE-CLAIRE DEVILLE AND H. DEBRAY,
Platinum is distinguished from all the metals with which it
is associated in its ores by the fact that it does not combine
directly with oxygen, in whatever position we place the two bodies.
With rhodium, palladium, and iridium the case is different. —
When heated in a muffle, if the temperature is not too high, these
metals combine with oxygen ; but their oxides are decomposed when
we raise the temperature sufficiently.
Osmium and ruthenium combine directly with oxygen. The
product of this oxidation is volatile, and is formed at the highest
temperatures.
Intelligence and Miscellaneous Articles. 395
The most strongly calcined osmium, much less alterable than the
osmium obtained at a low temperature, changes into osmic acid at
ordinary temperature*; at the highest temperatures osmic acid is
always obtained.
Ruthenium behaves altogether like osmium. The strongly cal-
cined metal oxidizes in a muffle at a temperature scarcely above
400° C., and volatilizes in great quantity. In what form, it is dif-
ficult to say ; for the material then exhales the odour of ozone, the
formation of which always accompanies the decomposition of hy-
perruthenic acid. The product deposited in the muffle is always
the binoxide of ruthenium. This oxide sublimates and crystallizes
in a porcelain tube traversed by a current of oxygen in which
substances containing ruthenium are heated. M. Frémy thus
proved its volatility, and discovered the means of extracting directly,
and under the most beautiful forms, some products of the roasting
of osmide of iridium. Ruthenium also, which in the metallic state
is one of the most fixed substances we know, evaporates very
quickly in a muffle, especially at a very elevated temperature.
These properties absolutely distinguish osmium and ruthenium
* The characteristic smell of osmic acid is at length perceptible in
bottles containing even crystallized osmium prepared at a high tempera-
ture. The stoppers then become covered with the black coating given by
the reduction of osmic acid.
+ By operating on a few grams of ruthenium we have been able in a
few hours to volatilize 24 per cent. of its weight ina highly heated muffle ;
in the blowpipe flame the volatilization is much more rapid and still
more considerable in amount.
From the fact that osmium and ruthenium volatilize very rapidly in the
oxyhydrogen flame of the blowpipe, giving osmic acid and binoxide of
ruthenium, it must not be concluded that these oxides are undecomposable
by heat. Osmic acid would be reduced, in the interior of the flame at
that high temperature, to sesquioxide of osmium, crystallizable in golden-
coloured scales, which we have made known. The final result would still
be the same: this oxide, on coming into the air, into a relatively cold
region, would there be changed into osmic acid. In supposing that the
oxide of ruthenium is not decomposed into a lower oxide, it is not neces-
sary also to admit that it is absolutely undecomposable at the temperature
of 2500° given by the combustion of hydrogen and oxygen. ‘This com-
bustion is not complete in the hottest parts of the flame; hydrogen and
oxygen exist there uncombined ; and if the oxide of ruthenium has a less
tension of dissociation than that of water at this high temperature, one
can conceive that it may not be decomposed. Oxide of ruthenium would
therefore be less readily decomposable than water by heat. To discover
whether it is really undecomposable, we must be able to heat it (as we
have pointed out forthe oxide of iridium) in a vacuum to high temperatures ;
but, unfortunately, there exist no vessels suitable for such experiments.
The hypothesis of the very great stability of the oxide of ruthenium,
however, is supported by the fact that this oxide, heated in a porcelain
tube, exhibits (like the oxide of iridium), at least at a bright red heat, no
sensible tension of dissociation ; it merely volatilizes, and is deposited in
the form of crystals and a coating of binoxide in the colder parts of the
porcelain tube.
396 Intelligence and Miscellaneous Articles.
from the other metals of the platinum group. These two bodies,
by the manner in which they behave in contact with oxygen, mani-
festly approach arsenic and antimony ; they might, like these, be
placed among the metalloids. It is not the same, we have said,
with rhodium, palladium, andiridium. These bodies once oxidized,
decomposing by heat, permit us to ascertain the laws of their dis-
sociation and the tension it takes at different temperatures. We
will only speak, in this Note, of the oxide of iridium, the only one
we have at present completely studied.
The oxide is put into a porcelain tray, this into a small platinum
waggon, which is introduced into a porcelain tube closed at one end
by a glass plate kept in its place by mastic. The other extremity,
by means of a lead pipe and a glass tube, attached one to the other
by mastic and to the porcelain tube, is put ito communication
with a Geissler mercury pump, and a manometric tube dipping in
the mercury.
Before introducing the iridium oxide into the porcelam” tube,
we assure ourselves that it maintains a vacuum at the ordinary
temperature and at a red heat, which does not always happen. In
fact, porcelain tubes which are air-tight when cold, at a red heat
often let in hydrogen and carbonic oxide from the hearth. 7
The porcelain tube is introduced into a cylindrical muffle capable
of containing at the same time a porcelain thermometer furnished
with its tube and compensator, of the form employed and described
by M. Troost and one of us*. The muffle is placed in a furnace
heated with petroleum or with heavy coal-oil, which is introduced
into the furnace through a piston-cock divided into at least 200
parts; so that the flow of the oil can be varied, and consequently
the temperature, with a perfection that could not have been ex-
pected. The oil-reservoir is furnished with a Mariotte tube, which
maintains it at a constant pressure. With this apparatus the
porcelain can be completely fused.
We commence by heating the muffle to the point at which the
tension of the liberated oxygen is from 30 to 40 centims. and
returns to the same when the apparatus has been several times ex-
hausted by means of the Geissler pump. We are then sure that
the composition of the undecomposed oxide of iridium no longer
varies. Then with the cock we lessen the flow of the coal-oil until
the pressure of the oxygen does not exceed a few millims. and
remains constant. This is noted, and the temperature determined.
We then successively augment the flow of the oil in order to
obtain higher temperaiures and stronger tensions of dissociation ;
these are noted when they have become constant. Thus the fol-
lowing numbers were found :—
* This apparatus has been simplified by employing a Sprengel pump,
which permits the thermometric material (nitrogen) contained in the re-
servoir to be taken out and measured as often as we wish, and the tempe-
rature to be calculated.
Intelligence and Miscellaneous Articles. 397.
Temperatures. Dissociation-tensions.
= millim.
822°8 5
1003°3 203°27
1112°0 710-69
1139-0 745:00
If, after a determined temperature and tension have been attained,
oxygen is withdrawn by means of the Geissler pump, the mercury
returns to the initial tension, provided, of course, undecomposed
oxide of iridium remains. ‘The dissociation-tension of this oxide
depends, then, solely on the temperature.
J£ the temperature be raised above 1139", the dissociation-tension
soon exceeding that of the atmosphere, oxygen is rapidly liberated
through the mercury; when this has quite ceased, we exhaust ;
and on taking out the tray containing the oxide from the cooled
tube, we find in it some metallic iridium, consequently reduced by
the mere action of heat.
The tension of oxygen in air being about 152 millims., it follows
from the above-cited numbers that the oxide of iridium decomposes
in the open air at a temperature below 1003°3, and consequently
that at that temperature, or at any higher one, iridium is absolutely
non-oxidizable in the air. .
When we break the porcelain tube in which the oxide was heated,
we observe that it is covered, in the parts which were but little
heated, with a very thin layer of blue oxide of iridium—which de-
monstrates a slight volatility of this oxide at the relatively low
temperatures at which it can exist. Above 1000° volatilization
becomes impossible in our atmosphere, since the oxide of iridium
ceases to exist there and the metal is at least as fixed as platinum.
We have likewise proved this feeble volatility of the oxide of iridium
in other experiments, made with M. Stas.—Comptes Rendus de
l Académie des Sciences, Sept. 23, 1878, tome lxxxvil. pp. 441-445.
ON A UNIVERSAL LAW RESPECTING THE DILATATION OF BODIES.
BY M. LEVY.
Between the specific volume of a body, its temperature, and the
pressure (supposed normal) which it supports, there exists, as is
known, a relation which permits one of these three quantities to be
expressed as a function of the other two—for example, the pressure
as a function of the volume and temperature.
Hitherto (to my knowledge at least) theory has supplied no in-
dication upon the nature of this relation, and nothing permits us to
affirm with certainty that it may not change in some way when we
pass from one substance to another. For every substance the phy-
sicist is condemned to seek it in every particular by experiment,
which, in a manner, necessitates oo? number of observations.
398 Intelligence and Miscellaneous Articles.
I purpose to demonstrate that this relation is far from being pos-
sibly arbitrary—that the pressure supported by any body whatever, so
long as the body does not change its state, can only be a linear fune-
tion of its temperature. In other terms, under a physical form, Jf
any body whatever be heated under a constant volume, the pressure
which it ewerts upon the immovable sides of the enclosure which con-
tains it cannot but increase in rigorously exact proportion to tts tem-
perature.
I say that this proposition is an absolutely rigorous corollary of
the two fundamental propositions of the mechanical theory of heat,
and of the hypothesis that the reciprocal actions of the atoms of
bodies are directed along the lines which join their points of appli-
cation, and depend only on the distances of these points from one
another.
To demonstrate the iaw above enunciated, let dQ be the quantity
of heat necessary in order to modify infinitesimally the volume »,
the pressure p, and tne temperature T of a body without its
changing its state. The first principle of the mechanical theory of
heat gives the classical equation
dQ=dU LAp dye! Jl ee eee
A= - being the thermal equivalent of the work, and U the func-
tion which is often called the internal heat. Let us take v and T
for the independent variables, so that
wwe ah aT + SE dy.
The signification of each of the two terms of the second member is
obvious: the first represents the quantity of heat necessary to pro-
duce an increment dT of the temperature without change of volume;
consequeutly, and since there is no change of state, the second ne-
cessarily represents the quantity of heat equivalent to the work of
the molecular actions during the increase of volume dv. Now, if
we represent by mm'f(r) the amount of the mutual action of two
molecules the masses of which are m and m’, placed at the distance
r the one from the other, this work is represented by an expression
of the form Zmm'f(r)dr, so that we have identically
Smm'f(r)dr= E id du.
The first member not containing the letter T, it is the same with the
second. Therefore ae depends only on the variable v alone; and
consequently U is of the form F(T)+/f(v). Hence this first con-
sequence :—The internal heat of a body cannot be any function of the
specific volume and the temperature of that body ; it can only be the
sum of two functions,—the one, of the volume alone; the other, of ia
temperature alone.
Intelligence and Miscellaneous Articles. 399
This first corollary also results immediately from the statement,
so luminous in its brevity, of the mechanical theory of heat, given
by M. Resal in his Mécanique générale.
We can therefore write
dU =A[T9'(T)dT + Rav],
R being a function of v only, and g'(T) any function of the tempe-
rature.
Observe now that, in virtue of the second general proposition of
the mechanical theory, we have, if T is the absolute temperature
and p denotes what M. Clausius calls the entropy,
dQ=Tdp=T (sf dT 4 dy r).
Introducing these values of dU and dQ into equation (1), we get
T ae — Ag a) | a(t —AR—Ap)tv=0,
which requires that we have separately
du TD) =
du ney ye
TH _AR=Ap=0.
From the first we derive, V being an arbitrary function of the va-
riable v alone,
p=Al o(T)+ | —
V
We thus get this second proposition :—
Whatever the body considered, the quantity called by M. Clausius
the entropy cannot be any function of the volume and the temperature ;
im the same way as the internal heat, the entropy can only be the sum
of two functions,—the one, of the volume alone; the other, of the tem-
perature alone.
Consequently the second of the equations obtained gives
(p-B RO Wia= Vi. int ot roe 4 anode Gon
which establishes the law above enunciated. Such is the necessary
form which connects the pressure, the volume, and the temperature
of any body whatever, R and V being two functions of v only.
We said, at the commencement, that theory had not hitherto
supplied anv certain and general indication like that which is in
question here. On this subject we must make one remark. M.
Hirn, in the last edition of his Exposition de la Théorie mécanique
de la chaleur, very judiciously divides that theory into two branches :
in the first he develops the rigorous consequences of the two funda-
mental propositions; in the second he states a great number of
400 Intelligence and Miscellaneous Articles.
philosophical views and intuitive results. In the second part, par-
ticularly, M. Hirn points out how one might, in his opinion, render
the laws of Mariotte and Gay-Lussac applicable to all bodies, on
condition of adjoining to the pressure », which enters into them, a
fictitious pressure R equivalent to what he calls the swm of all the
molecular actions, which would not be dependent on nate volume.
He thus arrives at the formula
(p+R) 7 =K= constant,
coinciding with the laws of Mariotte and Gay-Lussac for R=0.
It will be seen that this formula and our (A) would be identical
if it were admitted that, for all bodies, the function V, introduced
by our analysis, follows a simple law of proportionality. It is very
remarkable that analysis thus confirms, not in whole, but at least
in part, the results to which M. Hirn was led by the profound me-
ditations developed by him in what he calls the second part of ther-
modynamics, the part which might be named philosophic and spe-
culative. Our law (A), provided the fundamental hypothesis of
molecular mechanics be admitted, must evidently be ranged in the
first, the rigorous part.— Comptes Rendus de [Académie des Sciences,
Sept. 23, 1878, tome Ixxxvii. pp. 449-452.
ON DIFFUSION. .AS A MEANS FOR CONVERTING NORMAL-TEMPE=
RATURE HEAT INTO WORK.
To the Editors of the Philosophical Magazine and Journal.
GENTLEMEN,
In the Philosophical Magazine for September last is a translation
of a paper* by Professor Clausius, replying to an article of mine on
the subject of the work to be derived at the expense of normal-tem-
perature heat through diffusiont. After expressing his agreement
with the general principle involved, Professor Clausius states, “only
on one point I think I must express a view different from his.”
Will you allow me to express my thanks to Professor Clausius for
his kindly criticism, and, in justice to myself, to point out that I
had already seen my mistake and retracted itz.
I am, Gentlemen,
Yours faithfully
London, October 1878. S. TotvER PRESTON.
* Wiedemann’s Annalen, July 1878, p. 341.
1 ‘Nature,’ Nov. 8, 1877, p. 31; and Jan, 10, 1878, p. 202.
if ‘Nature,’ May 23, 1878, p- 92,
THE
LONDON, EDINBURGH, ann DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
et <oe—____——_-
[FIFTH SERIES.]
DECEMBER 1878.
LIII. On the Mechanical Theory of Crookes’s (or Polarization)
Stress in Gases. By G. JoHNSTONE Sroney, 1.4., F.BS.,
&c., Secretary to the Royal Dublin Society*.
Introduction.
a papers will be found in the first volume of the fifth
series of the Philosophical Magazine (March and April
1876), in which I endeavoured to explain the force that Mr.
Crookes had detected within vacuum-chambers, by pointing
out that when heat passes across the residual gas, the mole-
cules of the gas that tend respectively towards the heater and
towards the cooler must interpenetrate one another in a greater
degree than they would if the gas were in its ordinary or
unpolarized condition, and that this behaviour will render
the stresses within the gas unequal, causing the stress to be
greatest in the direction in which the augmented interpene-
tration takes place.
When writing the foregoing papers, and afterwards when
writing a paper on the transfer of heat which accompanies
the phenomenon, I was under the mistaken impression that
the flow of heat between a heater and cooler in fixed positions,
and at constant temperatures, will become greater if the num-
ber of gaseous molecules that intervene is reduced below the
number required for the transfer of heat by the laws of “ con-
* From the ‘Scientific Transactions of the Royal Dublin Society’ for
the year 1878. Read February 18, 1878. Communicated by the Author.
Phil. Mag. 8. 5. Vol. 6. No. 89. Dee, 1878. 2D
402. Mr. G. J. Stoney on Polarization Stress in Gases.
duction’’*; and for this supposed increased flow of heat I
suggested the name penetration. It has recently been pointed
out by Dr. Schuster (‘ Nature,’ vol. xvii. p. 148) that experi-
ments have been made which show that the flow of heat dimi-
nishes instead of increasing when the limit for “ conduction ”
is passed. It thus appears that what I have called penetration
is always feebler than conduction, and is to be sought, in the
figures representing De la Provostaye and Desains’s experi-
ments, in those portions of the curves which slope steeply
downwards. Accordingly my paper on Penetration (Phil.
Mag. December 1877), and especially that part of it in which
I apply the theory to experiment, requires considerable mo-
dification, and some of the statements I made in my earlier
papers on Crookes’s force need amendment. Although the
corrections that are required do not affect any material part
of the theory of unequal stresses within polarized gas, it has
appeared desirable to resume the subject and present the
theory freed from the error that has been pointed out. In
doing this I have taken the opportunity of introducing the
conception of the reflecting tube, which greatly facilitates the
inquiry into the mechanical effect of the interpenetration ; and
T have also availed myself of the admirable method of treating
the problem, described by Mr. George F. Fitzgerald in
‘ Nature,’ vol. xvi. p. 200, to obtain a complete expression for
the stress, and to show that my theory is not at variance
with results established by Professor Clausius, as has been
asserted by Professor Osborne Reynolds in ‘ Nature,’ vol. xvii.
p- 122.
Part I.— Treatment of the Problem by General Mechanical
: Considerations. :
1. If a drop of water or other volatile liquid is allowed
to fall into a smooth and sufficiently hot metal dish, it con-
tinues a liquid drop instead of spreading out or flashing off
into vapour, and it exhibits an appearance of great mobility.
The drop is then in what has been called the “ spheroidal
state.” Now, when a drop of liquid is so situated a chink
may be observed between it and the hot surface beneath; so
that the drop does not rest directly upon the metal, but is in
reality floating upon a layer of vapour. We further learn
* It is known that gases feebly conduct heat by diffusion, and that
the amount of heat which passes in this way between a heater and cooler
is independent of the density of the intervening gas, provided that the
density of the gas does not fall below a certain limit. The question
that presented itself was as to what happens below that limit.
Mr. G. J. Stoney on Polarization Stress in Gases. 4038
from these observations that after the brief interval of adjust-
ment is over the layer of vapour presses upwards and down-
wards more than it presses sideways ; for the pressure side-
ways must equal the pressure of the atmosphere so soon as the
adjustment is over, otherwise air would still be entering or
leaving the chink, whereas the pressure upwards must exceed
the pressure of the atmosphere by an amount able to support
the drop. It is my object to explain how this difference of
pressures, this Crookes’s pressure as it has been called, comes
into existence.
2. The thermal conditions of the problem are easily traced,
but need not detain us here. It is enough to state that
they show the metal dish and drop to be at different tempera-
tures, so that they are a heater and cooler on either side of
the layer of vapour. Hxperiment further shows that the
heater and cooler may be either one a liquid and one a solid,
as in the case already considered, or both liquids, or both
solid, and that the intervening layer may be either vapour or
permanent gas. This last important fact has been established
by Mr. Richard Moss in an admirable series of experiments
lately made by him to test the theory of the present communi-
cation (see ‘ Scientific Proceedings of the Royal Dublin So-
ciety,’ vol. i. p. 89). Itis also found to be immaterial whether
the heater or cooler is uppermost, or whether they face one
another sideways.
Other facts of importance have been elicited by the experi-
ments at low tensions, of which the most significant are:—that
when the heater and cooler are maintained at given tempera-
tures the Crookes’s stress between them may be increased
either by bringing the heater and cooler closer together, or by
attenuating the gas until a certain point is reached which
varies from one gas to another; and that when that point is
passed, the force decreases and apparently without limit.
3. We may express these facts in a very convenient form for
our present purpose if the heater and cooler are extensive flat
parallel surfaces at fixed temperatures. Conceive two exactly
similar patches on the heater and cooler directly opposite to
each other, and each occupying a unit of surface, and con-
sider that portion of space which lies between these. Then
the observations show that there is one definite quantity of
the gas to be left in the volume so marked out, if we wish to
produce the strongest Crookes’s stress. And, further, by com-
paring Mr. Crookes’s experiments on the mechanical action
with those of De la Provostaye and Desains on the flow of
heat, we learn another important fact, viz. that the maximum
stress occurs when the quantity of gas is too little to admit of
D 2
404 Mr. G. J. Stoney on Polarization Stress in Gases.
the passage of heat under the laws of the conduction of heat
in gases. Now these facts also follow as consequences from
the theory advanced by the author, and therefore become con-
firmations of it.
4, This theory seeks to account for Crookes’s force by show-
ing that a layer of gas placed between a heater and. cooler is
in a polarized condition of sucha kind that the stresses within
the gas are different in different directions. Gas is polarized
whenever the molecules within a spherical element of volume
are moving towards different quarters with numbers or velo-
cities that are not distributed alike in all directions, the velo-
cities being measured from the centre of mass of these mole-
cules. This definition excludes the case of mere wind, which
is to be regarded as unpolarized gas travelling forward in a
certain direction; but it includes the case of gas across which
heat is making its way, which is the case with which we have
here to deal.
5. Let us recur to the simple instance of a heater and cooler
with extensive flat parallel surfaces maintained at constant
temperatures, and with gas between them freed from the
action of gravity, and which has had time to adjust itself to
its position. Gas so circumstanced will become stationary
in the ordinary sense of the word; 7. e., though in active
molecular motion, it will have no currents like convection-
currents or wind passing through it*. We have now to show
that the stress across such a layer will be greater than the
stress sideways.
6. Imagine a unit of suface marked out on either heater
or cooler, and let perpendiculars to the surface be raised from
the boundary of this enclosure. These will trace out a straight
tube extending between the heater and cooler, and closed at
the ends by equal patches of the heater and cooler. These we
may call the pistons of the tube. The molecules which strike
the pistons are returned by them, and with altered velocity
whenever the pistons are at different temperatures ; but mole-
cules pass without hindrance through the sides of the tube.
Now it is evident that, if the molecules passing through an
element of the side of the tube are considered, those pass-
ing out in.a unit of time will be an exact counterpart of
those passing in, in such a sense that the state of the gas
would not be disturbed by making the sides of the tube im-
* There will be currents close to the boundary of the heater and
cooler; but these are secondary phenomena caused by, and in no
degree the cause of, Crookes’s stress. They will not be appreciable
within the layer at any considerable distance from the edge; and they
may be avoided by giving to the opposed surfaces of the heater and
cooler the form of concentric spheres.
Mr. G. J. Stoney on Polarization Stress in Gases. 405
pervious to molecules, provided that they were made at the
same time perfect reflectors of-molecules. By a reflector of
molecules is to be understood a surface endowed with the pro-
perty of throwing off any molecules that impinge upon it with
unabated speed, and at an angle of reflection which lies in the
same plane as the angle of incidence, and is equal toit. The
reflected molecules will affect the state of the gas within the
tube exactly in the same way as the molecules passing in from
outside had done before. We have now a portion of gas com-
pletely shut up inside a tube with sides that are perfect reflec-
tors of mojecules, and closed at the ends by pistons that are
patches of the heater and cooler, and which therefore scatter
such molecules as reach them; and we know that the beha-
viour of this gas will be the same as that of the corresponding
portion of the Crookes’s layer. We may call such a tube
a unit reflecting tube.
7. Let the pistons of such a tube be kept at the tempera-
tures T, and T, and let gas be introduced into it. After a
brief period of adjustment the gas will become stationary; 1. e.,
if a plane forming a cross section of the tube be considered,
the molecular motions are such that the same number of mole-
cules pass forwards as backwards through this plane per
second. But they will pass it with unequal average veloci-
ties, because the vis viva of those crossing it towards the cooler
must exceed the vis viva of those crossing it towards the heater
by an amount bearing a known ratio to the quantity of heat
advancing. Hence the gas is polarized, the molecular motions
being swifter when they are directed forward or towards the
cooler, and slower when directed backwards.
8. Suppose that we begin with dense gas and gradually
exhaust, and let us consider the succession of events that will
arise as the exhaustion proceeds, 7. e. when n, the number of
molecules in the unit tube, is progressively diminished. It is
known that the flow of heat cannot conform to the laws of
“conduction ”’ unless the number of molecules exceeds a cer-
tain limit which we may call N,—N depending upon the de-
scription of gas that is present, and upon the temperatures T,
and T. of the pistons which close the unit tube. We must
therefore divide the exhaustion into two periods, one lasting
while the number of molecules in the tube exceeds N, and
the other during the rest of the exhaustion. Throughout the
first period the flow of heat follows the known laws of con-
duction, and therefore remains constant. Hence, during this
part of the exhaustion the polarization of the gas (which may
be measured by ay v being the average velocity at any point
406 Mr. G. J. Stoney on Polarization Stress in Gases.
of the layer, and dv the average difference of the velocities
forwards and backwards at that station) is so rapidly on the
increase as quite to compensate in Kpv*dv (the expression for
the flow of heat, p being the density at the station, and K a
constant) for the diminishing density. During the second
period, 7. e. when the molecules have become fewer than N,
the polarization is still on the increase, but not so rapidly
as before, and at the same time the flow of heat decreases to
zero; for while p tends to zero as the exhaustion proceeds,
the polarization does not tend to infinity, but to a limit, viz.
7 where v, and vz are the velocities corresponding to T,
VzV2
and T,, the temperatures of the pistons. Now, when gas is po-
larized with this kind of polarization within a tube the sides
of which reflect the molecules, we can find limits between
which its thermal and mechanical properties must lie.
9. Before proceeding to determine these limits, it will be
well to guard ourselves against making mistakes by passing
under review the orders of the several magnitudes with
which we are dealing in this inquiry. No accurate mea-
sures appear yet to have been made of the thickness of the
chinks of air or vapour on which spheroidal drops rest. But
from approximate measures, some of which were made by Mr.
Fitzgerald and some by myself, I think it may be inferred
that this thickness is somewhere about the thickness of a sheet
of paper (2. e. about a fourth-metre or the tenth of a milli-
metre) when a spheroidal drop of the density of water, at a
temperature of 10° C. and 5 or 6 millims. in diameter, floats
over a surface of liquid which is about 10° warmer. We
further know that in this case the Crookes’s pressure, as it
supports the weight of this drop, must be about the two-
thousandth part of an atmosphere. These determinations are
very rude; but they at all events tell us what kind of magni-
tude we are dealing with, and therefore suffice for our pre-
sent purpose. They show that we shall not be far wrong in
assuming definitively that the phenomenon presented by ex-
periment which we have to explain is, that the stress across a
stratum of air will be s,455 part of the stress at right angles
to that direction, if this stratum occupies the space between
a heater and cooler at temperatures of 10° and 20° C., if,
moreover, this interval is a fourth-metre (a metre divided by
10*), and if the atmosphere has free access to the stratum of
air atitsedges. Let us now imagine a reflecting tube, such
as is described above, to be placed across this stratum. It
will therefore be a fourth-metre long ; and we may assign to it
Mr. G. J. Stoney on Polarization Stress in Gases. 407
any width we please. Let us take a width equal to the diameter
of the smallest object that can be seen with a microscope,
which is about 2°5 seventh-metres, or the 100,000th part
of an inch. We have now to compare the dimensions of
this tube with the number and motions of the molecules in-
cluded within it. The number of molecules in a cubic milli-
metre of atmospheric air is about a unit-eighteen (10"*). (See
Phil. Mag. August 1868.) Whence the average interval be-
tween them is about a ninth-metre. This is the 100,000th
part of the length of our tiny tube and the 250th part of its
breadth. Hence the tube will contain a vast number of mole-
cules, some such number as five thousand millions. Again,
the average striking-distance (7. e. the average length of path
between the encounters) of the molecules is about the 1500th
part of the length of the tube, or the fourth part of its breadth.
There is, therefore, abundant room within the tube, small as
it is, for a vast number of molecules and for much jostling
amongst them. The temperatures with which we are dealing
are such that the average velocity with which the molecules
of air dash about may be taken as 500 metres per second;
and the molecules meet with so many encounters, that the di-
rection of the path of each is changed somewhere about a
unit-ten of times (10,000,000,000) every second. To com-
plete the picture, we must remember that each molecule is in
a state of vigorous internal motion as well as travelling about
among its fellows, and that when an encounter takes place,
the energy which passes from one molecule to another is
employed in changing both those kinds of motion, and pos-
sibly (but not probably) another part becomes potential
energy, 1. €. energy expended in altering the configuration of
the parts of the molecule, or the position of its parts with re-
ference to the ether. The motions which go on within the
molecules are what give rise to the linear spectra of gases, and
are therefore those motions of the gas that act on the eether,
and are in turn partly controlled by it*. They are recurring
motions which, at least in some cases, are resolvable either
* May we not look, with some prospect of success, to the control which
is exercised by the ether on the internal motions of the molecule for the
explanation of the number of ‘‘ degrees of freedom ” of a molecule, which
(on the supposition that there is no potential energy) is in most gases 5
(see Watson’s ‘ Kinetic Theory of Gases,’ p. 39). The number 5 ap-
pears to indicate that the motions within the molecules are trammelled,
as here suggested. This view is, moreover, supported by the fact that
light is emitted by the gas, which could not be the case unless vast num-
bers of molecules moved in unison with one another; and the most pro-
bable account of this appears to be that they are all trammelled in the
same way by their common relation to the ether.
408 Mr. G. J. Stoney on Polarization Stress in Gases.
into harmonics like the vibrations of a string, or else into
guasi-harmonics not to be distinguished from harmonies by
observation (see Donkin’s ‘Acousties,’ § 194), like the trans-
verse vibrations of an elastic rod—probably the former. On
the more probable supposition that they are true harmonies,
the periodic times have been determined with great precision
in some cases, notably in the cases of a motion within the
molecules of hydrogen, which gives rise to three of its spec-
tral lines, and a motion within the molecules of chlorochromic
anhydride, which gives rise to 105 of its spectral lines. In
hydrogen the motion is repeated as often as 2,280,000,000,000
times each second in every molecule, and in the vapour of
chlorochromic anhydride rather more than 800,000,000,000
times*. Such are the periodic times on the supposition that
the motions are resolvable into true harmonics ; and whether
the fact be that the components of the motions are harmonics
or quasi-harmonics, their periodic times are at all events quan-
tities of this order. The general presumption, therefore, is
that the periodic times within the molecules of other gases are
also quantities of this order. But it is not necessary for our
present purpose to establish this. The only circumstance re-
lating to these inner motions with which we are here directly
concerned is that the energy which is transferred from mole-
cule to molecule is employed partly in altering the velocities
with which the molecules travel about, and partly in altering
these internal motions and (perhaps) collocations, and that
the proportion of the energy which is employed in the former
way bears on the average a numerical ratio to the whole energy
transferred which can be determined experimentally (see Max-
well’s ‘Theory of Heat,’ p. 299) and is denoted in the sequel
1
by 3
10. We now proceed to determine limits between which
the thermal and mechanical properties of the gas must lie.
For this purpose let us imagine a tube of the kind described
* The periodic times deduced from the observations are respectively
a—, 7 being the time that light takes to advance 1 millim.
A
76-18 °°” 2-70
in vacuo. (See Phil. Mag. April 1871, p. 295, and July 1871, p. 45. In
the former paper read 0:018127714 for 0:13127714.) The first of these
determinations was made by the present author, and the second by
the present author in conjunction with Professor Emerson Reynolds, of
Dublin; but, before either of these determinations were made, Professor
Clifton, of Oxford, had mentioned at the Exeter Meeting of the British
Association in 1869 that he had found two of the hydrogen lines (pro-
bably C and h) to be related harmonically. I am not aware that any re-
cord of this important observation has been published. .
Mr. G. J. Stoney on Polarization Stress in Gases. 409
above, with perfectly reflecting sides. Such a tube exerts no
friction on gas flowing along it, nor does it occasion any loss
of energy. Let it contain a large number of gaseous mole-
cules between pistons at temperatures T, and T,. And let us
further suppose that the molecules of the gas, as they leave
either piston, acquire the property of not interfering with
or being obstructed by the molecules that have last left the
other. This imaginary state of the gas would re sult in
two streams constantly travelling in opposite directions along
the tube. Let us follow one of these streams. It starts
from its piston with a mean of the squares of the veloci-
ties of its molecules v? determined by the temperature of the
piston, and in numbers per unit of time represented by p/w’,
p’ being the density of the stream and wu’ the average of the
normal components of the velocities at starting. Then, how-
ever the velocities and directions may have been distributed
at starting, the jostling of the molecules of this stream among
one another will reduce the stream as it advances to the condi-
tion of unpolarized gas travelling along the tube with the velo-
city u’. The molecules are henceforward moving with veloci-
ties among themselves which, measured from their advancing
centre of mass, have an average square of the velocities w’
which is given by the equation
: BU ther OU Gr bata cra fools)
8 being the known numerical coefficient representing the
ratio of the total energy of the gas to its “energy of agita-
tion.” This equation is only the symbolical expression of the
fact that no energy has entered or left the gas. The stream
moving in the opposite direction furnishes the similar equa-
tion
Bur wee Bul A Se ast: OR
And since the numbers of molecules reaching and receding
from each piston are equal, we have the further equation
Pat — PA a BS, easy 3 re
We have also
Bop Apia tie wx) 4 Fase ssn, 2S RED
Of the quantities which enter into these equations, p,
the density of the gas, is known, and x, vt», wu’, and wv” are
known functions of T, and T,, the temperatures of the pistons.
Hence these equations enable us to determine the remaining
quantities p’, p’’, w’, and w”.
Now, under the conditions that have been laid down, it is:
410 Mr. G. J. Stoney on Polarization Stress in Gases.
manifest that the stress * of the gas sideways would be
i LG ar oe ee 2k ws ae
while the stress spe the tube would be
P r= tp'w? +40’ ‘wl + plul® + pu Mee ; ; (6)
which accordingly exceeds the transverse stress be ;
ep bp. a he a rr
This, therefore, would be the Crookes’s stress in the case
supposed. It is a very large quantity, since w’ and w’’ would
be large if the streams could penetrate one another without
obstruction. The flow of heat, which we will designate by
the symbol G, would also be very large in the case supposed.
An expression for it can be easily found, but is not required
for our present purpose.
11. The other limit is one that really occurs. It arises
when the molecules coming up to either piston and those re-
tiring from it form complementary parts, such that their co-
existence in the same space constitutes stationary unpolarized
gas. This happens only when the two pistons are at the same
temperature. In this case it is manifest that no heat is con-
veyed by the gas, and that the gas exerts the same pressure
in all directions. In symbolical language,
Eral0).
ie
G being, as before, the symbol for the flow of heat, and « for
the Crookes’s stress. This case may be described as one in
which the streams described in the last section experience such
effectual opposition from each other that the speed with which
they advance is zero. Tor it is evident that the gas at any
station within the tube may, without any change of its pro-
perties, be described as consisting of two equal portions of
stationary unpolarized gas coexisting in the same space.
12. In all other cases the pistons that close the ends of the
unit tube are at different temperatures, and the gas between
any two cross sections of the tube is polarized. Let us con-
sider a slice between two such sections, which are sufficiently
close to entitle us to regard the included gas as being through-
out in nearly the same state. The actual condition of the gas
* The term “stress” is here applied to the presswre within the gas in
any direction, viewed in conjunction with the equal pressure in the opposite
direction. It is what Clausius has called “the positive momentum,’
meaning thereby the sum of the components of the momenta of the mole-
cules resolved in a given direction, and all estimated as positive, whether
of molecules that move forward or backward.
Mr. G. J. Stoney on Polarization Stress in Gases. 411
within the slice may evidently be conceived of as arising from
the coexistence of two streams travelling in opposite directions
along the tube, and each consisting of gas which is less pola-
rized (2. e. which deviates less from the condition of ordinary
gas) than the gas that results from their coexistence. Hach
stream is exposed within the slice to the mutual jostling of its
own molecules; and it is also attacked by molecules of the
other stream. The mutual jostling of its own molecules tends,
as explained in section 10, both to maintain the onward velo-
city of the stream and to reduce the gas of which the stream
consists still more towards the condition of unpolarized gas.
These encounters then, taken by themselves, tend to bring
about the state of the gas described in section 10. But the
interference of the two streams with one another counteracts
this. This interference modifies the effect of the encounters
within the streams, but it is incompetent to annul it; for
the two streams do not by their mere coexistence constitute
stationary unpolarized gas, and hence they would need time
before they could by their action upon one another reduce the
gas to this condition. It is, however, plain that whatever
action they exert is a step towards bringing about this condi-
tion; for the gas would become depolarized if the cross sec-
tions which bound the slice could be rendered impervious both
toe energy and molecules, so as to leave the two streams time
to act fully on one another. In reality, however, sufficient
time is not allowed to them, because the streams pass one ano-
ther, and the struggle is continually renewed within the slice
by fresh portions of the streams which come up in the same
state as those that had been obliged to pass on. These fresh
portions keep in the same state because a sufficient supply of
swift molecules is without intermission being thrown back
along the tube from one end by the heater, and a correspond-
ing supply of slow molecules from the other end by the
cooler.
13. The two streams, however, though not annulled, are
different from what they would have been if they had been
without influence upon one another. They do not consist of
the same molecules from one instant to another; for there is
such a perpetual shifting of molecules between them, owing
to the vast number of encounters that take place, that no one
molecule is likely toremain long in one stream. Again, after
an encounter between molecules of the two streams, both of
the colliding molecules will sometimes join the same stream ;
and it will most frequently happen that the stream so joined
is the hotter and swifter stream. Hence the stream from the
heater to the cooler receives an accession to the number of its
412 Mr. G. J. Stoney on Polarization Stress in Gases.
molecules as it travels forward, while the reverse effect is pro-
duced upon the stream making its way in the opposite direc-
tion. On both accounts there will be gradients of density
and temperature along the tube between the heater and cooler.
Again, every encounter between molecules of the two streams
diminishes the momentum of one or both streams; but, as we
have seen, the effect so produced does not go the length of
reducing the streams to rest.
14. Hence we must bear in mind the gradients of tempera-
ture and density along the two streams, and the continual |
fluctuation of the molecules that are to be referred to them, if
we want to regard the condition of the gas throughout the
whole length of the tube as arising out of the coexistence of
two streams of gas less polarized than itself. But with these
precautions the hypothesis may be made; and accordingly the
condition of the gas at every cross section of the tube ts tnter-
mediate between a structure represented by the coexistence of the
two streams of unpolarized gas travelling simultaneously in op-
posite directions, which the encounters within each stream tend
to develop, and the condition of stationary unpolarized gas,
towards which the mutual interference of the two streams mo-
difies the structure. Hence there is some polarization stress
and some flow of heat all along the tube, though of less amount
than in the case considered in section 10. We may still em-
ploy equation (7) as the expression for the polarization stress,
if we use for p’ and p” the densities of the streams at some
particular cross section of the tube, and if wu’ and w’’ are modi-
fied into what they become as the interference of the two
streams with one another is increased. It is not necessary
to ascertain what this modification will be: it is enough for
our purpose to know that wu’ and wv” will be some functions of
V’/—V” (where V” and V’” are the averages of the cubes of
the velocities of the molecules that pass forwards and back-
wards respectively through the cross section), and that they
will be proportional to this quantity when all three are small.
15. We may base upon this circumstance an investigation
into the laws of the phenomenon when the difference between
the temperatures of the heater and cooler is small compared
with their absolute temperatures. This case is of importance
because it is that which most frequently occurs, and is the
only one in reference to which accurate experiments have
been made. In this case p’ and p” will each be nearly 4p,
using p for the density of the gas at the position in the tube
which we are considering ; and V’—V”, being small, may be
appropriately represented by 6V. Then, remembering that w’
and w’’ are proportional to 6V, we obtain from equation (7)
Mr. G. J. Stoney on Polarization Stress in Gases. 413
the following expression for the polarization stress,
1 Op (ON Jere eee Th Ce Cah
where the symbol « means approximately varies as. Moreover
it can be shown* from various considerations that the flow of
heat
G ai pV OV,
or, by a simple transformation,
Gia p ov ee
T being the temperature measured from absolute zero. Hence
from the approximate equations (8) and (9) we obtain the
equation
2
Oe A? ° . . ° . . . . (A)
which contains only quantities of which we already know
enough to make use of them. Equation (A) may be thrown
into a still more convenient form by writing P for the tension
of the surrounding atmosphere of gas, which is nearly the
same as the stress which the gas at the station we are consi-
* One of the ways in which this may be proved is the following :—
Clausius has shown (Phil. Mag. xxii. p. 514) that
a eos
G=16p)" 1Fpdu,
whence
=1 p(L'V'?—I'"V"'),
where I’ and V* are the average values of I and V* under the integral
for positive values of p (2. e. for molecules traversing the section of the
tube towards the cooler), and I” and V’”* are the corresponding averages
for negative values of p, 7. e. for molecules traversing the section of the
tube in the opposite direction.
Now it is evident that these quantities are capable of expansion in the
following form :—
(8V)?
; OV
I =1+4, 5, +A, v2 foals ;
it éV
I =1TBiz-t+:.:)
. 5V
1a 2 NTS as aaa
Vo=V(140, 5 +...),
Mr: 5V
ve=ve(1+ D, te ),
in which V? is the average of the values of V® for all directions, Whence
G=169(A,—B,+ C0, —D,)V*6V
+ terms containing higher powers of dV.
414
dering would exert if depolarized.
nearly as pT, whence
G?
KO PT °
|
{
I
t
'
'
{
\
\
\
\
| i
formule, let us plot down on a diagram the value of «, the
Hen
x
polarization stress, for various tensions of gas between a heater
and cooler at constant temperatures and at a fixed distance
asunder.
Let the abscissas of the figure represent the tensions of the
gas. Then the curve Obcd, the ordinates of which represent
the flow of heat, is known. ‘The part representing conduction
is the parallel line ¢d; and Obc represents the outflow of heat
by that modified conduction which may be called penetration,
which occurs when the exhaustion has proceeded so far that
the number of molecules in a unit tube is less than N (see
16. As an example of the application of these approximate
ae
A
Mr. G. J. Stoney on Polarization Stress in Gases.
P will therefore vary
(B)
Mr. G. J. Stoney on Polarization Stress in Gases. 415
above, section 8). The curve Obed is therefore known; and
if by equation (B) we plot down from it the values of « (the
polarization stress), we find them approximately represented by
the ordinates of a curve of the form Oace, the portion to the
right of c being coincident with an equilateral hyperbola,
while to the left of ¢ the ordinates fall short of the hyperbola,
rising to a maximum and then falling off to zero. The posi-
tion of this maximum cannot be obtained with certainty,
because equation (B) is less to be depended on at very low
tensions. Bearing this in mind, the accordance of the theoretic
values with those determined experimentally by Mr. Crookes
and Mr. Moss is satisfactory.
17. From equation (B) we may obtain another useful for-
mula which expresses the approximate law according to which
polarization stress depends upon the interval between heater
and cooler, whenever this interval exceeds the limit determined
by the condition that there shall be a sufficient number of mo-
lecules in the unit tube to allow heat to pass by conduction.
In this case we know the equation of the gradient of tem-
perature (see Clausius’ equation (54), Phil. Mag. vol. xxiii.
p- 527), and that it is approximately represented by a straight
line when, as we have assumed, 7 is small, using AT for the
difference between the temperatures of the heater and cooler.
Hence, and from Clausius’ equation (56), it appears that
Go (ALE
Be og RS te
using X for the distance between the heater and cooler.
Introducing this value into equation (B), we find
(AT)’
ORS geet ah ae 2 Pe je iy h CC)
a result which agrees satisfactorily with Mr. Moss’s experi-
ments.
18. If we use X, for that interval between heater and cooler
which would make the number of molecules in the unit tube
equal to N, and if we use xy for the corresponding value of the
Crookes’s stress, then equation (C), and the obvious equation
Xp x sah furnish us with the following :—
fp eGR EY oF (2) POR S VERE
Now equation (C) enables us to plot down a part of the curve
representing the relation between « and X when AT and P
are kept constant; and although equation (C) cannot be relied
upon when X is less than Xo, it is nevertheless evident that
A416 Mr. G. J. Stoney on Polarization Stress in Gases.
the shape of the remainder of the curve must be one which is
independent of the particular value of P which we have used.
Hence, if « is the maximum value of « in that curve, it follows
that « and x) must remain proportional to one another when
P is.changed. Hence equation (10) furnishes
KeP. (AD. LD
We learn from this inquiry that the maximum polarization
stress which can be elicited between a given heater and cooler
by varying the distance between them will, if the tension of
the gas is altered, change in the same ratio as that tension, —
and that it will occur at intervals between heater and cooler
which vary inversely as that tension. ‘This fully accounts for
the powerful Crookes’s force which presents itself in experi-
ments at ordinary atmospheric tensions as compared with the
feeble force exhibited in radiometers. It accounts also for
the very short interval at which the heater and cooler must be
placed when the gas is dense.
Part Il. Investigation of a Complete Expression for the Stress.
19. As it has been asserted (‘ Nature,’ vol. xvii. p. 122) that
the views of the present writer are at variance with the results
established by previous investigators, I will proceed to show
that the theory of unequal stresses which I have put forward
is, on the contrary, the necessary sequel of them. I will show
this by continuing the method of investigation commenced by
Professor Clausius in his memoir on “ the Conduction of Heat
by Gases,” in the way which was pointed out by Mr. George
I’. Fitzgerald in ‘ Nature,’ vol. xvii. p. 200. This inquiry will
have the further advantage of furnishing a complete expression
for Crookes’s stress. :
Clausius (Phil. Mag. vol. xxiii. p. 514) has given the
following expression for the stress across a layer of gas con-
ducting heat, in the direction normal to a heater and cooler,
the opposed surfaces of which are parallel and extensive,
P,=4 pv, + Xe’,
e being a small quantity of the same order as the striking-
distance of the molecules, and X, being a coefficient of which
Clausius did not compute the value, as the scope of his inves-
tigation only required him to go as far as the first order of
small quantities. Now Mr. Fitzgerald, in his letter to ‘ Nature,’
and more fully in conversation with the writer, pointed out
that if an expression for P,, the stress parallel to the surfaces
of the heater and cooler, were calculated by a method similar
to Clausius’, the coefficient of e? in this expression could not
Mr. G. J. Stoney on Polarization Stress in Gases. A417
be the same as Xj, and that hence there must be a difference
between the two stresses—in other words, a polarization stress.
20. Clausius (loc. cit.) gives the following general expres-
sion for the normal stress—
+1
P.=t0| DM ae et ee)
ail
_ where I is the coefficient expressing the proportion of mole-
cules travelling in the directions which make an angle with
the normal or axis of x of which the cosine is #, and where
V? is the mean of the squares of their velocities.
Now if, employing a process exactly similar to that pursued
by Clausius on pp. 512 and 513 of his memoir, we use N for
the number of molecules in a unit of volume, then will Ndr
’ be the number of molecules within a slice of unit area and
thickness dr, which we may suppose to be placed perpendicular
to the vector r. Then
= Nlidrde
Ag
will be the number of molecules moving within the slice in
directions which lie within an element of solid angle do, which
we will suppose makes the angle w with the vector 7; so that
the time they take to cross the slice will be
dr.secyr
Remon
V being their velocity. Hence the number traversing the
slice in the specified direction within a unit of time is
~ - NIV cos bv. deo.
Multiplying this by mV cos we get the resolved part of
their momenta along 7. The sum of all such components of
the momenta, all estimated as positive, is P,, the stress in the
direction of 7. Whence, and writing p for mN, we find
a EA IV? cos? wdo,
the integration being extended over the unit sphere.
Hence the stresses in the directions of three rectangular
axes are ay
P,= 2. ((im cos’ ado,
An
Spb ( LV? cos? Bde
I Sor ;
sew Sd Wenn 4
pak ((n cos* ydo,
Phil. Mag. 8. 5. Vol. 6. No. 89. Dec. 1878. 2K
418 Mr. G. J. Stoney on Polarization Stress in Gases.
«, B, y being the director angles of the element of solid angle
do. Introducing polar coordinates, we have
da= sin 0 dé d¢,
cos a= cos 0,
cos B= sin @ cos d,
cos y= sin @sin ¢,
by which the expressions for the stresses become
fo
Qr (‘rT
p ( 2 20.: 7}
reclret 8 vee cos’ @ sin 6 dé dd,
2a (*3 |
1 P x79 °
2 = al { IV’ sin’ @cos*pd0dd, r. . (B)
27 { 7
yp —> : |
Py ae ( ( IV’ sin* @ sin’ ¢ dO dg. |
e 0 e 0
These are the most general expressions for the stresses in
three rectangular directions within gas polarized in any way ;
and they will be the only stresses between portions of the gas
separated by planes parallel to the planes yz, zz, zy, if the axes
are so chosen that there are no moments round them arising
from the molecular encounters*.
21. This condition is easily secured in the case which we are
investigating, viz. when heat is making its way between a
heater and cooler that are parallel to one another, and of large
extent compared with the interval between them, since the
polarization of the intervening gas will evidently be disposed
symmetrically round the direction in which the heat is travel-
ling. Hence, taking this direction as our axis of «, there can
be no moments round this axis, or round any axis at right
angles to it. The stresses (EH), therefore, are the only ones to
be taken into account. Moreover we can integrate equations
(E) at once by ¢, since IV? is, in this simple case, a function
* Equations (E) cannot be integrated unless IV? is given as a function
of @ and @, 7. e. unless the law of polarization in the gas is known. But
they show that in general the stresses im different directions are unequal,
which is here what is chiefly insisted on. al,
When the gas is unpolarized, I becomes equal to unity, and V? is in-
dependent of the direction, and may therefore be put outside the integrals.
In this case all three equations concur in giving the well-known expres-
sion for the stress in unpolarized gas, viz. 3 pV’.
Mr. G. J. Stoney on Polarization Stress in Gases. 419
of @ only. Doing this, and writing w for cos @, we find
oe
P= - ‘Yo IV2wdpy,
Sa ¥ (F)
1
P,=P.= a _ IV =p\du,
whence, since «, the polarization stress, =P,—P,, we have
finally
oS eee
c= : G2 Se 1 dice a)
—1
This, then, is the complete mathematical expression for
Crookes’s stress. It could be integrated if we knew the law
of the polarization of the gas; for then IV” would be a known
function of p.
22. Clausius, in investigating the diffusion of heat across
the layer of gas, makes the assumption (Phil. Mag. vol. xxii.
pp- 425 and 524) that the numbers and velocities of the mole-
cules “‘ emitted’ by a thin stratum of the gas (i. e. that have
passed out of the stratum after having encountered other mo-
lecules within it) may be adequately represented “ by assuming
at first motions taking place equally in all directions, and then
supposing a small additional component velocity in the direc-
tion of positive x to be imparted -to all the molecules.” In
other words, it is assumed that the motions of these molecules
may be represented by radii vectores from a slightly excentric
origin to points equally distributed over the surtace ofa sphere.
It will be instructive to trace the consequences of this hypo-
thesis, both because of what it will do and what it will not do.
Upon this hypothesis Clausius finds the following convergent
series for V? and I (loc. cit. pp. 484 and 516) :—
Veawt+ Ququwe + (Qur+qi)pe’ +. ioe
[=(1—}7'e +.. af petri we +. vo;
where 3¢e (loc. cit. p. 525) is the small component velocity
spoken of above, w is the mean velocity of molecules moving
in the plane yz, and the other letters have the meanings
assigned to them by Clausius. Multiplying these together,
going to the second order of small quantities, and arranging
by powers of yw, we find
TV?=w*(1—4r’e?) + Ayet+ Age’, . . (12)
where
ag% Ag= —2q? +2ur+ gun, 2... a 2 AB)
2K 2 < ei
420. Mr. G. J. Stoney on Polarization Stress in Gases.
Introducing the expression (12) into equations (F) and (G)
we find
P,=4pu?(1—4re?) +4 p Ase? +...,
P =P,=tpu'(1—fr'e*) + yspAce+..., 4+ + (14)
K = 7s pAge’ +. 2 ee
In these A, stands for the expression (13) ; and introducing
the following values, which are given by Clausius as correct
to the second order of small quantities (loc. cit. p. 526, foot-
note),
41
= 957?
Bild
Ue ee
266
Dh we 2
eee Bo)
re fi
Mets A,=13'84?.
From this and (14),
x=1°8 x pq’e’ + terms of the fourth and higher orders. (15)
But by Clausius’ theory (Joc. cit. p. 516),
G=4pu’qe + terms of the third and higher orders. . (16)
Whence, approximately, omitting the fourth and higher orders
of small quantities, and writing v for u, since they are nearly
equal, and then putting P for its equivalent Lv”,
1g PG?
SIRF tur vi») eee
Pett
Now, by Boyle and Charles’s law,
a
Bo Puta
where P,, p,, and T, have reference to standard temperature
and pressure. Whence, finally,
st G?
[ (1-8) a cop ie
an equation which assigns the same law as we obtained above
in equation (B) by the wholly different method of direct me-
chanical considerations.
23. Equation (18) appears to give also the amount of the
polarization stress. But thisisillusory. The hypothesis upon
which it rests is adequate as regards the conduction of heat,
but is insufficient for a quantitative investigation of the stress,
as I will now proceed to show.
Mr. G. J. Stoney on Polarization Stress in Gases. 421
_ The general formule for the conduction of heat and for the
polarization stress are the following—
igh ieee!
G=180 7 IV?. udp,
+1
«= tof IV?. (3n?—1)du
=i
(see Clausius’ memoir, p. 514, and equation (G) above).
Now yw and 3y,.—1, which occur as factors in these integrals,
are the first and second terms of a series of spherical harmonics
(Laplace’s coefficients) of the simple kind that are functions
of « only, and which therefore represent the radii of solids of
revolution from points on their axes. It is moreover obvious
that we can expand IV’ and IV® in series of spherical harmo-
nics of the same simple type. Doing this,
IV'=g,tnitgot---,
IW=kt+hythot..-,
the g’s and k’s representing spherical harmonics. Whence,
and from the fundamental property of spherical harmonics,
41
G=46 P|" nudy,
=)
+1
«= 40 ka 3p" —1)dp.
=)
Hence g, is the only term of the first series that produces any
conduction of heat, and /, is the only term of the second series
that produces any polarization stress.
Let us suppose radii drawn from a point in all directions, of
lengths proportional to the values of IV’ in those directions.
We thus obtain a solid of revolution which may also be arrived
at by plotting down radii equal to &,, and successively correct-
= the solid so found by the addition of ky, kz, &e. to its radii.
ow
ky=A,
k=B.p,
a=) . (3u7—1),
Xe. &e.
where A, B, C, &. are independent of w. In the case we are
considering, B, C, &. are small compared with A. From the
foregoing values it follows that if k, is plotted down by itself,
it will produce a sphere with its centre at the origin of radii.
422 Mr. G.J. Stoney on Polarization Stress in Gases.
Next, k) +4, may be plotted down by shifting the centre of
this sphere through the small distance B towards positive «,
and by then very slightly distorting the form of the sphere.
Again, to plot down k,+ 42, we should elongate the sphere in
the direction of the axis « by an amount equal to 4C, and nar-
row it equatorially by an amount equal to 2C, without shifting
its centre. Finally, 4, +4,+4, would be represented by radii
drawn to the surface of this last solid, after it had been slightly
distorted and removed through the distance B towards the
cooler. Through all these mutations the mean value of the
radii drawn from the origin remains unaltered*.
Comparing these figures with expansion (12), which is the
value for IV? furnished by Clausius’ hypothesis, we find that
the form and position of the solid which results from plotting
it down are such that (owing to the term containing w) there
is that separation between the origin of radii and the centre of
figure which gives a sufficient value to the function h,, but
that (the coefficient of uw’? containing only very small quanti-
ties) the solid is not elongated in the way which would allow
the function k, to attain any considerable value. That the
function ky is not wholly absent is because of such causes as
the slight distortion of figure before mentioned, which give rise
to very smallt terms of the form fy, k,, Xe.
* Since, by the fundamental property of spherical harmonics,
i “hydu=0,
("%du=0,
&c.
+ That &, is very small, if we adopt Clausius’ hypothesis, may also be
seen by comparing equation (18) with experiments on spheroidal drops.
Observation shows that, at atmospheric temperatures and pressures, a
spheroid of water some millimetres in diameter will be supported at a dis-
tance of about a fourth-metre (a metre divided by 10+) from the heater,
when the difference of temperatures is about 10°C. In G.C.S. (gramme,
: hee 1
centimetre, second) systematic measures, the hyper-milligram CF of the
gravitation of a milligram, g being gravity measured in metres per second)
per square centimetre is the unit of stress. Hence the Crookes’s stress
which supports this drop must amount to some hundreds of these units.
This is the amount indicated by experiment.
Formula (18) assigns to it a very different value. Clausius estimates
the flow of heat across air between a heater and cooler, each a square
metre in surface and a metre asunder, and kept at temperatures which
differ by 1° C., as amounting per second to 11 _ of the quantity of
heat which will warm a kilogram of water 1° ©.” About ten times this,
or 11. of this calory per second, would be the flow of heat between
On Atmospheric Electricity and the Aurora borealis. 428
This almost total absence of the elongated form arises from
Clausius’ fundamental hypothesis, that the motions of the
molecules emitted by a stratum may be represented by radii
drawn to a sphere from an excentric point; whereas it appears
from the discussion in the earlier part of the present memoir
that the encounters that take place within each of the two
_ streams into which the gas may be divided, give to the surface
to which the radii are to be drawn an elongated form. This
omission from Clausius’ hypothesis does not sensibly affect
the spherical harmonics of the first order, and accordingly his
hypothesis is adequate as regards the flow of heat, which de-
pends exclusively on one of these ; but it renders the hypo-
thesis an insufficient one as regards polarization stress, or any
other phenomenon which depends on spherical harmonics of
the second order.
LIV. Researches on Unipolar Induction, Atmospheric Elec-
tricity, and the Aurora Borealis. By i. EpLuND, Professor
of Physics at the Swedish Royal Academy of Sciences.
[Concluded from p. 371. ]
ys the magnetic properties of the earth cannot be fully ac-
counted for by assuming the existence of a magnet in its
interior, it is quite evident that the preceding consideration can
only indicate the general course of the phenomena in question.
We will now rapidly examine whether the results of that con-
sideration are conformable to those given by observation.
Atmospheric electricity has long been the object of repeated
investigations. These have been so numerous that to give an
two square centimetres at the distance of a fourth-metre asunder and kept
at temperatures that differ by 10° C. To turn this into kinetic measure
we must multiply by 41600 x 1000000; so that G would amount to about
1144000 in G.C.S. kinetic measure (7. e. in hyper-fifth-grammetres per
second), Again, we may take as rough approximations,
BMI
Po= 800’
dl pal be
ae
P,=P,=1000000.
Introducing these values into equation (18), we find approximately,
k=0°001
of a hyper-milligram per square centimetre—an amount which, as it
ought to be, is vastly smaller than that indicated by experiment.
424 Prof. EB. Edlund on Atmospheric Llectricity
account of them would require too much space ; and it is be-
sides the less necessary as we already possess a statement,
followed by a very well executed critical discussion, of those
observations *. Some physicists have essayed to explain the
results obtained by observation by assuming that the air itself
is electropositive in its normal state ; while others have thought
that the surface of the earth is electronegative, and that it pro-
duces by induction the electrical phenomena observed in the
atmosphere. Opinions have been much divided upon the true
cause of the electric state of the air or of that of the earth’s
surface. Some have assumed that evaporation from the sea,
lakes, and the wet surface of the ground renders the atmo-
sphere electropositive and the earth electronegative ; others,
on the contrary, that the distribution of electricity has its effi-
cient cause in vegetation, in the putretaction of organic mat-
ters at the surface of the earth, in the friction of the air against
the ground or the water, or in the condensation and rarefac- |
tion of the air, &e. More exact researches having shown that
none of these opinions can be correct, the phenomenon has
been attributed to a purely cosmic cause, having its seat in the
empty space surrounding the earth, or in other celestial bodies,
chiefly the sun. Ina word, up to this hour no one has suc-
ceeded, either in consequence of observations, or by theoretic
considerations, in assigning a valid and trustworthy cause for
the electric phenomena of the terrestrial atmosphere. From
the above-mentioned observations, however, it appears that the
atmosphere, under normal conditions, can be regarded as elec-
tropositive in its lower strata (accessible to observation), that
the amount of electricity increases with the height above the
earth’s surface, and that the amount is subject to a diurnal
and an annual variation.
From the preceding exposition of the cause of unipolar in-.
duction it follows that the atmosphere must be electropositive,
and the earth electronegative. The electric molecules at and
beneath the earth’s surtace are directed by the force of terres-
trial unipolar induction into the atmosphere, where they accu-
mulate until they attain a certain density, dependent on the
greater or less conductivity of the strata of air. It is only
successively that, impelled by the same force, they arrive in
the upper strata of the atmosphere, endowed with a high de-
gree of conductivity, but certainly inferior to that of the metals.
At the same time that the electric molecules rise above the sur-
face of the earth, they are carried, in both hemispheres, from
the lower into the higher latitudes, where the electric density
* Om den s. k. luftelektriciteten (Sur Velectricité atmosphérique), par .
H.-E. Hamberg. Upsala, 1872.
and the Aurora borealis. 425
in consequence perpetually goes on increasing. The forces
tending to conduct the electric molecules in the vertical and
horizontal directions are very feeble above and around the
magnetic poles; and consequently the electric density of the
atmosphere attains a maximum at a certain distance from
those poles. As we have seen, this maximum of electric den-
sity forms a zone enclosing, in the northern hemisphere, both
the magnetic and the astronomic pole ; and doubtless it is the
same in the southern hemisphere. The magnetic forces act
always with equal intensity, as the relatively slight variations
undergone by the terrestrial magnet from one period to another
can be neglected. If, then, the conductivity of the air were
equally invariable, the electrical tension of the lower strata of
the atmosphere would remain always the same; but as this
condition is by no means fulfilled, that tension must necessa-
rily vary. It is evident that the electric tension at a given
point near the surface of the earth does not depend solely on
the conductivity of the air around that point, but also on that
of the higher strata, up to the height where the conductivity
becomes sufficiently good in consequence of the rarefaction of
the air. Suppose, for example, that a fog envelops the terres-
trial surface, and that above the fog is a stratum of dry air
impenetrable to electricity ; the force of magnetic induction,
still active, will then direct the electric molecules from the
earth into the fog, which will soon show itself electropositive,
as observations have proved. If, on the contrary, the fog ex-
tended up to the higher, conductive strata of the air, doubtless
the electric charge of the lower strata would disappear sud-
denly. rom this we see how hazardous it is to attribute the
greater or less electric charge of the air at a given place to the
greater or less humidity of the air observed at the same place.
in my opinion it is highly probable that the periodic varia-
tions, both the diurnal and the annual, in the electric state of
the lower strata of the air have their cause in the variations of
the conductivity of the atmosphere ; but certainly it is not
enough to take into consideration only those variations which
happen upon the spot where the observations of atmospheric
electricity are made.
The electric condition of the air in the polar regions is espe-
cially interesting. Scoresby, in spite of reiterated trials,
found it impossible to discover in those regions the slightest
trace of electricity in theair*. The French expedition of the
corvet ‘ La Recherche,’ which passed the winter of 1838-39
at Bossekop in the Altenfjord (about 70° N. lat.), applied
themselves repeatedly to the examination of the electricity of
* An Account of the Arctic Regions, vol. i. p. 882: Edinburgh, 1820.
426 Prof. E. Edlund on Atmospheric Electricity
the air. MM. Lottin and Bravais, who made during the
summer experiments of this kind in lower latitudes, obtained
positive deflections upon a straw electroscope when it was
placed in metallic connexion with arrows shot into the air.
Now these deflections ceased to be obtained as soon as the
latitude of the North Cape was reached, In February and
March, however, they several times succeeded in detecting
feeble traces of positive electricity in the air on putting the
electroscope in connexion with kites which they raised to a
considerable height*. During the Swedish expedition to
Spitzbergen in 1868, M. Lemstrém tried in vain to discover
traces of electricity in the air (80° N. lat.)t. M. Wijkander
had better luck in the expedition of 1872-73 to the same re-
gions. Furnished witha more sensitive apparatus than those
employed by his predecessors, in the autumn of 1872 he con-
tinually obtained proofs of positive electricity in the air.
During the winter, from the middle of January to near the
end of May, on the other hand, the electricity shown was
sometimes positive, sometimes negative. In fact he obtained
20 positive and about an equal number of negative observa-
tions. The observations made in the course of the spring,
when the temperature approached zero, gave the same results
as the summer observations—namely, slight traces of positive
electricity. It is, moreover, a remarkable fact that the air
was generally positive during the winter days when aurorze
boreales appeared, but on other occasions most frequently ne-
gative. Respecting this the following remark is made by M.
Wijkander, which in my opinion is well worthy of considera-
tion :—‘‘All the observations which were made agree in this,
that, in the latitudes in question, at the highest temperatures
the air conducts electricity with great facility—a circumstance
to which have been attributed the absence of thunder and the
presence of the aurora borealis. Divers physicists have be-
lieved that this may be assumed to depend on the humidity of
the air in those regions ; but that other causes also contribute
to it is proved by the fact that the same temperature and the same
degree of humidity do not exert this action to so high a degree in
lower latitudes” t.
These observations prove indubitably that the cause to which
the positive electricity of the air in those regions is due is
very feeble. It cannot, in my opinion, be attributed to the
humidity and consequent conductivity of the air. If that
* Voyage en Scandinavie et en Laponie: Magnét. terr., t. iii. ; and verbal
communications from M. Siljestrom, who took part in this expedition.
+ Oversigt af Kongl. Vetenskaps-Akademiens Forhandlingar, 1869.
t Ofversigt, 1874,
and the Aurora borealis. 497
were the case, fog in lower latitudes ought only to betray in-
significant traces of electricity, since the conductivity of fog
is surely as good as that of the air of the polar regions under
ordinary circumstances. Now we know that, notwithstanding
its high conductivity, fog is very strongly electropositive.
The real cause of the above-mentioned results of observa-
tion is, in my opinion, that the vertical component of the force
of induction, or, in other terms, the force tending to direct
the zther (electropositive fluid) from the earth to the air, is
_very insignificant. The electropositive charge of the air must
therefore be feeble, and sometimes so slight that the air be-
comes negative by communication with the earth, as is shown
by M. Wijkander’s observations. The earth itself, on the
contrary, must always be electronegative in those regions.
If no exterior force acted upon the electric fiuid, the earth
and the atmosphere would be in the neutral state; but as a
portion of the electropositive fluid which belonged to the earth
has been conveyed into the atmosphere in consequence of the
action of the induction-force, the earth itself must be electro-
negative. The earth being a good conductor of electricity,
and at the same time constituting a spheroid, its negative
electricity must be distributed in a pretty equal fashion at its
surface; consequently the terrestrial surface must likewise
show itself electronegative in the polar regions, although the
vertical component of the force of induction is there very
feeble. With the exception of some rare occasions when it
was difficult or impossible for him to detect traces of electri-
city, M. Wijkander also found that the earth was constantly
electronegative. It follows also from the proposed theory that
the conductivity of the air in the polar regions should, as M.
Wijkander describes, appear greater than at lower latitudes
for the same temperature and with the same humidity. Ifa
conducting body placed in the atmosphere is charged with
electricity, evidently it must be influenced by the vicinity of
an electronegative body so large as the earth. If the conduc-
tive body is charged with positive electricity, this electricity
is attracted downward by the negative earth; if the charge is
negative, the reverse takes place, for the same reasons. Con-
sequently, in both cases the loss of the electricity in the air is
accelerated by the negative earth being in the vicinity of the
charged body. Now the force of induction of the earth acts
upon the electricity of the body in the opposite direction. If
the body is electropositive, that force tends to direct the elec-
tricity of the body from below upwards, and vice versd if the
body is electronegative. Therefore the earth’s induction-force
tends to diminish the influence of the earth’s electricity upon
428 Prof. E. Edlund on Atmospheric Electricity
the charge of the body. In the regions of the terrestrial sur-
face where the force of induction is either zero or very little,
the body will in consequence more readily lose its electric
charge than in the localities where that force is greater ; the
conductivity of the moist air will therefore appear greater in
the polar regions than at lower latitudes. The composition of
pure air is, without any doubt, the same in the frigid as in the
temperate zone ;, at the same temperature and under the same
pressure it must in both regions contain, when saturated, the
same quantity of aqueous vapour; and it is impossible to dis-
cover any reason for which its electric conductivity should be
different. Itis, therefore, to exterior causes that we must at-
tribute the rapid loss of the charge of electrified bodies in the
polar regions ; and the exterior causes are probably those which
have just been indicated.
According to the proposed theory it is self evident, without
any other explanation, that the air would, as was proved by
the observations of M. Wijkander, exhibit traces of positive
electricity on the days distinguished by intense aurore
boreales.
The cause just given for the electric state of the atmosphere
is probably the only one which acts uninterruptedly every-
where ; but no doubt there exist others, the action of which,
connected with certain localities, is of a more accidental cha-
racter. To these belong, for instance, the development of
electricity described by M. K.-A. Holmgren, who found that,
on the division of a liquid into drops, an electromotive force
arises at the point itself where the division is effected *. To
the same force is probably due the negative electricity of the
fine drizzle carried away by the air in cascades or powerful
cataracts. As to evaporation, vegetation, the friction of the
molecules of the air against one another or against the surface
of the earth, as well as several other phenomena in which some
have been willing to trace the cause of the electricity of the
air, they have assuredly no sensible influence upon the pheno-
menon in questiont. Ofcourse, however, if clouds in the
/
* “De l’Electricité comme Force cosmique,”’ par K.-A. Holmgren,
Mémoires de Vv Académie des Sciences, t, x1. (1872).
+ Ofall those so-called causes of the electricity of the air, and of the aurora
borealis, evaporation is, without doubt, that which has attracted most
notice; but manifold reasons may be cited for the opinion that evapora-
tion has nothing to do with this phenomenon. We may observe, in the
first place, that no one has ever succeeded in definitively proving, by ex-
periments made in the laboratory, that evaporation produces electricity.
This opinion, therefore, is not founded on a solid basis of experiment.
Further, according to this opinion the electricity of the air ought to be
more intense in summer than in winter, seeing that the evaporation is
and the Aurora borealis. 429
atmosphere have been charged, in the way indicated, with po-
sitive electricity, other clouds may in turn be negatively elec-
trified by influence.
As was said above (p. 864), the electropositive fluid (the
ether) flows from the upper strata of the atmosphere to the
earth in the direction of the dipping-needle. The vertical
component of the induction-force in general diminishes as we
remove from the equator towards the pole, while the density
of the electric fluid present in the atmosphere increases with
the latitude. On arriving near enough to the pole for that
component and the electric resistance of the air to be no longer
capable of opposing a sufficient obstacle, the positive fluid
flows down into the electronegative earth. The localities where
this takes place form a continuous zone surrounding, in the
northern hemisphere, both the magnetic and the astronomic
ole, and descending in America to lower latitudes than in the
Old World. In my opinion, to the passage of these currents
through the rarefied air we must ascribe the production of the
aurora borealis™.
greater in the former season than in the latter. Now, as every one knows,
what takes place is precisely the contrary. The positive electricity pro-
duced by evaporation, chiefly in the torrid zone, would rise into the at-
mosphere with the ascending aqueous vapour, would then be conducted
by the upper currents of air (the counter-trades) towards higher latitudes,
where it would form the aurora borealis by its descent to the earth. But
these currents are at an insignificant height from the ground in compa-
rison with that of the auroree boreales; and, besides, they descend to the
surface of the earth long before arriving at the regions marked by the
principal frequency of these phenomena. Although complete confidence
cannot be accorded to the measurements of the altitude of the aurora
borealis, we are certain that it is sometimes very considerable. Some de-
terminations made during the above-mentioned French expedition indi-
cate a height of 150 kilometres; and the height has been found still
greater on other occasions. (At the highest latitudes, however, the
aurora borealis may from time to time appear at ashort distance from the
terrestrial surface, as is proved by the observations of Farquharson,
Wrangel, Parry, Lemstrom, and several other arctic voyagers.) At so
great an elevation the extremely rarefied air is assuredly not troubled by
winds; and it is difficult to conceive how that rarefied air could become
electric through the evaporation produced in the equatorial regions. If
there existed no special force to raise the electropositive fluid into the at-
mosphere, this fluid must immediately descend to the earth, and the atmo-
sphere would certainly exhibit no traces of electricity.
* On the passage of electric currents through the air M. Lemstrém
has made some experiments which throw much light upon the pheno-
menon in question (Archives des Sciences Phys. et Nat. t. liv. pp. 72,
162). With the aid of a Holtz machine he kept at a determined electric
charge a metal knob furnished with some metallic points. With this
view the knob was connected by a conducting wire to one of the poles of
the machine, while the other pole was in communication with the earth,
430 Prof. E. Edlund on Atmospheric Hlectricity
It is evident, therefore, that aurore boreales must become
more numerous in proportion as we come nearer to this ring
from the south, and that their greatest frequency will be under
this ring itself, while they commence to decrease again in
number and in brightness at still higher latitudes. Southward
of the ring, the observer sees the aurora in the north ; if he is
beneath it, the aurora occupies, when seen under favourable
circumstances, the greater part of the sky ; and, lastly, if he
is northward of the ring, the aurora appears on the south,
It can hardly be admitted that this ring occupies an absolutely
fixed position in the atmosphere ; rather is it probable that on
one occasion it is situated more to the south or more to the
north than on another—a circumstance which may depend on
the modifications of the electric conductivity of the terrestrial
atmosphere. If, then, the place of the observer is at a point
of the earth’s surface over which the ring is usually situated,
he may see the aurora borealis sometimes to the north, some-
times to the south. If this ring formed a true circle with the
magnetic pole for its centre, if the intensity of the descending
current were the same at every point, and consequently pro-
duced everywhere the same intensity of light, an observer on
the earth to the south of the ring would necessarily see the
crown of the boreal arc in the plane passing through the place
of observation, the centre of the earth, and the magnetic pole.
Now, if the declination-needle placed itself entirely in this
plane, one would, in consequence, always perceive the summit
of the boreal arc in the plane of terrestrial magnetic declina-
tion. But the ring in question does not form a perfect circle,
nor can we assume that the descending currents possess every-
where the same luminous intensity. Besides, the plane in
At a certain distance from the knob some Geissler tubes were fixed to an
insulated stage permitting them to be brought near to or moved away
from the knob. The tubes were, as usual, furnished at their extremities
with thin platinum wires. The posterior extremities were connected with
the earth by a conducting wire, while the anterior extremities, or those
turned towards the knob, were insulated in the air. Although there was
no metallic communication between the tubes and the knob, they never-
theless commenced to be luminous as soon as the machine was put in mo-
tion, and that even when the distance between the tubes and the knob
rose to 2 metres. The current which produced the luminous appearance
must therefore have traversed a length of 2 metres through a stratum of
air of ordinary density. It was natural that no luminosity was produced
in this layer of dense air. These experiments appear to me to have much
analogy with the phenomena produced on a grand scale at the formation
of the aurora borealis in the terrestrial atmosphere: the electric currents
coming from the upper strata descend into the earth without producing
luminous phenomena in the lowest strata of the atmosphere.
and the Aurora borealis. 431
question indicates only approximately the direction of the
declination-needle. From theory, then, it follows that the
direction of the declination-needle must indicate generally and
approximately the summit of the boreal arc, though we are not
authorized to maintain that the two must entirely coincide
with one another.
In the localities on the terrestrial surface situated beneath
the ring of maximum electric density the electricity descends
in the direction indicated by the dipping-needle of the locality;
for, as we have demonstrated above (p. 364), the action of the
inductive force of the earth is equal to zero in that direction.
The descending currents cannot be compelled to deviate
from the above-mentioned direction, unless, in consequence of
an accidental meteorological state of the atmosphere, the elec-
trical resistance of the air is greater in that direction than in
another, in which case the intensity of the descending current
will be most considerable in the direction of least resistance.
As a case of this kind may easily occur, we are authorized to
maintain, on the ground of the theory, only that the descend-
ing currents must be in general parallel to the dipping-needle.
Now the current betrays its path through the air by a line of
light. If those luminous lines parallel to one another be
viewed from the surface of the earth, they will appear to con-
verge to a point, by the same laws of perspective to which is
due the visual convergence of the rows of trees of a long
avenue. As to the point, it will be found in the direction
which the dipping-needle at the place of observation indicates
in the sky. To this optical phenomenon is due the auroral
crown which appears in complete aurore boreales. The cur-
rents in question are formed as soon as the difference of elec-
tric tension between the atmosphere and the earth is great
enough to surmount the obstacle presented by the resistance
of the air. Now, the earth being a good conductor of elec-
tricity, and constituting a sphere, its negative charge must be
nearly the same everywhere. Doubtless no one will maintain
that the positive charge of the air in the southern hemisphere
is constantly equal to the same charge in the northern hemi-
sphere. The forces which tend to render the air electropositive
and the earth electronegative are equal in the two hemispheres;
but the result of the activity of those forces depends in part
on the meteorological state of the air, which may be different
for each hemisphere. Nevertheless, as we have said, there
cannot be any great difference in the negative charge of the
earth; and consequently one at least of the causes on which
the discharge depends is common to both hemispheres. There-
fore nothing very extraordinary can be found in the fact that
432 Prof. EH. Edlund on Atmospheric Electricity
auroras are often simultaneous in the northern and the south-
ern hemisphere. |
If we compare the theoretic deductions above formulated
with the results of observation, we shall find that there exists
a satisfactory accordance between them.
According to Loomis, in North America, under the meridian
of Washington and at the 40th parallel, 10 auroras per year
are seen; under the 42nd parallel the number amounts to 20;
and near the 45th the number is 40. In the latitude of 50°,
the number of aurorz boreales yearly is stated at 80; and
between this latitude and that of 62° the aurora appears nearly
every night. Between the last two latitudes the aurora
borealis appeared quite as often to the south as to the north.
Here, then, is situated the zone, properly so called, of the
aurore boreales, of which about 56° may be considered
the mean latitude. To the north of 62° the auroras appear
almost exclusively on the south side, and they diminish in
number and brightness as we advance northward. At 67° lat.
their number has fallen to 20, and is only 10 in the vicinity of
78°. The same fact presents itself at the meridian of St. Pe-
tersburg ; but here the zone of the auroras is situated much
more northward than in America: it is only between the 66th
and 75th degrees of north latitude that the annual number of
aurore boreales is stated at 80*.
A multitude of measurements upon the position of the auroral
are were made at Bossekop in the winter of 1838-39, by the
French Expedition to Spitzbergen and Norway. The result
of more than 200 measurements was, that the crown of the
arc was situated 10° west of the magnetic meridian. Arge-
lander had arrived at results nearly the same by his observa-
tions made at Abo, in Finland. In consequence of accidental
circumstances, the crown of the auroral arc appeared several
times to the east of the magnetic meridian. The position indi-
cated being the mean of all the observations, is cleared of acci-
dental perturbations. The fact that the crown of the auroral
arc must in those regions appear, on the average, to the west
of the magnetic meridian flows directly from the theory, if we
take into consideration the geographical situation and the mag-
netic declination of the locality, as well as the form and situa-
tion of the annular space of the maximum of electric density.
It is easy, in the same way, to understand the accuracy of
Argelander’s observations. In North America, on the con-
trary, as in Siberia, the crown of the auroral arc must more
nearly coincide, on the average, with the magnetic meridian ;
* Loomis, Annual Report of the Smithsonian Institution, 1866.
+ Sur les Aurores boréales vues a Bossckop et a Juprig: Paris, 1846.
and the Aurora borealis. -433
I am not, however, acquainted with any results of observations,
freed from accidental perturbations, of a nature to confirm or
refute this asswmption. :
Wilcke* had already observed that the place of the auroral
crown is in the zenith of the magnetic meridian, or in its vi-
einity. The correctness of his observations has been many
times confirmed since then by other physicists. The above-
mentioned French Expedition made 43 determinations, the
mean result of which was, that the situation of the crown de-
viates less than 1° from the magnetic zenith. The difference,
however, between the two positions amounted to 15° on one
eccasion, and to 12° on two others.
In explaining the annual period of frequency of the aurorse
boreales shown by the observations, the following circum-
stances must be considered :—The electric fluid accumulated
im the earth’s atmosphere by the unipolar induction of the ter-
restrial magnet descends to the surface of the earth either by
disruptive discharges (thunder-storms), or in feeble continuous
currents. The former have their principal frequency between
the tropics, and the latter in high latitudes. The fluid which
does not flow to the earth in the first of these two ways, is
conducted by the magnetic force to higher latitudes, where it
flows dewn in the form of continuous currents. From this it
follows that the rarer and weaker the tempests, the more in-
tense and numerous must the aurore boreales be, and vice
versd. In the zone of calms, immediately to the north of the
equator, thunder is heard throughout the year; but the limits
of this zone vary from one season to another. Outside of that
zone, but between the tropics, thunder-storms travel, like the
rainy seasons, with the sun. We can therefore assume that
the quantity of the electric fluid which within the tropics de-
scends to the earth in tempests is not the same all through
the year. As is known, the aurore boreales present two
maxima, viz. at the spring and autumn equinoxes. According
to our view the tempests would consequently be the weakest,
or, rather, the least quantity of electric fluid would descend in
lightning from the atmosphere to the surface of the earth,
within the tropics, when the sun crosses the equinoctial line.
We have not sufficient materials of observation for deciding
whether this view is correct or notf.
It cannot be admitted that the electric fluid flows down upon
the earth only on the occasion of aurore boreales. Beyond all
doubt the flow is continual, although mostly the currents do
* Kongl. Vetenskaps-Akademiens Handlingar for 1777 (vol. xxxviii.).
+ it appears to follow from the observations made upon the aurora
borealis by the Austro-Hungarian Arctic Expedition of 1872-1874, that
Phil. Mag. 8. 5. Vol. 6. No. 39. Dec. 1878. 2
434 Prof. BE. Edlund on Atmospheric Electricity
not possess the force to render the air luminous. The electric
fluid is driven into the air, by forces incessantly active, from
every point of the earth from the equator to the localities
where the downflow is effected ; and that fluid is at the same
time conducted from the lower to the higher latitudes. We
must therefore admit the incessant passage of currents from
the equator towards the poles, while the electric fluid cireu-
lates in the opposite direction within the earth. This does not
mean that the direction of these currents is entirely north and
south, many causes contributing to make them deviate from
that direction. We picture to ourselves the atmosphere cut by
a plane parallel to the equatorial plane and situated between
that plane and the auroral ring. ‘The electric fluid driven by
the active forces of the earth into the atmosphere between the
equatorial plane and the plane in question must then pass
through the latter. The sum of the currents passing through
a plane of this kind will therefore be greater in proportion as
the latitude of the plane is higher; consequently the intensity
of the currents increases from the equator towards the poles.
Although the electromotive forces to which these currents are
due are always the same, yet their intensity must be subject
to incessant variations, seeing that it of course depends also
on the resistance they meet with in their course. This resist-
ance must depend in great part on the constitution of the air
in its lower strata: when these are saturated with humidity,
the electric resistance is much less than when they are rela-
tively dry. As, for this reason, these primitive currents often
vary in intensity, induction currents will result, of a sort to
complicate still more the system of currents we are here con-
sidering,
It.is obvious that these currents must act upon a declina-
tion-needle placed at the surface of the earth; but to calculate
the intensity and direction of the action is not soeasy. In the
first place, the currents in question act directly on the declina-
tion-needle almost in the same manner as the current which
passes through the circuits of a galvanometer acts on the
needle of that instrument ; and, in the second place, it must
be remembered that the earth contains a quantity of magneti-
zable materials, the magnetic condition of which is modified
the zone of maximum of aurore boreales shifts so as to be found more
northward during the winter and summer than at the periods of the
autumnal and vernal equinoxes. If this be confirmed by future observa-
tions, the annual variation ascertained at lower latitudes may be accounted
for by this displacement. (See Nordhichtbeobachtungen der dsterretchisch-
ungarischen arktischen Expedition 1872-1874, by C. Weyprecht: Vienna,
1878.
and the Aurora Borealis. AZO
by these currents. All these circumstances have a marked
influence upon the declination. Thus, although it may be im-
possible beforehand to determine exactly the action of these
currents upon the declination-needle, we can compare the va-
riations of the declination with the results given by the obser-
yations.
_ The relative humidity of the air is in general greater during
the night than during the day. It may be taken as a rule that
the diurnal variation of that humidity increases with the varia-
tion of its temperature: it is consequently greater in summer
than in winter. The conductivity of the air, and, in consequence,
also the intensity of the currents in question, have therefore a
diurnal and an annual period. Now, if it be admitted that
the diurnal variations of the declination depend chiefly on the
variations in the intensity of the currents we are considering,
it follows that the diurnal variations of the declination should
be greater in summer than in winter, and should moreover in-
crease with the distance from the equator—a deduction con-
firmed, as we know, by the observations. To this may be
added that the action upon the declination-needle does not de-
pend exclusively on the nature of the air and the intensity of
the current at the locality in which the needle is placed; the
intensity of the currents in localities the most distant acts also,
although in a less degree. Besides, it is evident that here we
have to do with the humidity of the air not merely at the sur-
face of the earth, but also in the upper strata of the atmo-
sphere. We ought not, then, to expect that the variations of
declination at a given place will be in direct proportion to the
humidity of the air at the same place.
When, for one cause or another, the current descending. to
the earth from the upper regions of the atmosphere has ac-
quired sufficient intensity, it produces a luminosity in the rare-
fied air, aud we then have the aurora borealis. If the current
is endowed with an invariable intensity (as appears to be the
case in some of the feebler aurore boreales), the needle remains
pretty steady; but when there are rapid variations in the in-
tensity of the current, or when its maximum of intensity shifts
from one point to another (in which case the aurora becomes
sparkling and changes its aspect continually), the needle, as
can be readily understood, becomes agitated and moves vio-
lently. This agitation extends over a considerable portion of
the earth’s surface, and thus indicates what is going on in the
atmosphere, even when no aurora borealis is perceived.
_ The thesis that the aurore boreales are produced by electric
currents is not new; the majority of physicists have long been
agreed in regard to this, with good reason. But hitherto no
21 2
436 Mr. O. Heaviside on a Test for Telegraph Lines.
one has been able to discover the true and most active cause
of those currents, as well as of the electrical phenomena of
the atmosphere in general. In fact there are good grounds
for asserting that none of the explanations given, up to the
present, of these phenomena will bear the examination of scien-
tific criticism. If, till now, no one has seen in these pheno-
mena the results of the unipolar induction of the earth, it is,
without any doubt, because an idea has been formed of the
nature of that induction which did not permit its application
to this object.
There still remain many things that are obscure in the phe-
nomena of the aurora borealis and atmospheric electricity.
Of these it will be sufficient to indicate the secular periods in
the frequency of aurore boreales. The relation of these pe-
riods with the solar spots gives positive evidence of the coope-
ration of extratellurian forces. The preceding statement has
no claim to be presented as a complete theory of atmospheric
electricity and aurore boreales. My intention has been simply
to show that the unipolar induction of the earth plays a most
important and significant part in the explanation of those phe-
nomena, and that it ought not to be neglected by those physi-
cists who hereafter apply themselves to this matter.
LV. Ona Test for Telegraph Lines.
By Ouver HEAVISIDE*.
HE true conduction and insulation resistances of a uni-
form line may be found from the potential and current
at the ends, when a constant electromotive force acts at one
eng. Suppose at one end A of the line there is a battery of
electromotive force H, and a galvanometer, the two together
of resistance R, ; also at the other end B of the line a galva-
nometer of resistance R,, the circuit being completed through
the earth. If the potential at distance « from A, where x=0,
is v, the current at the same point y, the conduction and insu-
lation resistance & and 7 respectively per unit of length, then
dv
dae = hn,
where
/?= k 3
1
and —
or 1 dv
Te dee
* Communicated by the Author.
Mr. O. Heaviside on a Test for Telegraph Lines. 487
v=ae™ + be~™,
1 babel cab)
(ae"* aS be ee
whence
where a and b are undetermined constants.
If now the potential and current at A are v; and y,, and the
same at B are v, and y2, then it may easily be shown from
equations (1) that
(f= ST nea
jeage
Since the length of the line does not appear in (2), the rela-
tion therein expressed applies to any two points of the line.
The reason is that the product of the conduction and insulation
resistances is the same for any length, the one varying directly
and the other inversely as the length. Now the insulation of
land-lines is in this country very variable, while the real con-
duction resistance (1. é. its resistance if it were perfectly insu-
lated) is nearly constant. It follows that (2) may be used for
determining 7, considering & as constant. In (2), |
v= Hh —Rhin, : (3)
v2 = Royo.
R, and R, being interposed resistances are, of course, known;
so that three quantities have to be observed, viz. E, y,, and
¥23; or equivalent information must be obtained. To make
the test in its simplest form, let the resistances R, and R, be
small compared with the line resistance. _ Also, let equally
sensitive tangent-galvanometers be used, and let n, and ng be
the deflections corresponding to y,; and yp, and n; the deflec-
tion EK gives through 1000 ohms. Then (2) becomes
n
ko oe SOP Lian suas ao ree
1
where & and are both in ohms; or if kis in ohms and iin
megohms, the 10° must be cancelled.
If R, and R, are taken into account, then instead of (4) we
have
jee (10?n; — Ryn)” — (R,n-,)? Z
MN,
and if the galvanometers are not equally sensitive, the deflec-
tion nm. must be multiplied by the ratio of the sensitiveness of
the galvanometer at B to that at A.
Using formula (4), the test can be easily made, though it is
438 Prof. W. C. Réntgen on Electrical
obvious that the line must be long enough to make an appre-
ciable difference between the sent and received currents.
We may also determine & and 7 separately from the same
data. IfJ/ is the length of the lme, then
k= Vlog 1 t1Y fi, .
Vote ki
a = V+ JS ki ? ; : j (5)
7= V ki log Y1 |
Voaty2V ki J
It is to be observed that these formule give the true con-
duction and insulation resistances. The measured resistances,
or those deduced from observations with the bridge, differen-
tial galvanometer, &c., at the battery-end alone, are very dif-
ferent from the true, when the line is long and badly insulated.
The measured is always less than the true conduction resist-
ance, and the measured always greater than the true insulation
resistance ; while the measured conduction resistance can never
be greater than V éi, and the measured insulation resistance
never less.
LVI. On Electrical Discharges in Insulators. By Dr. W. C.
RonteEen, Professor of Physics in the University of Stras-
burg*.
ai the following communication are contained the results
of an experimental investigation begun long since, but
often interrupted, on the disruptive discharge of electricity
through insulators; for I had set myself the task to discover
whether in such a discharge there exists any expressible rela-
tion between the physical constitution of the insulator, the
difference of potential required for a discharge, and the quan-
tity of electricity discharged. The investigation extended to
solid, liquid, and gaseous bodies; but up to the present time
I have only succeeded with the latter in finding such a relation.
The solid bodies, mostly crystals, were placed, in the form
of thin plates, between two rounded-off brass points, one of
which was led away to earth, the other connected with a source
of electricity, mostly a Holtz machine. By slow rotation of
the machine the potential was raised until a spark passed
through the thin plate. An electrometer specially constructed
for the present case permitted the course of the potential to be
* Translated from a separate impression, communicated by the Author,
from the Nachrichten der Kon. Gesellschaft zu Gottingen, 1878.
Discharges in Insulators. 439
traced, and the potential itself to be accurately determined at
the moment of the discharge. I hoped in this way to obtain,
with plates of different substances and especially with plates
cut in different directions out of the same crystal, a charac-
teristic difference of potential for each substance and for each
direction ; but hitherto all my endeavours have been fruitless,
_I found it impossible, with one and the same plate, to obtain
satisfactorily accordant values from the different experiments
of one and the same series. The cause of this irregularity is
doubtless to be sought in an unavoidable difference in the dis-
position of the electricity on the points and the plate. The
difference of potential necessary for a spark-discharge is essen-
tially dependent on this disposition, which, in the method of
experiment chosen, changes before the spark passes, in con-
sequence of a less or greater conductivity of the plate and its
surface, as well as in consequence of electricity added by con-
vection from the point in an irregular and uncontrollable
manner. Perhaps, if experiments were made with much larger
plates and with very obtusely pointed electrodes, more fayour-
able results might be obtained.
The experiments which I made with liquids are, notwith-
standing their number, still too imperfect, and offer too few
general points of view, for their details to be communicated.
As is well known, electrical discharges in gases have often
been the subject of investigation; both the spark-discharge
with greater and less pressures and also the slow discharge
known by the name of dissipation have been repeatedly ex-
amined. From these experiments no simple relation can be
with certainty deduced between any constant of the different
gases and the difference of potential corresponding to each
gas, necessary for a discharge, or the amount of electricity
discharged. Yet it would be hazardous to conclude, on the
ground of those experiments, that such a relation does not
exist. For, in the first place, with spark-discharges it is
always to be feared that the decomposition which doubtless
takes place in some gases, as well as the considerable alteration
of temperature in the path of the spark, may possibly conceal
any such relation; and, secondly, some hitherto unpublished
experiments made by M. Warburg have shown that in gases
dissipation cannot with certainty be demonstrated ; while the
loss of electricity by conductors which are insulated in gases,
observed by Coulomb, Riess, Warburg, and others, is very
probably brought about only by the insulating supports and
by particles of dust*.
I therefore, after numerous preliminary experiments and
* See Boltzmann, Pogg. Amn. vol. cly. p 415.
440 Prof. W. C. Réntgen on Electrical
mature reflection, resolved to select for my purpose a kind of
discharge which has hitherto been but little studied, viz. the
so-called dischar ge by convection, such as is known to take
place between a very sharp point and a large smooth plate.
I believe 1 may indeed attribute it to this selection, if I finally
succeeded in discovering the relation sought.
The method of experiment at last found serviceable was the
following. A Holtz machine was kept in action with as con-
stant and high velocity of rotation of its disk as possible, by
means of a Schmidt water motor. One of the electrodes was
connected with the earth by the gas-pipes ; and from the other a
copper wire covered with gutta percha led to the inside coat-
ings of two Leyden jars constructed according to W. Thom-
son’s plan, of well-insulating glass and containing sulphuric
acid, the outside coatings of which were led away to earth.
These jars formed an electrical reservoir of considerable
capacity, and were intended to diminish as much as pos-
sible the variations of potential which might be occasioned
by an irregular development of electricity by the machine.
Behind these jars. the wire was divided. One branch went
to a narrow glass tube filled with glycerine, which served
as a rheostat; by lowering into or drawing out of it a metallic
conductor to earth, the resistance of the glycerine could be
fixedly diminished or augmented. The other branch led first
to the point in the discharge-apparatus, and from that to an
electrometer constructed expressly for the investigation.
The discharge-apparatus consisted of the following parts:—
A vertical brass rod, provided beneath with a gilt sewing-
needle, passed well insulated through the tubular neck of a
glass bell, which was fitted air-tight upon the plate of an air-
pump. In the space enclosed by the bell stood, carefully
insulated from the plate, at a distance of 19:3 millims., with
its centre opposite the point, a polished brass disk of 132 mil-
lims. diameter; this was in conducting connexion with one
end of the coiled wire of an extremely delicate mirror-galva-
nometer consisting of a great number of turns; the other ex-
tremity of the wire led to the gas-pipes. By an air-pump and
further suitable arrangements the bell could be filled with
different gases at various pressures determined by a mano-
meter.
The electrometer made use of proved, it is true, serviceable
for the present investigation; but it still has some defects,
which must be removed; Iam therefore engaged in construct-
ing a better apparatus, of which I hope subsequently to give
an account. I will only mention further that it was arranged
after the manner of Thomson’s quadrant-electrometer, and that
Discharges in Insulators. 441
the readings were reduced to comparable measure by compa-~
rison with a long-range electrometer which I had made for
the most part according to Thomson’s description.
It was found that 6 of the units in which in the follow-
ing the differences of potential are expressed correspond to a
potential-difference of about 5 Daniells. I would not, how-
ever, lay too much stress upon these data, since the battery
at my disposal was too small to enable me to accomplish a
more accurate determination.
Now, if we assume that the Holtz-machine electrode which
is connected with the gas-pipes conducts away negative elec-
tricity, the positive electricity issuing from the other electrode
finds two paths—the first through the rheostat to the gas-
pipes, and the second through the discharge-apparatus and the
galvanometer, likewise to the gas-pipes. The quantity of
electricity which passes through the discharge-apparatus can
now be varied within wide limits by altering the resistance of
the rheostat. The galvanometer indicates this quantity ; and
the electrometer measures the difference of potential between
the point and the plate.
I soon observed that the discharge does not take place with
every difference of potential, but that rather a perfectly fixed
difference is always necessary in order to induce it. If at
the commencement of the experiment the resistance of the rheo-
stat has been made nearly = 0 (when of course the deflections
of the galvanometerand electrometer are likewise = 0), and if
now the resistance be gradually increased, on the electrometer
indeed a steady rise of the potential will be observed, but the
potential must have reached a certain value before the galva-
nometer will show, by a sudden, proportionally great, and
constant deflection (if the resistance of the rheostat remains
invariable), that the discharge has commenced. When once the
discharge is present the resistance of the rheostat and conse-
quently the potential can be again diminished, through which
the discharge, it is true, steadily decreases, but does not at
once sink to zero. Only with a considerably less potential-
difference than that with which the discharge commenced does
it again entirely cease.
I found, further, that the commencement of the discharge
was dependent on many collateral circumstances, e. g. whether
a discharge had taken place a shorter or a longer time pre-
viously ; unavoidable dust particles, too, have probably an
influence. On the other hand, determinations of the difference
of potential at which the discharge ceases, derived from differ-
ent experiments separated from one another by considerable
442 Prof. W. C. Réntgen on Electrical
intervals of time, gave values which agreed excellently with
each other. I resolved on this account, at least preliminarily,
to direct my attention chiefly to the determination of this dif-
ference of potential, which we will name the minimum poten-
tial-difference, and, for brevity, denote by M. P.
The moment when the discharge ceases is, for the most
part, characterized by this—that the already much diminished
galvanometer-deflection (amounting to only 2-4 scale divi-
sions), after a further very slight lessening of the resistance in
the rheostat, suddenly becomes zero. At this instant the M. P.
is read off at the electrometer. I am inclined to account for
this phenomenon by the small variations which the potential
undergoes notwithstanding the insertion of the Leyden jars.
The electrometer, which is provided with a powerful damper,
gives the mean value of the variations of the potential. The
fact that the discharge had now really ceased I verified also
in another way: that is to say, if the galvanometer was made
considerably more sensitive by being rendered more perfectly
astatic, its deflection vanished at exactly the same difference
of potential as before; in like manner an electroscope, which
instead of the galvanometer was connected with the plate in
the discharge-apparatus, was not charged, and the characteristic
star-shaped luminous appearance visible in the dark, which
was present during the discharge, disappeared when the M.P.
was attained. | |
In all the following experiments the distance of the point
from the plate remained the same. Further, the temperature
was constant, at least in those experiments which were to be
compared with one another; and, lastly, it is to be noticed
that the point was always positive when the contrary is not
expressly stated.
Unfortunately, the investigation had to be interrupted, first
because the seasons of spring and summer are very unsuitable
for working with static electricity, and secondly because for
its continuation the reconstruction of some of the apparatus,
especially of the electrometer, had become absolutely neces-
sary. Consequently, of the many questions which might be
put, only a few can be answered. The results are given below.
1. How does the M. P. ina gas depend on the pressure ?
The question was repeatedly answered for dry air free from
carbonic acid. Fig. 1 represents the result of one experiment:
the pressures in millims. of mercury were laid down as ab-
scissee, and the M. P. as ordinates. The unit in which the
latter are expressed is not directly comparable with that men-
tioned above.
Discharges in Insulators. 443
eee ei “17° sade a4
eat millims 1 s[51a 49] 449/885)200| 108158 68) 29 109 71
pm anette 21. 639|602)977 547 503 489 402/361 301258 198 189 |
[eal
It follows from these experiments that with pressures above
200 millims. the increase of the pressure is at least nearly pro-
6ac fF
500 |
400 |
100
100 200 300 400 500 60u
portional to the increase of the M. P.; below that limit the
M. P. diminishes much more quickly in proportion. Similar
ratios were found with other gases.
2. How, in a gas which is subjected to a fixed pressure, is
the quantity of electricity discharged connected with the dif-
ference of potential between the point and the plate?
Dry air, free from carbonic acid, was tried with the pres-
sures 391, 294, 203°4, 109-7, and 51°8 millims. mercury. The
highest difference of potential which could be determined with
my electrometer was 3684 units (6 units = 5 Daniells); the
greatest quantity of electricity that could be measured amounted
to something over 500 arbitrarily chosen units.. The follow-
ing Tables contain in the first column the differences of poten-
tial, in the second the corresponding amounts of electricity
discharged; and in the third I have given, under the name of
“‘ disposable potential-differences,”’ the differences between the
numbers in the first column and the M. P. corresponding to
each pressure, the quantity of electricity discharged being of
course =(). I have calculated these differences, and given
them the name above mentioned, because possibly the view is
444 Prof. W. C. Réntgen on Electrical
correct that the M.P. is compelled to overcome a certain transi-
tional resistance, and that only the disposable potential-ditfer-
ence measures the quantity discharged. The latter shall, for
shortness, be denoted by D. P.
Pressure 51°8. ; Pressure 109°7. |
Pot.-diff. | Discharge.| D.P. Pot.-diff. | Discharge.| D. P.
1462 ee ea Slee on 0
1727 We 265 2094 38 288
2004 171 542 2859 208 1053
2199 271 737 3396 - 370 1590
2349 371 887 8684 522 1878
2487 471 1025 .
Pressure 203°4. © Pressure 294.
2162 0 0 2433 0 0
2645 45 483 2859 29 496
2859 67 697 3396 72 963
3396 138 1234 3684 105 1251
3684 192 1522
|
Pressure 391.
Pot.-diff. | Discharge. 1D es
2775 0 0
3169 24 394
3684 65 909
The first of these Tables, corresponding to the pressure
51-8, is graphically represented in fig. 2 ; the abscisse denote
the quantities discharged, the ordinates the D. P. The curves
for the other pressures have a similar form.
3. Ina gas with a determined difference of potential, in
what manner does the amount of electricity discharged depend
upon the pressure? Dry air, free from carbonic acid, with the
potential-difference 3684, was examined in detail.
641:2
0
466°4
41°5
391°0
65
294-0
105
2034
192
109°7
522
Pressure in millims. of mercury
Amount of electricity discharged
This Table is graphically represented in fig. 3; the abscisse
denote the amounts of electricity discharged, the ordinates the
pressures. Other gases behaved similarly.
In these experiments, as already mentioned, the difference
of potential was constant. But as, according to No. 1, with
different pressures the discharge ceases and commences respec-
Discharges in Insulators. 445
tively at different potential-differences, the D. P. were not the
same; it was consequently still questionable whether any
1004
100 200 300 400 500
sunple relation subsisted between pressure and electricity dis-
charged, if with different pressures not the absolute but the
disposable potential-difference was found constant. The ques-
tion can be answered from the data of No.2. I have extracted
from the Tables the following comparison, valid for the D. P.
= 1000:—
301
(0
203°4 | 109°7
106 194
518
294 |
450 |
79
ie See ch ee
| Pressure in millims. of mercury ...
| Amount of electricity discharged
In fig. 4 will be found the graphic representation. A
simple relation is not perceptible. To be sure the product of
the pressure into the quantity of electricity for the last four
pressures is nearly constant; but with the pressure 391 there
is a considerable deviation from this rule. For the purpose of
fully answering questions 2 and 3, experiments with different
gases, between wider limits of the potential-differences, the
pressures, and the quantities of electricity discharged, will be
absolutely necessary.
4. Does an expressible relation exist between the minimum
ditterence of potential and the nature of the various gases in
which the discharge takes place ?
The gases were all tried at two pressures, approximately 205
and 110 millims. mercury ; experiments with higher pressures
Hb IE et
|
if Iso
446 Prof. W. C. Réntgen on Electrical
were excluded, because with some of the gases the electrometer
was not equal to measuring the corresponding differences -
of potential. I must mention tnat these experiments are not
directly comparable with the preceding ones. The following
Table contains the mean values of various satisfactorily ac-
cordant determinations.
G M.P. at 205 M. P. at 110
ases. La eae
millims. millims.
Hydrogen: s) jws2.0533 1296 1174
OXV SON: ec ci tk cons bass 2402 1975
Carbonic oxide...... 2634 2100
Marsh-gas .......++... 2777 2317
Nitrous oxide ...... 3188 2548
Carbonic acid ...... 3287 | 2655
In this Table the gases are arranged in the order of ascendin
values of the M. P. If this series be compared with that which
is obtained when the gases are arranged in the order of dimin-
ishing values of their mean molecular path-lengths, at both
205 and 110 millims. pressure perfect agreement will be found.
Since the minimum difference of potential is a direct measure
of the insulating-power of a gas, the result contained in the
above Table can be expressed in the following manner :—The
shorter the path of its molecules, the greater is the insulating-
power of a gas. Now itis known that the smaller the gas-
molecules the greater is the length of their paths ; consequently
we can also say:—The larger the molecules of a gas the greater
is its power to insulate.
The connexion between the M. P. and the length of path
becomes still more convincingly evident when for each gas we
form the product of the path-length and M. P.
Product of path-length and M. P.
Gases.
Pressure 205 Pressure 110
millims. millims.
Noh (choses esranemeneaes 240 218
OXY SON. oj ons-tep aes 254 209
Carbonic oxide ..... 259 207
Marsh-gas ...3.. 020: 236 197
| Nitrous oxide ...... 217 Ws
Carbonic acid ...... 224 181
ers —$—_$_—__—_!
The path-lengths are taken from Graham’s transpiration
Discharges in Insulators. 447
experiments and O. H. Meyer’s Gastheorie, the factor a being
everywhere omitted. 10*
From these numbers we obtain a remarkable relation: it
follows, namely, from both the first and the second series, that
the product of the path-length and the minimum difference of
potential, measured at equal pressure, has nearly the same value
with all the gases investigated.
Stefan pointed out the connexion between path-length and
index of refraction; Boltzmann’s experiments have shown
that the dielectric capacity of gases stands to the index of
refraction in the relation required by Maxwell’s law; and the
present investigation brings the insulating-power of gases into
causal connexion with the three above-mentioned properties.
Accordingly the insulating-power of a gas is by so much less as
the inductive capacity of the gas is greater, and vice versd.
Similar simple relations exist between path-length and M. P.
for one and the same gas at different pressures; a simple dis-
cussion of the experiments spoken of under question 1 leads to
this result.
Besides the gases above adduced, olefiant gas was examined.
It was not found to conform to the same law ; for the products
of the M. P. and the path-length at the pressures 205 and 110
_ millims. were respectively 149 and 123. I believe, however,
that no importance need be attached to this deviation, since
the phenomena attending the discharges were of quite a differ-
ent character from those with the other gases, and permit us
almost certainly to conclude that decomposition of this gas
took place.
In conclusion, in moist air the M. P., and consequently the
insulating-power, was much greater than in dry air.
5. A series of experiments with air and hydrogen prove
that, ceteris paribus, the M. P. is less when the point is charged
with negative than when it is charged with positive electricity;
whether the like takes place also in regard to the difference of
potential at which the discharge commences I have not yet
been able to decide.
Strasburg, May 1878.
Grrr
LVIT. On the Nebular Hypothesis.—X. Predictions. By
Priny Harpe Cuase, LL.D., S.P.AS., Professor of Phi-
losophy in Haverford College*.
qe accordance with a suggestion of Professor Robert E.
Rogers, I endeavoured to find what modes of central
force will best represent some of the most general forms of
chemical activity, more especially those which are the base of
the law of Avogadro and Ampére—of combination by volume,
and of approximate constancy in the product of atomic weight
by specific heat.
The simplicity of the ratio between the energy of H, O and
the solar energy at Harth’s mean distancet furnishes good
grounds for such an investigation, while the record of a para-
bolic orbit connecting the Sun with the nearest fixed stars t
indicates a proper course for conducting it. Although there
may be some doubt as to the degree of certainty which belongs
to the recent hypotheses of internal gaseous structure, there
can be none as to the graphic representation of orbital activi-
ties under forces varying inversely as the square of the dis-
tance. Circular orbits denote constancy of relations between
radial and tangential forces ; elliptic orbits, variability of rela-
tions accompanied by cyclical oscillations ; parabolic orbits,
variability of relations without cyclical oscillations ; hyperbolic
orbits, variability of relations complicated by the action of
extraneous force.
In a rotating mass, the orbits of the several particles are
circular. Ifthe uniform velocity of any particle in the equa-
torial plane is less than V/r, the mean action of the central
force is impeded by internal collisions or resistances. If the
velocities of all the particles in the plane vary precisely as V fr,
there is a condition of perfect fluidity, marking a limit between
complete aggregation and incipient dissociation. Any cyclic
variations of velocity between constant limits indicate elliptic
orbits, with tendencies to aggregation through collisions near
the perifocal apse. A perifocal velocity of V 2/r marks a pa-
rabolic orbit, and a limit between complete dissociation and
incipient association. A velocity greater than V 2fr is hy-
perbolic, indicating the intervention of a third force in addi-
tion to the mutual action between the two principal centres of
reference.
If all physical forces are propagated by etherial undulations
* Communicated by the Author. 5.
+ Proc. Soc. Phil. Amer. xii. p. 824; xiii. p. 142.
t Ibid. xii. p. 523, and subsequent papers.
Prof. P. EH. Chase on the Nebular Hypothesis. 449
between resisting points, those points tend naturally to nodal,
and from internodal positions. In order to matntain unifor-
mity in the wave-velocity, the etherial molecules must be
uniform, not only in volume, but also inaggregate inertia. As
the inertia of the resisting points increases, the inertia due to
internal zetherial motions should therefore diminish, and vice
versd. In other words, the uniform elementary volume may
be represented by the product of atomic weight by specific
heat; and the laws of Boyle (or Mariotte), Charles, and Avo-
gadro follow as simple and necessary corollaries.
In order that uniform undulations should produce motion,
there must be at least two points of resistance. Those points
-would approach each other until the interior undulating resist-
ance equalled the exterior undulatory pressures, when their
motion would be converted into rotation or into orbital revo-
lution. Their common centre of revolution might become the
centre of a new elementary volume, thus giving rise to the
various laws of combination by volume, combination without
condensation, condensation of two volumes into one, three
volumes into two, or four volumes into two, as well as to
general artiad and perissad quantivalence.
When peritocal collisions change parabolic or elliptic into
circular orbits, there should be increasing density towards the
principal centre of the system. Further collisions and con-
densations would produce tendencies to both nucleal and atmo-
spheric* aggregations, and consequent binary groupings.
These laws are exemplified in the solar system by the general
division into an intra-asteroidal and an extra-asteroidal belt,
_and by the subdivision of each belt into two pairs,—the inner
belt being denser than the outer, and the inner member of each
pair being denser than its companion—Mercury being denser
than Venus, Harth than Mars, Jupiter than Saturn, Uranus
than Neptune. This arrangement towards the Sun as a prin-
cipal centre appears, however, to be of more recent date than
the tendency to condensation in the Telluric belt; for Harth
is denser than Venus, and the great secular ellipticities of Mars
and Mercury suggest the likelihood of a quasi-cometary origin.
Similar tendencies would contribute to the chemical grouping
of atoms by pairs, which is essential for polarity and for the
already enumerated laws of chemical combination.
In the “‘ nascent state” particles may be regarded either as
parabolically perifocal, with the velocity of complete dissocia-
tion from a given centre, or as relatively at rest, and ready to
obey the slightest impulses of central force, The mean vis
viva of a system formed by two such particles would be
mx (/2)?+mx0=2m x1,
* Proc. Soc. Phil. Amer. xiv. p. 622 seqq.
Plat. Mag. 8. 5. Vol. 6. No. 39. Dec. 1878. 2G
450 Prof. P. EB. Chase on the Nebular Hypothesis.
representing a change from parabolic to circular orbits and a
condensation of two volumes into one.
At the parabolic limit between complete dissociation and
incipient aggregation, if the
focal abscisse x, = V F, is
taken as the unit of wave-
length, the value of the suc-
cessive ordinates, as well as
the velocity communicated
by uniform wave influence
acting through the entire
length of the ordinates, will vie 2 4k nls gs ee
be represented by V4, ; Ws
the resulting vis viva, and
the consequent length of
path, or major axis, commu-
nicable against uniform re- a
sistance, by 42, ; the succes- Ve
sive differences of major axis Vv
by 4. Hach normal, v 7,49, ; Via
equals the next ordinate,
Untifnti; there are, therefore, triple tendencies, both in the
axis of abscissas and on each branch of the curve, to successive »
differences of 4 in the major axes of aggregation, In conse-
quence of the meeting of abscissal, ordinal, and normal waves
in the axis, and the meeting of tangential, normal, and abscissal
waves upon the curve. Ateach node of aggregating collision
two of the wave systems are due to normally alternating rect-
angular oscillations, the third serving as a link between the
axial and the peripheral waves. The bisection of the normals
by their equivalent ordinates adds importance to the normal
major axes, and increases the tendency to aggregation at their
respective centres of gravity.
Chemical molecules and atoms are so small that we are un-
able at present to show so conclusively as in cosmical gravita-
tion that the “nascent” velocity, or the mean radial velocity
at the limit between complete dissociation and incipient aggre-
gation, is equivalent to the velocity of light. But the analogies
which are here presented are strengthened by the frequent
vivid, luminous, and thermal accompaniments of chemical
change, and by the electric polarity of combining elements.
It seems, therefore, reasonably certain that the same limiting
unit of velocity and vis viva, which can be easily traced in
light, heat, electricity, and gravitation, is also fundamentally
efficient in chemical affinity. M. Aymonnet, in his commu-
nication of a “Nouvelle Méthode pour étudier les Spectres
Prof. P. E. Chase on the Nebular Hypothesis. 451
Calorifiques,’’* says :—“ Je ferai remarquer, avant de terminer,
que l’étude des spectres calorifiques d’absorption, faite avec
des corps portés A diverses températures, peut et doit conduire
& la connaissance de lois physiques reliant les phénomenes
d’association et de dissociation des corps aux phénoménes calo-
rifiques et lumineux.” In another paper recently presented
to the French Academy, “Sur le Rapport des deux Chaleurs
Spécifiques d’un Gaz” t, M. Ch. Simon deduces the theore-
tical ratio C:¢::1:4:1. The first attempt at a solution of
the problem upon & priori grounds, appears to have been Pro-
fessor Newcomb’st{, who found from the hypothesis of actual col-
lisions, the ratio 5 : 3 if the particles were hard and spherical, or
4: 3if they were hard and not spherical ; the second, my own§,
based on the general consideration of all internal motions, which
led to the ratio 14232: 1; the third, M. Simon’s, which took
account of rotations and neglected other internal vibrations.
No surer test of any hypothesis has ever been suggested
than its furnishing a successful anticipation, or prediction, of
facts or phenomena that were previously unknown.
The harmonic progression which starts from Jupiter’s centre
of linear oscillation as a fundamental unit, and which has 4 for
its denominator-difference, was taken as the ground for sucha
prediction, in the communication which I read to the Ameri-
can Philosophical Society on the 2nd of May, 1873]|. Kirk-
wood had, a short time before, computed a probable orbit for
“Vulcan,” which satisfactorily represented the second interior
term of the series; and this accordance was one of the prin-
cipal sources of the confidence with which I ventured upon a
publication of the prediction.
Forty-one days afterwards, on the 19th of June, De la Rue,
Stewart, and Loewy communicated to the Royal Society cer-
tain conclusions, based upon three sets of sun-spot observa-
tions, taken in three different years, and extending over periods
respectively of 145, 123, and 139 days. Those observations
indicated some source of solar disturbance at ‘267 of Harth’s
mean radius vector, which represented the first interior term
of my series and gave the first conclusive verification of my
prediction. In announcing this fact to the Society, I pre-
sented three nearly identical series—the first being determined
solely by Jupiter, the second by Harth, and the third by rela-
tions of planetary and solar masses]. I gave precedence to
the first of these series, both because of Jupiter’s predominant
importance, and because of the many planetary harmonies
which are determined by Jupiter’s mean perihelion **.
* Comptes Rendus, 1xxxiii. pp. 1102-4, December 4, 1876.
T Ibid. p. 727, October 16, 1876. { Proc. Amer. Astr. Soe. v. p. 112.
§ Proc. Soc. Phil. Amer. xiv: p. 651. || Ibid. xiii. p. 238.
| Ibid. pp. 470, 472. a Ibid. p. 239.
2G2
452 Prof. P. KE. Chase on the Nebular Hypothesis.
At the time of the late total solar eclipse, Watson and Swift
each observed two small planets between the orbit of Mercury
and the sun. By comparing the published position of the
planet which was first announced by Watson, with some of the
most trustworthy of the recorded obser vations which were
thought by Leverrier to indicate intra-Mercurial Transits, |
Gaillot and Mouchez found an orbital period of 24:25 days*,
which represents the third interior term of my series and the
second strict verification of my prediction.
If a nebula condenses until all the particles in the equato-
rial plane have an orbital velocity, the mean radial vis viva at
the orbital centre of linear oscillation (47) is equivalent to the
orbital vis viva at 97. This equality may, perhaps, help to
account for the following approximate division of the planetary
system, the unit being Sun’s radius :—
9’7= 8lr. Mercury’s mean radius vector...... 83'17r.
937729724. Asteroid. (6 tte eceescs se. Sear eee 732°42 r.
9*7=65617r. Neptune’s extreme radius vector...6546°67 r.
The relatively rapid motion of Phobos (the inner satellite of
Mars), as well as the newly found meteoroidal character of the
corona, may reasonably lead us to look for an indefinite number
of further verifications among the results of future discovery.
Many of them, like many of the Neptunian harmonies which
are modified by the overshadowing mass of Jupiter, will pro-
bably elude all attempts at discovery; but the apparent import-
ance of 9 as a cosmical factor gives interest to the second series
in the following Table. The denominators in the first series are
of the general form (4n—3); those in the second series are of
the form (4v—3= 144n—111) , v being equivalent to 9(4n—3).
According to the nebular hypothesis, when Sun was ex-
panded to the present orbit of Jupiter, the collisions of subsi-
ding particles would tend to form a ring at two thirds the dis-
tance, or at 3'469 times Harth’s mean radius vector. If we
take this as a harmonic unit, }, we find that Venus’s mean
soon is well represented by 4, Mercury’s mean distance
by 2 $ and Kirkwood’s estimated semi- major axis of “‘ Vulean’”’
by zl. Here are, therefore, four terms of the first fu
series, th a denominator-difference of 4.
First Series.
No. Harmonic prediction. Confirmation.
Lae 1 = 5d 469 Node of subsidence 3-469
Diitee eset t ae 694 Venus, mean perih. *698
Oo eee: 1 = "385 Mercury, meand. °387
A ist wntoe a)5 = 267 ~~ Dela Rue, Stewart,
and Loewy ...... "267
D: Vy = 204 Kirkwood ‘ate sr-s: "209
Ge aytis3 oy = 165 Watson.06.c08-2%: "164
* Comptes Rendus, August 5, 1878,
Prot. P. E. Chase on the Nebular Hypothesis. 453
Second Series.
No. Harmonie prediction. Confirmation.
) ae ee ghy = SOE Helse aotesecshiseule ‘1060
Die Da 7 = ‘0196 PRET SH ys eareecene ee "0196
2: See shir = ‘0108 hmomniia, sy. eno ‘0108
A ek eae =hs = ‘0074 Phaost oss. ao saneee ‘0075
eke ack sty = “0057 IOW@AIVS adborsbc deer "0056
Ghai a = "0047 Sun’s surface...... ‘0047
Sv)
The first term of the second series (Helios) represents an
orbital node in which the time of revolution would be synchro-
nous with that of a solar half-rotation. This, as I have already
said, is equivalent to the time in which the continuous accele-
ration or retardation of Sun’s superficial gravitation would
communicate or overcome the velocity of Light. In order to
maintain equality of areas, the time of rotation in an expand-
ing or contracting nucleus should vary as the square of radius.
But g varies inversely as the square of radius; so that gt
should be constant at all stages of solar condensation, past,
present, or future.
The second term of the series (Themis) represents an orbital
node in which planetary revolution would be accomplished in
a sidereal day, or synchronously with Harth’s rotation on its
axis. The closeness of its relation to Karth, and its accordance
with the laws of harmony, are both fitly designated by its
name—hemis having been regarded as the daughter of Heaven
and Harth, and as the goddess of law and order.
The third term of the series (Hunomia) represents an or-
bital node in which planetary revolution would be accom-
plished synchronously with Jupiter’s rotation on itsaxis. Its
designation has also a double fitness; for Hunomia was the
mythical daughter of Jupiter and Themis, her name signifying
“good government.”
The fourth term of the series (Phaos) represents an orbital
node in which planetary revolution would be synchronous with
two planetary revolutions at Sun’s surface.
The fifth term of the series (Lychnis) represents an orbital
node at which Herschel’s theoretical “ subsidence’? would
give Sun’s present velocity of rotation.
The sixth term of the series represents a node which is some-
what within Sun’s apparent surface, or at its actual surface, pro-
vided the depth of the photosphere is 1 per cent. of Sun’s radius.
The one hundred and eighty-seventh term of the first series
represents an orbital node at the upper surface of Sun’s pho-
tosphere. Its harmonic denominator represents the ratio of
Sun’s mass to the aggregate planetary mass.
We see, therefore, in the second series, not only the nodat
influence of the largest two bodies in the system (Sun and
454 Sir J. Conroy on the Light reflected
Jupiter), but also an accordant influence of our own planet,
which is the central orb and the largest planet in the belt
which is bounded by the secular perihelion of Mercury and the
secular aphelion of Mars.
Herschel’s modified presentation of the nebular hypothesis,
and Gummere’s criterion, furnish the needful grounds for a
satisfactory explanation of such remarkable velocities as that
of the inner moon of Mars. ‘They also seem to require that
secondary orbs, when they revolve in less time than is required
for the rotation of their primaries, should be denser than the
primaries. There is therefore good reason for the further pre-
diction that, whenever the density of Phobos is ascertained, it
will be found to be greater than that of the planet itself. If
Mars has any other moons which have an orbital period of less
than twenty-four hours, they should also be of like superior
density. In these harmonies, as well as in many others, the
pointing to the primeval organizing agency of light is inter-
esting and suggestive. At the theoretical period of each of
the harmonic divisions, and at all other stages of nebular con-
densation, the rhythmical rotation of our day-star has been
repeating its unvarying confirmation of the old, old record.
In the dim and distant past, in the living present, and through
all coming time, from the great ‘‘ Beginning,” until the cul-
mination of prophecy when “the elements shall melt with
fervent heat,’’ nothing but divine intervention has disturbed,
or can disturb, the equality between the accumulated action
of solar gravity for a half-rotation and the velocity of light.
The harmonic hypothesis forecasts the same requirement at
the surface of the central orb in every stellar system; so that
the closing refrain in the hymn of each of the morning stars
is, was, and ever shall be:—
‘“‘ And God said, Let there be light; and there was hehe
“LVIIL On the Lig co r ae by Potassium Per rmanganate.
By Sir Joun Conroy, Bart.,
aad light reflected from the surface of sas perman-
ganate was originally examined by Haidinger, who an-
nounced (Sitzwngsberichte der kaiserlichen Akademie der Wis-
senschaften, Band vill. 1852, p. 1383), that when the light
reflected from the surface of the crystals and of the substance
rubbed on a plate of glass was examined with a dichroiscopic
lens, the portion polarized in the plane of incidence was light
yellow at low angles, and became white as the angle increased,
whilst the portion polarized perpendicularly was light yellow,
and became green and blue as the angle increased.
* Communicated by the Physical Society.
by Potassium Permanganate. A455
Professor Stokes found (Phil. Mag. vi. 1853, p. 400) that
the reflected light contained four bright bands, corresponding
in position to the dark bands of the absorption spectrum of a
solution of the substance, and that when the reflected light
was separated into two streams polarized in, and perpendicular
to, the plane of incidence, and then examined by a prism, the
bands were hardly visible in the one, and the other at a certain
angle consisted mainly of them.
HE. Wiedemann has recently published (Pogg. Ann. cli.
1874, p. 625) an account of some experiments he has made
on the same subject. He found that whilst the dark bands of
the reflection spectrum did not even partially cover those of
the absorption spectrum, they did not lie exactly intermediate
between any two of them—and, further, that the position of
the bands was independent of the angle of incidence, both with
ordinary light, and with that polarized in the plane of inci-
dence; but with light polarized perpendicularly to this plane,
the bands occupied the same position up to a certain angle,
and then with a slight increase of the angle suffered sudden
displacement towards the blue, and a new band appeared near
D. He also found that with light polarized perpendicularly
to the plane of incidence, the position of the bands was inde-
pendent of the nature of the surrounding medium, being the
same when the permanganate was in air, benzene, and bisul-
phide of carbon ; but when the light was polarized in the plane
of incidence, with the increase of the refractive index of the me-
dium the bands were more and more displaced towards the blue.
For some experiments I have made on the same subject 1
have used a Babinet’s goniometer, which has, in addition to the
ordinary horizontal stage, a vertical one so arranged that the
reflecting surface can be placed over the axis of the instru-
ment. Sunlight was used, which could be polarized in any
plane by a Nicol supported by the fixed arm of the goniometer ;
and a small direct-vision spectroscope, by Hilger, with a
“bright-point’”’ micrometer and a reflecting prism for bring-
ing a second spectrum into the field, was carried by the other
arm of the goniometer. By placing a beaker on the horizontal
stage, and, after the surface of the permanganate had been pro-
perly adjusted, filling it with the liquid and limiting the inci-
dent beam by a narrow vertical slit, the light reflected from
the surface of the substance when immersed in a liquid could
be examined.
The experiments were usually made with potassium per-
manganate crushed, and burnished with an agate on a piece of
finely-ground glass; and it was found that the light reflected
from the surface of crystals and from-that of the substance
rubbed on glass was identical; except that the blue rays were
456 Sir J. Conroy on the Light reflected
more intense in the light reflected by the crystals, and the
higher bands were more distinctly seen.
The surface-colour of potassium permanganate, and the posi-
tion and intensity of the bands in the spectrum of the reflected
light, are independent of the relative position of the plane of
incidence to the long axis of the crystal, or to the striz pro-
duced by rubbing, w anon the powdered substance burnished on
glass is used.
1, Surface-Colours.—Freshly prepared surfaces of potas-
sium permanganate appear of a pale yellow when light, either
unpolarized or polarized in any plane, is incident upon them
at low angles. But with ordinary light, and with light pola-
rized in the plane of incidence, the amount of white light
reflected is so great at high angles that the surface-colour, if
any, is completely masked.
When the incident light is polarized perpendicularly to the
plane of incidence, or when unpolarized light falls on the sur-
tace and a Nicol is placed between the eye and the permanga-
nate, with its principal section in the plane of incidence, the
surface-colour is seen to change as the angle increases, becom-
ing successively green and blue, and finally white and metallic.
The surface-colours alter with the surrounding medium.
The following Table gives, approximately, the colour at various
incidences, (A) when the light is either unpolarized or pola-
rized in the plane of incidence, and (B) when it is polarized
perpendicularly to that plane, for potassium permanganate in
air, tetrachloride and bisulphide of carbon.
}
| Surrounding medium.
| Angle of
| incidence. Ne ‘Tetrachloride of Bisulphide of
: | carbon. carbon.
3 { INa EE Pale yellow. | Yellow-green. | Yellow-green.
i u IB Assess ” ” ey) 9 _ Green. |
| 35 (APE. Pale yellow. Yellow-green. | Yellow-green. |
Erne \ * 0 5 Green. |
40 A ,.....| Pale yellow. Yellow-green. | Yellow-green. |
: 1B ess a a | Green. Green. |
45 a, Pale yellow. Yellow-green. | Yellow-green.
of} 1B f Sonk Hotes ,§ Green. Blue-green.
50 { AS meee | White. Yellow-green. | Yellow-green. |
“EB Liteee Pale yellow. Bright green. | Blue-green. |
| gg f Aes White. Green. Yellow-green.
lid gio 1 Bes | Yellow, with a | Blue-green. Blue-green.
green tinge.
60 le Sain White. Green. Green. |
5 {3 ert Brilliant green.| Blue-green. Blue-green.
6h oD EAD White. Green, Green.
pA sete] Blue-green. Blue-green. Blue-green.
ro, {Aue 4 White. Greenish. | Greenish white. |
ho iB Nie ' Blue. * 2 --
Sh Pee oh White. |
‘i 1B Tee Metallic, with | |
| blue shade. | |
by Potassium Permanganate. 457
2. Reflection Spectra.—With unpolarized light, and still more
with light polarized in the plane of incidence, the dark bands
in the spectrum of the reflected light are never very distinct.
I was not able to observe whether the bands shifted or not
as the angle of incidence increased, as the amount of white
light reflected at angles of 55° and upwards was so great as to
render the bands invisible. They appeared, however, as long
as they were visible, to coincide exactly with the bright spaces
in the absorption spectrum of a dilute solution of potassium
permanganate, which was thrown into the field by means of
the reflecting prism.
When the incident light is polarized perpendicularly to the
plane of incidence, the dark bands are far more distinctly seen.
At angles of less than 40° there are four bands, and the blue
end of the spectrum is very weak. As the angle of incidence
increases, the intensity of the blue rays diminishes; and then the
amount of light in the red decreases ; and at about 55° nearly
the whole of the light comes from the bright bands.
As the angle of incidence increases beyond this amount, the
dark bands gradually move towards the blue end of the spec-
trum; and at about 60° a new band appears near D. With any
further increase of the angle more of the blue rays are reflected;
and the bands fade away, those in the more refrangible part
of the spectrum disappearing first. The relative intensity of
the dark bands varies with the angle of incidence. When this
is small, the third and fourth bands, counting from the red end,
are darkest; with the increase of the angle the second, the
first, and finally the new band, become successively darkest.
I have not been able to obtain any satisfactory measure-
ments of the amount of the displacement of the bands, as,
when a spectroscope of sufficient power to render it an easily
measurable quantity is used, the bands become so ill-defined
that it is impossible to measure them. Approximately the
displacement amounts to about *006 in “ tenth-metres ;”’ and
the bands tend to coincide with the dark bands of the absorp-
tion spectrum, instead of with the bright bands as they do
when the angle of incidence is about 55° or less.
The shaded portions of the diagrams are intended to give
the relative amount of light, as determined by eye estimations,
in the different portions of the absorption and reflection
spectra of potassium permanganate—the ordinates being taken
to represent the intensity, and the abscissee wave-lengths. The
curved line gives the intensity of the light in the different
portions of the normal spectrum, as determined by Mossotti *
from Fraunhofer’s measurements, neglecting the minor irre-
gularities in the curve as given by him.
* Pogg. Ann. lxxii. p. 509.
458 = On the Light reflected by Potassium Permanganate.
Fig. 1 is the absorption spectrum of a solution of potassium
permanganate in water.
Figs. 2, 8, and 4 the reflection spectra, when the incident
light is polarized perpendicularly to the plane of incidence,
and falls on the surface at angles of 50°, 60°, and 70°.
E 450 F 500 550 D 600 650 C
As has already been announced by Wiedemann, the position
of the bands in the reflected light depends on the nature of the
surrounding medium. [rom the experiments I have made, it
appears that, with unpolarized light, the first dark band of the
reflection spectrum corresponds in position with the first bright
band of the absorption spectrum, whether the permanganate
is in air, benzene, or either bisulphide or tetrachloride of car-
bon; these liquids, however, act on the permanganate, and
after a short time the surface becomes altered, and then the
bands correspond with the dark bands of the absorption spec-
trum.
Figs. 4 and 5 represent the distribution of light in the spec-
trum, with fresh surfaces of potassium permanganate in bisul- &
phide and tetrachloride of carbon, when unpolarized light is
incident upon them at an angle of about 55°: in both cases
the bands are wider apart than in air.
A
ek 4500 2
LIX. On a possible Cause of the Formation of Comets’ Tails.
By AS. DAvis, Meas
T is well known that the phenomena observed during the
formation of a comet’s tail point to the conclusion that
the material which forms that appendage is being continually
emitted from the head of the comet with great velocity by
some force acting in a direction directly away from the sun.
The material appears in most cases to be first ejected from that
side of the comet’s nucleus which is turned towards the sun,
and afterwards, under the influence of this force, to be turned
backwards to form a tail. It is the object of this paper to
suggest an explanation of this force.
The remarkable identity which has been found to exist be-
tween the orbits of certain comets and the orbits of certain
meteoric clouds renders it little short of certain that comets
are themselves masses of solid or liquid bodies separated from
one another by great intervals, except perhaps at the nucleus,
where they may be closer together, and may even contain a
solid core. The spectroscope indicates the presence of gas in
a state of incandescence in the comet’s head and nucleus; but
how this incandescent gas is produced is not known.
The violent action which is observed to take place as a comet
approaches the sun, on that side of its nucleus which is
exposed to the solar radiation, appears to indicate that the
comet consists largely of matter which is rapidly volatilized
under the influence of the sun’s rays.
Let us assume that such is the case, and let us consider
what will be the effect of evaporation on the motion of one of
the bodies undergoing it.
In the first place the mass of a comet is so small, that the
force of gravitation towards the centre on any of the bodies at
some distance from the nucleus must be so small that it may
be left out of consideration. We know that a molecule of
matter in the gaseous condition has at ordinary and high tem-
peratures a very quick motion of translation. A molecule, as
it evaporates from the surface of one of the bodies composing
the comet, must acquire a velocity relative to the body of
several hundred yards per second. The body must in conse-
quence suffer a recoil in an opposite direction to that in which
the molecule escapes. Now since the evaporation is caused
by the sun’s heat, it must take place chiefly on that side of the
body which is exposed to the sun’s rays. The resultant effect
of all the small recoils due to the evaporation of the different
molecules will therefore be to drive the body in a direction
away from the sun. If the body has a motion of rotation, the
* Communicated by the Author.
460 Mr. A. 8. Davis on a possible Cause of
whole surface might in turn become exposed to the sun’s rays,
and evaporation would probably take place even on the side
turned away from the sun. But unless the body be of a re-
gular shape, the effect of evaporation will be to gradually stop
any rotation which it might at first have; for the force of
recoil from the evaporation would act upon it in the same way
as the wind does on a vane, and it would at length take up a
position with its longest axis in the direction of the sun.
Now let V be the average velocity relative to the body with
which the molecules escape from it. Let M be the mass of
the body just before the escape of a molecule of mass uw from
it. Then the velocity due to the recoil as this molecule escapes
will be = V. Now the molecules as they evaporate will start
off in various directions, but almost always more or less towards
the sun. Let us suppose, as being not far from the truth, that
the inclination which their directions have to a straight line
passing through the sun is on the average 45°; then the ave-
rage velocity due to recoil acquired by the body on the evapo-
é l :
ration of mass dm will be — es and the velocity acquired
whilst the mass of the body is being reduced by evaporation
from mj, to m, will be
m
eM,
NG (2. dons my,
ye ( a= Sg 1boa x logion”
Now the average velocity of hydrogen molecules at 0° C. is
1:06, of oxygen ‘266, and of water vapour *35 mile per second.
For the sake of illustration, let us suppose that V=-35, and
“+= 1000000, these being the values we should have to assign
2
if the body were a block of ice containing one gramme of sand
or any other non-volatile substance, the block itself being equal
in mass to a cubic metre of water. The velocity due to recoil
by evaporation would then be 3:42 miles per second, or about
295,000 miles per day. A tail would thus be formed which
would increase in length nearly a million miles in every three
days. The visible portion of this tail would consist of solid or
liquid matter which had resisted evaporation; but there would
also be present in the tail a large portion of the gas formed
during evaporation ; for since the evaporating gas has a velo-
city relative to the body from which it is evaporating of °35
mile per second, those portions of the gas which have evapo-
rated since the body acquired by recoil a velocity greater than
-35 mile per second will be also carried backwards into the
tail. The estimate of the rapidity of tail-formation | have
the Formation of Comets’ Tails. 461
just made has been made on the supposition that the tempera-
ture of the escaping gas is 0° C. If the absolute temperature
in Centigrade units of the gas be ¢, we must multiply the
t
273,
of tail-formation greatly exceeded one million miles in three
days, except in the case of those comets which have approached
very near to the sun, and where, consequently, the tempera-
ture at which the evaporation has taken place must have been
very great. Donati’s comet is one of the most striking ex-
amples of comets with large and rapidly formed tails which
have not approached very near to the sun; and in Donati’s
comet the tail increased in length from 14 million miles on
August 30 to 51 million miles on October 10, or at an average
rate of somewhat less than a million miles in a day.
Those comets which have formed large tails with exceptional
rapidity have approached very near to the sun. Thus the
comet of 1680, which formed a tail 60 million miles long in
two days during its perihelion passage approached so near to
the sun as to be exposed to a solar radiation 25,600 times more
intense than that to which the earth is exposed. To use Sir
John Herschel’s words, ‘‘ In such a heat there is no solid sub-
stance we know of which would not run like water, boil, and
be converted into vapour or smoke.” It seems probable that it
is only the shortness of the time during which the comet is ex-
posed to such a temperature which prevents its being altogether
converted into vapour. The smaller fragments of the comet
will, I conceive, be entirely evaporated ; and the last portions
of vapour from any fragment will, as I have shown, be carried
backwards with immense velocity into the tail. After this
vapour has arrived in colder regions, it seems probable that it
will condense and become visible as a cloud of finely divided
solid or liquid matter. In these cases then the visible tail will
consist, not of matter which has resisted evaporation, but
largely and perhaps almost entirely of matter which has eva-
porated and has recondensed.
In conclusion, if this be the true explanation of the pheno-
menon of comets’ tails, then every meteoric cloud of matter
which approaches sufficiently near to the sun to undergo rapid
evaporation must become tailed like a comet, as it passes
through its perihelion passage. I would suggest that we
may have here an explanation of the radiated structure of the
sun’s corona. As different masses of meteoric matter approach
close to the sun, the smaller fragments will be almost or entirely
evaporated, a large portion of the vapour from them being
carried rapidly away from the sun, thus giving rise to a
above estimate by Now in no case has the rapidity
462 Notices respecting New Books.
coronal protuberance. Thus the radiated structure, and the irre-
gular and variable form of the corona would be accounted for.
Cheltenham College,
October 21, 1878.
LX. Notices respecting New Books.
The Theory of Sound. By Joun Witi1aM Strutt, Baron Ray-
LEIGH, W.A., PRS, formerly Fellow of Trinity College, Cam-
bridge. Volume II. London: MacMillan and Co. 1878. 8vo,
pp. 302.
E noticed the First volume of this work shortly after its pub-
lication (5th ser. vol. v. p. 66). The Second volume—which, we
presume, completes the work *—is now before us. We could not,
perhaps, give it higher praise than to say that it is worthy of its
predecessor. Not to speak of actual contributions to our knowledge
of the Theory of Sound which have been made by the author, it is
scarcely possible to overestimate the value to the student of a
perfectly trustworthy work which brings together the substance
of memoirs scattered through a variety of periodicals. Not fewer
than about a hundred and twenty or thirty memoirs are referred
to in the course of these volumes, most of which would be inac-
cesible to students living away from the chief centres of intel-
lectual activity. These, however, are not the only students who
are benefited by such a work as the present. Even those who
are more favourably situated rarely look at the memoirs unless
they are distinctly interested in their subjects at the time of
publication; and this is particularly the case with memoirs on
such a subject as the Theory of Sound, the mere reading of which
may involve a considerable expenditure of time and labour.
The subject of the present volume is Aerial Vibrations. In its
general method it resembles its predecessor. Thus, in the former
volume, the discussion of Vibrating Systems in general (chap. iv.
and vy.) is preceded by a very careful consideration of a particular
case, viz. that of a system having one degree of freedom (chap. iii.) ;
so, in the present volume, the discussion of the general problem
of vibrations in three dimensions (chap. xiv. and xv.) is preceded
by that of the cases of Vibration in tubes (chap. xii.), and of some
other special problems, including the Reflection and Refraction of
Plane Waves (chap. xiii.). These four chapters, together with an in-
troductory chapter on ‘‘ Aerial Vibrations ” (chap. xi.), fill more than
half the volume. The remainder is divided into chapters on the
Theory of Resonators (chap. xvi.), on Applications of Laplace’s
Functions to Acoustical Problems (chaps. xvu. and xviii.), and on
Fluid Friction (chap. xix.).
* The Work, as it stands, might certainly be accepted as a complete
treatise on what is generally understood by the Theory of Sound, viz. the
Kinetics of Acoustical Vibrations; and we should have supposed the
work to be complete had not the publisher made himself responsible for
an announcement of Vol. iii., and also for a notice as to volumes subsequent
to the first.
Notices respecting New Books. 463
The seventeenth and eighteenth chapters are almost wholly oc-
eupied with contributions made by the author to the Theory of
Sound. Thus the seventeenth chapter does, indeed, begin with a
long extract from Professor Stokes’s paper, “On the Communication
of Vibrations from a Vibrating Body to a Surrounding Gas,” in
which he applies his determination of the complete value of w (the
symbol which represents a disturbance propagated wholly outwards)
to the explanation of “‘a remarkable experiment by Leslie, according
to which it appeared that the sound of a bell vibrating in a partially
exhausted receiver is diminished by the introduction of hydrogen”
(vol. 1. p. 207). The explanation of this seemingly paradoxical
phenomenon, it may be remarked, had escaped the penetration of
Su J. Herschell, who “thought that the mixture of two gases
tending to propagate a sonnd with different velocities might pro-
duce a confusion resulting in a rapid stifling of the sound” (p. 214,
vol. i1.). So far the contents of the chapter are due to Professor
Stokes ; the remainder is taken from two papers by the author
published in the ‘ Proceedings of the Mathematical Society ’—** On
the Vibrations of a Gas contained within a Rigid Spherical Enve-
lope,” and an “Investigation of the Disturbance produced by a
Spherical obstacle on the Waves of Sound.”
The eighteenth chapter contains a discussion of considerable in-
terest from a mathematician’s point of view, viz. “‘a Proof of La-
place’s Expansion for a Function which is Arbitrary at every point
of a Spherical Surface.” But to put this in a proper light we must
look back to vol. i., where a proof is given of Fourier’s Series. The
method adopted may be indicated as follows:—The author first
considers the motion of a vibrating string when the ends are
not absolutely fixed—a state of things which he represents by sup-
posing a mass (M), treated as unextended in space, attached to
each end and acted on by a spring () towards the position of equi-
librium,—and then particularizes his solution in two ways, first, by
supposing M=0and p=, so that the ends of the string are fast;
secondly, by supposing that both p and M are zero, a case which
might be represented by supposing the ends of the string capable
of sliding on two smooth rails perpendicular to its length. From
the results thus obtained Fourier’s Theorem is shown to follow.
In connexion with this proof, the author remarks :—‘‘So much
stress is often laid on special proofs of Fourier’s and Laplace’s
Series, that the student is apt to acquire too contracted a view of
the nature of those important results of analysis ” (p. 159, vol. i.);
and he adds, in a note, that ‘“‘ the best system for proving Fourier’s
Theorem from Dynamical considerations is an endless chain stretched
round a smooth cylinder, or a thin re-entrant column of air inclosed
in a ring-shaped tube” (p. 160, vol. i.).
It will be observed that the remark above quoted implies a
promise of a similar discussion of Laplace’s Series; and this is ful-
filled in chap. xvii. The ‘‘ system ” adopted is that of a thin sphe-
tical sheet of air. In chap. xvil.,as we have seen, there is a
discussion of the vibrations of a gas contained within a rigid sphe-
464 Intelligence and Miscellaneous Articles.
rical envelope ; and it is observed (p. 238) that a similar treatment
will apply to the vibrations of air between two concentric spherical
envelopes ; but when the difference between the radii is very small
in comparison with either, the problem reduces itself to that of a
spherical sheet of air. The case in which the velocity-potential W
is symmetrical with reference to the poles, is treated first ; and itis
shown that it can be represented by a series whose general term is
JS 3
where ” is an integer even or odd, and P,,(u) Legendre’s function.
If now ¢=0, w is an arbitrary function of the latitude, and we see
that P=A,+A,P(u)+. . -+AnPa(u)+.. .
‘This is, of course, only a particular case of Laplace’s Series. But
by similar reasoning on the general value of ~ Laplace’s Series is
established. At each step of the process the case is considered in
which the radius of the sphere becomes infinite, and we pass physi-
cally to the case of a plane layer and analytically from Laplace’s
to Bessel’s functions. ‘‘ The vibrations of a plane layer of gas are
of course more easily dealt with than those of a layer of finite cur-
vature ; but I have preferred to exhibit the indirect as well as the
direct method of investigation, both for the sake of the spherical
problem itself with the corresponding Laplace’s expansion, and
because the connexion between Bessel’s and Laplace’s functions
appears not to be generally understood” (p. 265, vul. ii.).
This discussion is, as we have already remarked, of purely ma-
thematical interest ; and, indeed, from the nature of the case, by far
the largest part of the work is addressed to mathematicians. Here
and there, however, are discussions of which the interest is purely
physical, such as, in the present volume, that on Whispering Gal-
leries (p. 115), that on the Refraction of Sound by Wind (p. 123),
and others. But our limits will not allow us to do more than
mention their existence.
LXI. Intelligence and Miscellaneous Articles.
A FEW MAGNETIC ELEMENTS FOR NORTHERN INDIA.
BY R. 8. BROUGH.
HAYvY G recently had occasion to measure the dip of the needle
and the strength of the horizontal component of the earth’s
magnetic force at Calcutta, Jubbulpore and Allahabad, with a view to
ascertaining to what extent the indications of an arbitrarily cali-
brated galvanoscope uncorrected for the local value of the earth’s
magnetism, would be trustworthy, | think it desirable to put the
results on record.
The horizontal intensity was measured with a Kew-pattern port-
able unifilar magnetometer; and the observations have been corrected
for temperature, torsion and scale error. _
Intelligence and Miscellaneous Articles. 465
| | | Horizontal |
Stations. Longitude. | Latitude. | Date. forcein ; Dip.
| dynes.
a i ea a See
Calcutta ....| 88 22 50 | 22 32 32 | Jan. 1878 | 0°37158 | 28 59 30 |
Jubbulpore ..| 80 00 00 | 23 10 00 | Dec. 1877 | 036667 | 29 23 30 |
Allahabad ....| 81 54 12 | 25 27 43 | Dec. 1877 | 0°35915 | 33 18 45
Dividing the horizontal component by the cosine of the dip, we
obtain the total force thus :—
Calcutta . 0°42482 dyne.
Jubbulpore. 0°42084 __,,
Allahabad . 0°42977 _,,
There are on record several observations of the dip in Calcutta,
which it will be interesting to bring together here.
The dip appears to have been measured for the first time when
the French corvette ‘La Chevrette’ visited these waters in 1827,
by M. de Blosseville, who found it then to be*
26° 32’ 38”.
Ten years later, in 1837, on the occasion of the visit of another
French corvette, ‘La Bonite, to the Hugli river, the dip was
measured at Kalagachia (Diamond Harbour) by the chief Hydro-
grapher, who found it to bet
| 26° 39' 04",
exhibiting a change of only 0° 06’ 26” from the result of the
earlier measurement.
The next and most recent measurement was made by the brothers
Schlagintweit in March 1856 and in April 1857, in which years it
was found to be respectively ¢
28° 06° 43”
and 28° 22' 56”.
The same observers found the dip at Jabalpur in December 1855
to be§ 28° 31' 08"
Their measurements of the horizontal force gave :—
0°37386 dyne at Calcutta in March 1856,
036644 ,, . in April 1857,
0°39959 ,, at Jabalpur in December 1855.
A very valuable series of observations was made in 1867-68 by
the late Captain Basevi, R.E., under the orders of Colonel J. T.
Walker, C.B., R.H., Superintendent of the G. T. Survey (now
Surveyor-General of India), at 14 stations, extending from 15° 6'
to 30° 20’ north latitude||; but none of them are coincident with
the three stations under consideration.
The values of the dip and horizontal intensity at the limiting
stations of the series were as follows :— |
* Asiatic Researches, vol. xviii. part i. p. 4.
+ Proceedings, Asiatic Society of Bengal, Wednesday, 3rd May, 1837.
t ‘Observations in India and High Asia,’ vol, i. § Loe. cit.
| General Report of the Operations of the Great Trigonometrical Survey
of India during 1867-68.
Phil. Mag. 8. 5. Vol. 6. No. 89. Dee. 1878. 2 H.
466 Intelligence and Miscellaneous Articles.
| | les
Horizontal
| Stations. | Latitude. |Longitude.; Date. intensity. Dip.
LS ea a BS I] ee
|Namthabad | 15 06 00 | 7
| Deyrah ....} 80 20 00 | 7
7 36 00 |April 1868] 0:37401 | 11 40 56
8 06 00 | Jan. 1867] 0-33604 | 41 27 34 |
—Proceedings of the Asiatic Society of Bengal, February 1878.
ON MOLECULAR ATTRACTION IN ITS KELATIONS WITH THE .
TEMPERATURE OF BODIES. BY M. LEVY.
The demonstration which we have given, in our last communica-
tion, of a general law upon the dilatation of bodies rests on the two
fundamental propositions of thermodynamics, and upon this other
proposition—that the mutual actions of the molecules of a body are
independent of their temperatures.
This last proposition we have assumed as an hypothesis ; we wish
now to prove that it flows from the first proposition of thermody-
namics, so that our law itself will be found to be built solely upon
the two propositions which serve as a foundation for that science.
To justify this assertion, let us conceive any body in motion under
the influence of :—(1) external forces, F; (2) mutual actions, f, on
the nature of which we will make no hypothesis; (3) a certain quan-
tity of heat received from without.
Let d’Q be the quantity, positive or negative, of heat received
during an infinitely short interval of time dt (we will employ the
characteristic d’ for the infinitely small quantities which are not
exact differentials or which are not known a priori to be so): a
portion d’g of this heat is empioyed for increasing the temperatures
of the various points of the body; the surplus, or d’Q —d’q, is trans-
formed into work, and gives rise to a quantity of work E(d'Q—d’Q),
E being the mechanical equivalent of heat. .
Suppose that the body describes any complete cycle, which means
not only that all its points describe closed curves and resume their
velocities at the end of the orbit, but also that they resume their tem-
peratures. If to this cycle we apply the theorem of the vires vive,
weiget 0= faO,F+(20.f+E(Q—E fag,
©, denoting an elemental work.
But, in virtue of the first proposition of thermodynamics,
{2€.F+E feQ=o,
whence
VG, 7. Be )—0,.05 ee (a)
which is equivalent to saying that the quantity under the symbol
is the total differential of a certain function of all the variables,
which resume their values at the end of the cycle—that is, not only
of the coordinates «;, y;, zi of the various points of the material
system considered, and which we suppose to be n in number (so
that 1=1, 2, 3,...n), but also of the temperatures T; of those
Intelligence and Miscelianeous Articles. 467
points. Thus SO fa Bd HAW, a sce eed &. ()
U being a function of the 4n variables 4;, y;, z;, T;. This function
is no other than that which is called the internal heat.
The equation (a), or its equivalent (6), is the only one that can
be directly deduced from the first proposition of the mechanical
theory of heat, if no preconceived idea on the nature of heat be ad-
mitted ; and we do not understand the reasonings by which some
have attempted to deduce from it that 3@,f is a differential. It
has certainly been proved that, for certain particular cyles, during
which the temperature or the quantity of heat received remains
invariable, we have fa. f=0; but from this it is not permissible
to conclude that =@, f is a differential.
I now say that, whatever idea may be formed of the nature of heat,
the quantity of heat d'q employed to raise the temperatures of the
various points of the body, without displacement of those points, is
necessarily the exact differential of a function of the n variables T;.
In fact, the quantity of heat necessary for raising by dT; the
temperature of a molecule of mass m; is necessarily an expression
of the form m,y,;dT;, as y; can only depend on the temperature T; of
the molecule and on the specific constants relating to the material
of which it is composed.
Therefore the total quantity of heat remaining in the sensible
state is d'q= Tmyat, =< yi f vy, aT, :
dq being thus a differential, so also is XT,/f, in virtue of (a); and
as this sum is an expression of the form
>, (Xda; + Y,dy; -- Z;dz;)
containing no term in @T;, it cannot but be the differential of a
function not containing the variables T;, consequently containing
only the coordinates 2;, y;, 2;.
Jt follows from this :—first, that molecular attractions admit a
function of the forces; secondly, that this function remains the
same whatever may be the temperatures of the various points of
the body ; and, thirdly, that consequently the mutual action of two
molecules of a body i is quite independent of the temperature—which
completely justifies the law laid down in our last communication,
and places it among the necessary consequences of the two propo-
sitions of thermodynamics.
That law, that the pressure of a body heated under constant
volume varies linearly with the temperature, proves that the empiric
definition of temperature adopted by Dulong and afterwards by
Regnault, viz. the pressure of a gaseous mass with constant volume,
might be easily extended to the case in which, instead of a gaseous
mass, any other body was in question.
Finally, without wishing here to draw from this law all the con-
sequences which it admits of, we will nevertheless make the follow-
ing remark :—
In a previous communication we have sought to discover what
are the data strictly necessary to be derived from experiment to
enable one to study a body from the thermodynamic point of view ;
468 Intelligence and Miscellaneous Articles.
and the importance of this question will be especially apparent if
we observe that in the best treatises superabundant data are taken
from observation, even for constructing the simplest theory of all
(that of gases). "We then arrived at a result which can in brief be
enunciated thus :—'To know all the isothermal lines of a body, and
one of its adiabatic lines, is sufficient.
The law which forms the object of the present investigation con-
ducts to the following much more satisfactory and quite unexpected
result :—Jn order to know all the isothermal lines and all the adiabatic
lines of a body, and consequently to be able to study it completely,
at is necessary and sufficient to know two of rts rsothermal lines and
one only of tts adzabatic lines.
In physical terms, one may say that it is sufficient to observe :—
Ist, the dilatation of a body under two different pressures, or, more
generally, for two series of states answering to two curves arbitra-
rily traced 1 in the plane of the ( pv)’s (which i is equivalent to saying
that the w? observations, of which we spoke at the outset of our
previous communication, are replaced by two simple infinities of
observations); 2ndly, one of the specific heats, or one particular
pressure only, or, more generally, for a single series of states of the
body corresponding toa curve arbitrarily traced in the plane.
If we admit, with MM. Clausius and Hirn, that the thermal
capacity of every substance is a constant, this second series of ob-
servations reduces itself to a single observation.—Comptes Rendus
de Académie des Sciences, Sept. 30, 1878, t. Ixxxvu. pp. 488-491.
THE SONOROUS VOLTAMETER. BY THOMAS A. EDISON, PH.D.
The sonorous or bubble voltameter consists of an electrolytic cell
with two electrodes—one in free contact with a standard decompo-
sable solution, and the other completely insulated by vulcanized
rubber except two small apertures, one of which gives the solution
free access to the insulated electrode, and the other allows the
escape of bubbles of hydrogen as they are evolved by electrolysis.
With a given current and a given resistance a bubble is obtained
each second, which is seen at the moment of rising, and which at
the same time gives a sound when it reaches the air. The resist-
ance may be reduced so as to give one bubble in one, five, ten, or
fifty seconds, or in as many hours. I have compared this instru-
ment with the ordinar y voltameter, and find it much more accurate.
By the use of a very small insulated electrode and but one aperture,
through which both the gas and water current must pass, great in-
crease of resistance takes place at the moment when the bubble is
forming ; and just before it rises, a Sounder magnet included within
the battery-circuit opens, closing again when ‘the bubble escapes,
thus allowing by means of a Morse register the time of each bubble
to be recorded automatically. This apparatus, when properly made,
will be found very reliable and useful in some kinds of work, such
as measuring the electromotive force of batteries &c. By shunting
the voltameter and using a recorder it becomes a measurer, not only
of the current passing at the time, but also of that which has passed
through a circuit from any source during a given interyal.— Silh-
man’s American Journal, Noyember 1878.
469
INDEX to VOL. VI.
ABNEY (Capt.) on photography
at the least-refrangible end of the
solar spectrum, 154.
Acoustic repulsion, on, 225, 270.
Alloys of copper, zine, and nickel, on
the analysis of, 14.
Amalgam surfaces, on motions pro-
duced by dilute acids on some, 211.
Ammonio-argentic iodide, on the
behaviour of, 73.
Audition, on some phenomena of
binaural, 383.
Aurora borealis, on the, 289, 360, 423.
Ayrton (Prof. W. E.) on the electri-
cal properties of bees’-wax and lead
chloride, 132.
Ball (Dr. R. 8S.) on the principal
screws of inertia of a free or con-
strained rigid body, 274.
Bayley (T.) on the analysis of alloys
containing copper, zinc, and nickel,
14
Becquerel (H.) on the magnetic ro-
tation of the plane of polarization
of light, under the influence of the
earth, 76.
Bees’-wax, on the electrical proper-
ties of, 132.
Blaikley (D. J.).on brass wind instru-
ments as resonators, 119.
Blake (Rev. J. F.) on the measure-
ment of the curves formed by Ce-
phalopods and other mollusks, 241.
Boltzmann (Prof. L.) on some prob-
lems of the mechanical theory of
heat, 236.
Bonney (Prof. T. G.) on the serpen-
tine and associated igneous rocks
of Ayrshire, 149.
Books, new:—Ferrers’s Spherical
Harmonics, 66; Blanford’s Indian
Meteorologist’s Vade Mecum, 67 ;
Smyth’s Astronomical Observa-
tions, 145; Clifford’s Elements of
Dynamic, 806; Proctor’s Moon,
309; Tait and Steele’s Dynamics
of a Particle, 891; Baron Ray-
leigh’s Theory of Sound, 462.
Bosanquet (R. H. M.) on the relation
between the notes of open and
stopped pipes, 63.
Brass wind instruments as resonators,
one LIS:
Brough (R. 8.) on some magnetic
elements for Northern India, 464.
Brown (J.) on the theory of voltaic
action, 142.
Callaway (C.) on the quartzites of
Shropshire, 233.
Cephalopods, on the measurement of
the curves formed by, 241. |
Chase (Prof. P. E.) on the nebular
hypothesis, 128, 448; on Watson’s
intra-Mercurial planet, 320.
Chemical change, on the laws of, 371.
Chemistry, recent researches in solar,
161.
Clarke (Col. A. R.) on the figure of
the earth, 81.
Clausius (Prof. R.) on the mecha-
nical theory of heat, 237, 400.
Comets’ tails, on a possible cause of
the formation of, 459.
Conroy (Sir J.) on the light reflected
by potassium permanganate, 454.
Cooper (W.-J.) on the action of per-
manganate of potash on certain
gases, 288.
470
Copper, on the analysis of alloys con-
taining, 14.
Croll (Dr. J.) on the origin of ne-
bule, 1; on the cataclysmic
theories of geological climate, 148.
Crova (A.) on the spectrometric in-
vestigation of some sources of light,
314.
Cryohydrates and cryogens, on, 35,
105.
Davis (A. 8.) on the formation of
comets’ tails, 459.
Debray (I1.) on the dissociation of
the oxides of the platinum group,
ood.
Deville (H. Ste.-Claire) on the disso-
ciation of the oxides of the plati-
num group, 394.
Dicarbopyridenic acid and salts, 21.
Dilatation, on a universal law respect-
ing the, of bodies, 397.
Dipicoline, on some compounds of, 30.
Disruptive discharge in air, on the
effect of variation of pressure on
the length of, 185.
Draper (Prof. H. ) on the solar eclipse
of Jan. 29th, 1878, 318.
Dvorak (V). on acoustic repulsion,
220.
Earth, on the figure of the, 81; on
the properties of the matter com-
posing the interior of the, 263.
Edison (Dr. J. A.) on the sonorous
voltameter, 468.
Edlund (Prof. E.) on unipolar induc-
tion, atmospheric electricity, and
the aurora borealis, 289, 360, 423.
Electrical discharges in insulators,
on, 438.
Electricity, researches on atmo-
spheric, 289, 360, 423; on the ex-
citation of, by pressure and fric-
tion, 316.
Electrodes, on the depolarization of
the, by solutions, 159.
Electromagnets, on the resistance of
telegraphic, 177. .
Ennis (J.) on the origin of the power
which causes the stellar radiations,
216.
Fielden (Capt. H. W.) on the geolo-
gical results of the Polar expedi-
tion, 71.
Fluid-motion, on the applicability of
Lagrange’s equations in certain
cases of, 354,
INDEX.
Foyaite, on, 153.
Fritsch (H.) on the excitation of elec-
tricity by pressure and friction, 316.
Gases, on the action of permanganate
of potash on certain, 288; on the
mechanical theory ‘of Crookes’s
stress in, 401.
Geikie (Prof. J.) on the glacial phe-
nomena of the Outer Hebrides, 146,
Geological climate, on the cataclys-
mic theories of, 148.
Geolgical Society, proceedings of the,
68, 146, 233, 310.
Glacial period, on the distribution of
ice during the, 149.
Glaisher (J. W. L.) on multiplication
by a table of single entry, 331.
Gordon (J. E. H.) on the effect of
variation of pressure on disruptive
discharge in air, 185.
Gray a on the determination of
magnetic moments in absolute
measure, 321.
Greenstones, on the so-called, of
Cornwail, 69.
Guthrie (F.) on salt-solutions and
attached water, 35, 105.
Hautefeuille (P.) on the crystalliza-
tion of silica, 78.
Heat, on the actinic theory of, 79;
on the mechanical theory of, 236,
237, 400.
Heaviside (O.) on the resistance of
telegraphic electromagnets, 177;
on a test for telegraph lines, 436.
Hennessy (Prof. H.) on the proper-
ties of the matter composing the
interior of the earth, 263.
Hicks (Dr. H.) on the me tamorphic
rocks of Loch Maree, 150.
Hood (T. J.) on the laws of chemical
change, 371.
Hug hes (Pr of.) on the physical action
of the microphone, 44.
Hydrodynamic problems in reference
to the theory of ocean currents,
192.
Induction, researches on unipolar,
_ 289, 3860, 423.
Insulators, on electrical discharges
in, 438.
Isopyridine, on some compounds of,
28.
Jamieson (T. F.) on the distribution
of ice during the glacial period,
149.
INDEX.
Lea (M. C.) on ammonio-argentic
~ lodide, 73.
Lead, on the electrical properties of
the chloride of, 132.
Lévy (M.) on a universal law respect-
ing the dilatation of bodies, 397 ;
on molecular attraction in its re-
lations with the temperature of
bodies, 466.
Light, on the magnetic rotation of
the plane of polarization of, under
the influence of the earth, 76;
spectrometric study of some sources
of, 314; on the, reflected by potas-
sium permanganate, 454.
Lippmann (M.) on the depolarization
of the electrodes by the solutions,
159.
Lockyer (J. N.) on recent researches
in solar chemistry, 161.
Lutidine, on the oxidation of, 19.
Magnetic elements for Northern
India, on, 464.
figures illustrating electrody-
namic relations, 348,
moments, on the experimental
determination of, in absolute mea-
sure, 321.
Mayer (Prof. A. M.) on acoustic re-
pulsion, 231.
Meldola (R.) on a cause for the ap-
pearance of bright lines in the solar
spectrum, 50.
Microphone, on the physical action
of the, 44.
Millar (W. J.) on the transmission
of vocal and other sounds by wires,
115.
Mills (Dr. E. J.) on thermometry, 62.
Molecular attraction in its relations
with the temperature of bodies,
on, 465.
Mollusks, on the measurement of the
curves formed by, 241.
Moore (C.) on the paleontology of
the Meux’s- Well deposits, 310.
Mosandrum, on the newelement, 238.
Multiplication, on, by a table of
single entry, 351.
Nebulz, on the origin of, 1.
Nebular hypothesis, on the, 128, 448.
Nickel, on the analysis of alloys con-
taining, 14.
Ocean currents, on the theory of, 192.
Phillips (J. A.) on the so-called
greenstones of Cornwall, 69.
471
Photography at the least-refrangible
end of the solar spectrum, on, 154.
Picoline and its derivatives,researches
on, 19.
Pipes, on the relation between the
notes of open and stopped, 63.
Plateau’s film-systems, on the pro-
duction of, 75.
Platinum group, on the dissociation
of the oxides of the, 394.
Polarization stress in gases, on, 401.
Potassium permanganate, on the light
reflected by, 454.
Preston (8. T.) on the proper motion
of the sun in space, 393; on diffu-
sion as a means for converting nor-
mal-temperature heat into work,
400.
Prestwich (Prof.) on Artesian wells,
234
Puluj (Dr. J.) on the friction of va-
pours, 157.
Purser (Prof. J.) on the applicability
of Lagrange’s equations in certain
eases of fluid-motion, 354.
Puschl (Prof. C.) on the actinic
theory of heat, 79.
Radiation, on the origin of solar, 128.
Rainbows, on certain phenomena ac-
companying, 272. .
Ramsay (Dr. W.) on picoline and its
derivatives, 19.
Rance (C. E. De) on the geological
results of the Polar expedition,
fis
Rayleigh (Lord) on acoustic repul-
sion, 270.
Resonators, on brass wind instruments
as, 119.
Rontgen (Prof. W. C.) on electrical
discharges in insulators, 438.
Sabine (R.) on motions produced by
dilute acids on some amalgam sur-
faces, 211.
Salt-solutions and attached water,
on, 35, 105.
Screws of inertia of a free or con-
strained rigid body, on the prin-
cipal, 274.
Sheibner (Dr. C. P.) on Foyaite, 153.
Siemens (W.) on telephony, 93.
Silica, on the crystallization of, in the
dry way, 78.
Silver, on the combination of the
iodide of, with ammonia, 73.
Sky, on the blue colour of the, 267.
472
Smith (J. L.) on the new element
mosandrum, 288.
Solar chemistry, recent researches in,
161.
eclipse of July 29th, onthe, 318.
spectrum, on a cause for the
appearance of bright lines in the, 50.
Sound, on the production of aerial
currents by, 229.
Sounds, on the transmission of vocal
and others, by wires, 115.
Stars, on the origin of the, 216.
Stellar radiations, on the origin of
the power which causes the, 216.
Stoney (G. J.) on the mechanical
theory of Crookes’s stress in gases,
401.
Sun, on the proper motion of the, in
_ space, 393.
Telegraph lines, on a test for, 436.
Telephony, on, 93.
Terquem (A.) on the production of
Plateau’s film-systems, 75.
Thermometry, researches in, 62.
Thompson (Prof. S. P.) on certain
ella accompanying rain-
ows, 272; on magnetic figures
illustrating electrodynamic rela-
tions, 348; on some phenomena of
binaural audition, 383.
INDEX.
Unwin (Prof. W.C.) on the discharge
of water from orifices at different
temperatures, 281.
Ussher (W. A. E.) on the triassic
strata of the South-western coun-
ties, 68; on the triassic rocks of
Normandy, 152.
Vapours, on the friction of, 157.
Voltaic action, on the theory of,
142.
Voltameter, on the sonorous, 468.
Wanklyn (Prof. J. A.) on the action
of permanganate of potash on cer-
tain gases, 288.
W ater, on salt-solutions and attached,
30, 105; on the discharge of, from
orifices at different temperatures,
281.
Watson’s intra-Mercurial planet, note
on, 320.
Wichmann (Dr. A.) on the micro-
scopical investigation of some Hu-
ronian clay-slates, 311.
Worthington (A. M.) on the blue
colour of the sky, 267.
Zinc, on the analysis of alloys con-
taining, 14.
Zoppritz (Dr. K.) on the theory of
ocean currents, 192.
END OF THE SIXTH VOLUME.
Priuted by Taytor and FRAncis, Red Lion Court, Fleet Street.
Phil Mag.5.5. Vol. 6. PI. 1.
w”
>|
Youn
5 la ie Sle ee
FL
FN
“9ZTS [TF = STBIS
“SLNIOd 1VGON
Mintern Bros hth.
D.J.B. del.
Apaanon pu03sy
15°6 Megoluns. |T15°6Megohms
Temperature.
x
100°C.
ints (235 ole
Phil Mag. S. 5. Vol. 6. PL.
Ih voces
IPT Bie Fe
60°C
=e
"Ormarantes. Time. 50 minutes
3 th
‘61°C
Mintern Bros hth.
Fi 6. 4.
75*6Megoluns.
15°6Megohans
Fig. 5.
ve
4
S|
$
a 100°C,
Fié.6.
Ayzarq oA pPUry
R
Phil Mag. S. 5. Vol. 6. Pl Il.
Fig.3.
185870 Megoluns.
(67135 Megohms.
4
SS
Temperature. ae
1h fhe Ze
x.
50 muuites
(61°C
Mintern Bros lith.
7 Y
a |
« =
my
7A
7
;
a
/
;
i
| Phil. Mas. S.5. Vol. 6. PL. IL
|
oo oa
LEVATION. | |
METHOD oF
THE EFFECT OF ALTE
ON THE L
ELECTRIC DIS
E
ae. A.
PIXHOU
7
PLAN.
Mintern Bros imp.
Phil. Mag. S.5. Vol. 6. PL.IIL.
METHOD oF MEASURING
THE EFFECT OF ALTERATION OF PRESSURE
ON THE LENGTH OF
ELECTRIC DISCHARGES IN AIR
BY
J.E.H. GORDON
PIXHOLME 1878
k-=--- fe 6M-----3
N.
IN ELEVATIO ,
[eRe ommpiengeegecs 0)
SCALE.
fi
3
INGHES,
Mintern Bros imp.
Phil Mag S.5.Vol 6.PL IV.
Big. 2.
Mintern Bros imp.
=
é
ipo Be
Phil. Mag. S.5.Vol 6 PL IV.
Fig. 6.
Mintern Bros imp-
EMC ERSEUELAVSSIAL
Phil. Mag. $.5.Vol.6. PLV.
150
SECTIONAL ELEVATION.
120
90
30
Mintern Bro® lith
200
500
600
700 800 900
Ald 919A S'S SEW Ta
Phil.Mag.S.5.Vol.6: PL.VI.
Whiteman &Bess, PhotpLithe tothe Oneen.
MAGCNEDIG BIGURES
ILLUSTRATING ELECTRO-DYNAMIC RELATIONS.
Phil.Mag. S.5.Vol.6. PL.VIL.
Whiteman &Bass, PhotoLitho to the Oneen,
MAGNETIC FIGURES
ILLUSTRATING ELECTRO-DYNAMIC RELATIONS.
2
ts
Phil. Mag. S.5. Vol. 6. Pl. VII.
Fig. 4.
Mintern Bros lith
Phil. Mag. S.5.Vol. 6. Pl. VII.
UL
q Ope er
oO LS re .
7m
Th re) b a ee
~
JON. A SX al
c
Fig. 3. ue
Fig 4
Mintern Bro® lith
JULY 1878. = Nd 34
Published the First Day of every Month.—Price 2s. 6d.
THE
LONDON, EDINBURGH, anp DUBLIN
|| PHILOSOPHICAL MAGAZINE,
| AND
JOURNAL OF SCIENCE.
Being a Continuation of Tilloch’s ‘Philosophical Magazine,’
Nicholson’s ‘Journal,’ and Thomson’s ‘Annals of Philosophy.’
™~
CONDUCTED BY
: SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.C.8.
SIR WILLIAM THOMSON, Kuyt. LL.D. F.R.S. é&e.
AND
| WILLIAM FRANCIS, Pu.D. F.L.S. F.R.A.S. F.C.S.
: FIFTIL SERIES.
. Sy
| N° 34.—JULY 1878. Rane
LONDON:
PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET,
Sold by Longmans, Green, Reader and Dyer; Kent and Co.; Simpkin, Marshall and
Co. ; and Whittaker and Co.;—and by A. and C. Black, and Thomas Clark, Edin- |
FPN SA Sth Sate ater defy Ot os* ahs" ds,
burgh ; Smith and Son, Glasgow :—Hodges, Foster, and Oo., Dublin:—Putnam,
New York:—and Asher and Co., Berlin. ;
ay"
BRITISH ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE,
22 ALBEMARLE STREET, LONDON, W.
The next ANNUAL GENERAL MEETING will be held at DUBLIN,
commencing on WEDNESDAY, August 14.
President-Elect,
W. SPOTTISWOODE, Esq., LL.D., F.R.S., F.R.A.S., F.R.G.S.
Notice to Contributors of Memowrs.—Authors are reminded that, under an
arrangement dating from 1871, the acceptance of Memoirs, and the days on which
they are to be read, are now, as far as possible, determined by Organizing Commit-
tees for the several Sections before the beginning of the Meeting. It has therefore
become necessary, in order to give an opportunity to the Committees of doing
justice to the seyeral Communications, that each Author should prepare an
Abstract of his Memoir, of a length suitable for insertion in the published Trans-
actions of the Association, and that he should send it, together with the original
Memoir, by book-post, on or before August 1, addressed thus:—“General
Secretaries, British Association, 22 Albemarle Street, London, W. For Section
aa eee ” Ifit should be inconvenient to the Author that his Paper should
be read on any particular day, he is requested to send information thereof to the
Secretaries in a separate note.
G. GRIFFITH, M.A.,
Assistant General Secretary, Harrow.
With 112 Illustrations and 5 Maps of the Stars. 8vo, 18s.
POPULAR ASTRONOMY.
By SIMON NEWCOMB, LL.D.,
Professor U.S. Naval Observatory.
“Tt is unlike any thing else of its kind, and will be of more use in circulating
a knowledge of Astronomy than nine-tenths of the books which have appeared
on the subject of late years.”—Saturday Renew.
MacmiiLian and Co., London.
THE GEOLOGICAL RECORD.
The First Volume of this yearly publication has been issued. It describes or
notices works on Geology, Mineralogy, and Palzontology published during the
year 1874, and contains upwards of 400 pages.
Copies can be had of Messrs. Taylor and Francis, Red Lion Court, Fleet Street,
London. Price 15s.
The Second Volume, describing works published in 1875, is now published.
Price 10s. 6d. to Subscribers and 16s. after publication.
Subscribers’ names and remittances should be sent to the publishers, Messrs.
Taylor and Francis, Red Lion Court, Fleet Street, London, E.C.
UNIVERSITY OF LONDON.
Now ready, price 4s. (post-free, 4s. 73d.).
THE CALENDAR FOR THE YEAR 1878,
Containing the Regulations for each Examination, the Examination Papers set
during the past year, Lists of Graduates, and other information.
TayLor and Francis, Publishers to the University,
Red Lion Court, Fleet Street, E.C.
[ADVERTISEMENTS continued on 3rd page of Cover.
eee i ee ee Le a Re eS
——
Vol. 6. AUGUST 1878. No. 35.
: Be
ne Published the First Day of every Month.—Price 2s. 6d. %
THE
LONDON, EDINBURGH, snp DUBLIN
PHILOSOPHICAL MAGAZINE,
AND
JOURNAL OF SCIENCE.
Being a Continuation of Tilloch’s ‘Philosophical Magazine,
Nicholson's ‘Journal,’ and Thomson’s ‘Annals of Philosophy.’
CONDUCTED BY
SIR ROBERT KANE, LL.D. F.R.S. M.R.IA. F.C.8.
SIR WILLIAM THOMSON, Knr. LL.D. F.R.S. &e.
sp AND
WILLIAM FRANCIS, Pu.D. F.L.S. F.R.A.S. F.C.S.
FIFTH SERIES. ;
| ae
N° 35.—AUGUST 1878. 4
WITH TWO PLATES,
Tlustrative of Mr. D. J. Buarxixny’s Paper on Brass Wind Instru-
‘ments as Resonators, and Prof. Ayrton’s Paper on the Electrical
Properties of Bees’-wax and Lead Chloride.
LONDON:
PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET,
Sold by Longmans, Green, Reader and Dyer; Kent and Co.; Simpkin, Marshall and
Co. ; and Whittaker and Co. ;—and by A. and ©. Black, and Thomas Clark, Edin-
burgh; Smith and Son, Glasgow :—Hodges, Foster, and Co., Dublin :—Putnam,
New York :—and Asher and Co., Berlin.
New Edition, in post 8vo, price 14s. cloth,
ROCKS CLASSIFIED AND DESCRIBED.
By BERNARD VON COTTA.
An English Translation, by P. H. LAWRENCE (with English, German,
and French Synonymes), revised by the Author.
“ Certainly, the finest work on lithology as yet presented to British readers.” —
Popular Science Review.
London: LoneMANs and Co.
A SCIENCE PRIMER.
ON THE NATURE OF THINGS.
By JOHN C. MACVICAR, LL.D., D.D.
Crown 8vo, with Illustrations, 3s. 6d.
Published this day, to be had of all Booksellers.
Witi1am Biackwoop and Sons, Edinburgh and London.
Just published, price 2s., royal 8vo,
NITRATE AND GUANO DEPOSITS
IN THE
DESERT OF ATACAMA.
(Published by authority of the Government of Chili.)
TAYLOR AND FRANcIS, Red Lion Court, Fleet Street, E.C.
THE GEOLOGICAL RECORD.
The First Volume of this yearly publication has been issued. It describes or
notices works on Geology, Mineralogy, and Paleontology published during the
year 1874, and contains upwards of 400 pages. .
Copies can be had of Messrs. Taylor and Francis, Red Lion Court, Fleet Street,
London. Price 15s.
The Second Volume, describing works published in 1875, is now published.
| Price 10s. 6d. to Subscribers and 16s. after publication.
i Subscribers’ names and remittances should be sent to the publishers, Messrs. -
Taylor and Francis, Red Lion Court, Fleet Street, London, H.C.
UNIVERSITY OF LONDON.
Now ready, price 4s. (post-free, 4s. 73d.).
THE CALENDAR FOR THE YEAR 1878,
Containing the Regulations for each Examination, the Examination Papers set
during the past year, Lists of Graduates, and other information. —
Taytor and Francis, Publishers to the University,
Red Lion Court, Fleet Street, E.C.
[ADVERTISEMENTS continued on 3rd page of Cover.
: Published the First Day of every Motth. Price 2s. 6d.
THE
LONDON, EDINBURGH, ayp DUBLIN
| PHILOsoPHicaL MAGAZINE,
“AND
JOURNAL OF SCIENCE.
Being a Continuation of Tilloch’s ‘Philosophical Magazine,
Nicholson's ‘Journal,’ and Thomson’s ‘Annals of Philosophy.’
“CONDUCTED BY.
ae SIR ROBERT KANE} LL.D. F.RS. MBIA. FCS.
= SIR WILLIAM THOMSON, Kyr. LL.D. F-.RB.S. ke.
Bs AND =?
| WILLIAM FRANCIS, Ps.D. F.LS. ERAS, F.C.8,
- - ~——= N° 36.—SEPTEMBER 1878.
WITH A PLATE.
" lustrative of Mr. J. E. H. Gorpon’s Paper on the Effect of Vauidtion: of
pa eure on the Length of Disruptive Discharge in Air.
eee) LONDON:
_ PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET,
by Longmans, Green, Reader and Dyer; Kent and Oo.; Simpkin, Marshall and
and Whittaker and Co. ;—and by A. and O. Black, and Thomas Clark, Edin-
“Smith and Son, Glasgow :—Hodges, Hort, and Co., Dublin; eae
Ne eee ont Asher and Oo., Berlin,
. ‘SEPTEMBER 1878. =~ - No. 36;
FIFTH SERIES. SSN
ae
oy DF
|
Errata in No, 35 (August 1878).
0
Page 89, line 8 from bottom, for 2 dx+- — i read 5 dx+ z
— 90, — 18, for 7’=cy>? read 2@= Cyt?
Price 7s. 6d, crown 8vo, with numerous Woodcuts,
AN ELEMENTARY TREATISE ON STATICS,
With numerous Examples and Solutions, for the use of Students preparing for
Examination.
By J. W. MULCASTER, F.R.A.S.,
Military Tutor.
TayLor and Francis, Red Lion Court, Fleet Street, E.C.
Price 2s., royal 8vo,
NITRATE AND GUANO DEPOSITS
IN THE
DESERT OF ATACAMA.
(Published by authority of the Government of Chili.)
TAYLOR AND Francis, Red Lion Court, Fleet Street, H.C.
In a few days, price 2s. 6d., post-free 3s.
THE UNIVERSITY COLLEGE CALENDAR.
The CALENDAR for 1878-79, containing the Bye-laws, Regulations, Me-
morials, List of Students, Exhibitioners, &c., together with much useful infor-
mation respecting the College and School.
TayLor and Francis, Red Lion Court, Fleet Street, E.C-
THE GEOLOGICAL RECORD
Describes or notices works on Geology, Mineralogy, and Paleontology.
Volume for 1874, price 15s; for 1875, price 16s. Price to Subscribers 10s. 6d.
per volume.
The volume for 1876 nearly ready.
Subscribers’ names and remittances should be sent to the publishers, Messrs.
Taylor and Francis, Red Lion Court, Fleet Street, London, H.C.
The Annals and Magazine of Natural History.
Including Zoology, Botany, and Geology.—Monthly, price 2s. 6d.
Complete sets (in Numbers) may be obtained at the following prices :—
The First Series, in 20 volumes, from 1838 to 1847. Price £10,
The Second Series, in 20 Volumes, from 1848 to 1857. ,, £10.
The Third Series, in 20 volumes, from 1858 to 1867. 55 Sole
TayLor and Francis, Red Lion Court, Fleet Street, E.C.
THE LONDON, EDINBURGH, AND DUBLIN
Philosophical Magazine and Journal of Science.
A Journal devoted to Physics, Astronomy, Mechanics, Chemistry, Mineralogy,
and the Allied Sciences. Monthly, price 2s. 6d.
Complete sets (in Numbers) may be obtained at the following prices :—
A set of the First Series, from 1798 to 1826 (wanting a few plates), in 68
volumes. Price £15.
The Second Series, from 1827 to 1832, in ]1 volumes. Priee £2 4s.
The Third Series, in 37 volumes, from 1832 to 1850. ges 2
TAYLor and Francis, Red Lion Court, Fleet Street, E.C.
[ADVERTISEMENTS continued on 3rd page of Cover.
a ae VULODER 1875. INO. 34
Published the First Day of every Month.—Price 2s. 6d.
: THE ’
: LONDON, EDINBURGH, anyp DUBLIN
| PHILOSOPHICAL MAGAZINE,
AND
JOURNAL OF SCIENCE.
|| Being a Continuation of Tilloch’s ‘Philosophical Magazine,’
Nicholson’s ‘Journal,’ and Thomson's ‘Annals of Philosophy.’
CONDUCTED BY
7 SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.GS.
i SIR WILLIAM THOMSON, Knr. LL.D. F.RS. &e.
: | : AND
WILLIAM FRANCIS, Ps D. F.LS. F.R.A:S. F.C.S.
FIFTH SERIES. ~~. 6,
N° 37.—OCTOBER 1878.» 7
WITH TWO PLATES.
Illustrative of the Rev. J. F. Buaxe’s Paper on the Measurement-of
the Curves formed by Cephalopods and other Mollusks, and Prof,
E. Epiunn’s on Unipolar Induction, Atmospheric Electricity, and
the Aurora Borealis.
LONDON:
PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET,
Sold by Longmans, Green, Reader and Dyer; Kent and Co.; Simpkin, Marshall and
Co.; and Whittaker and Co. ;—and by A. and C. Black, and Thomas Clark, Edin-
burgh; Smith and Son, Glasgow :—Hodges, Foster, and Co., Dublin:—Putnam,
New York :—and Asher and Co., Berlin, |
mE TE PS
A
Ce
ROYAL SCHOOL OF MINES.
DEPARTMENT OF SCIENCE AND ART.
During the Twenty-eighth Session, 1878-79, which will commence on the
ist of October, the following COURSES of LECTURES and PRACTICAL
DEMONSTRATIONS will be given :—
. Chemistry. By E. Frankland, Ph.D., F.R.S.
. Metallurgy. By John Percy, M. 1: ERS.
: Natural History. By T. H. Huxley, LL.D., F.R.S.
Manerstvey: \ By Warington W. Smyth, M.A., F.R.S., Chairman.
. Geology. By John W. Judd, F.R.S.
‘ Applied Mechanics. By T. M. Goodeve, M.A.
. Physics. By Frederick Guthrie, Ph.D., F.R.S.
. Mechanical Drawing. By Rev. J. H. Edgar, } M.A.
The Lecture Fees for Students desirous of becoming Associates are £30 in one
sum, on entrance, or two annual payments of £20, exclusive of the Laboratories.
Tickets to separate Courses of Lectures are issued at £3 and £4 each.
Officers in the Queen’s Service, Her Majesty’s Consuls, Acting Me Agents
and Managers, may obtain Tickets at reduced prices. :
Science Teachers are also admitted to the Lectures at reduced fees.
For a Prospectus and information apply to the Registrar, Royal School of
Mines, Jermyn Street, London, 8.W.
OMsID OP ON
TRENHAM REEKS, Registrar.
GOVERNMENT GRANT OF £1000.
A Meeting of the Government-Grant Committee will be held in February
1879. Itis requested that applications to be considered at that Meeting be
forwarded to the Secretaries of the Royal poe meee House, before
the 3lst of December 1878.
GOVERNMENT FUND OF £4000
FOR THE PROMOTION OF SCIENTIFIC RESEARCH.
A Meeting of the Government-Fund Committee will be held in February
1879. It is requested that applications to be considered at that Meeting be for-
warded to the Secretaries of the Royal Society, Burlington House, before the
3lst of December, 1878.
FOREIGN BOOKS AT FOREIGN PRICES.
WILLIAMS AND NORGATE’S NATURAL HISTORY CATALOGUE :—
Anthropology, Zoology, Physiology, Botany, Geology, Paleontology, &c., in
French, German, and other F oreign Languages. Post free, ld.
WILLIAMS AND NORGATE’S NATURAL SCIENCE CATALOGUE :—
Mathematics, Astronomy, Meteorology, Physics, Electricity, Chemistry, Micro-
scopy, Optics, Mechanics, Engineering, Technology, &c. Post free, 1d.
14 Henrietta Street, Covent Garden, London; and
20 South Frederick Street, Edinburgh.
THE GEOLOGICAL RECORD
Describes or notices works on Geology, Mineralogy, and Paleontology.
Volume for 1874, price 15s; for 1875, price 16s. Price to Subscribers 10s. 6d.
per volume.
The Volume for 1876 is nearly ready.
Subscribers’ names and remittances should be sent to the publishers, Messrs.
Taylor and Francis, Red Lion Court, Fleet Street, London, E.C.
[ADVERTISEMENTS continued on 3rd page of Cover.
Published the First : Day of ever ry Month.—Price 2s. 64d.
THE
LONDON, EDINBURGH, anp DUBLIN
fe OP HICAL MAGAZINE,
AND
JOURNAL OF SCIENCE.
|
| _ Being a Continuation of Tilloch’s ‘Philosophical Magazine,
Nicholson’s ‘Journal,’ and Thomson's ‘Annals of Philosophy.’
CONDUCTED BY
SIR ROBERT KANH, LL.D. F.R.S. M.R.LA. F.C.S.
SIR WILLIAM THOMSON, Knr. LL.D. F.R.S. &e.
AND
WILLIAM FRANCIS, Pu.D. F.L:S. ys F.C.S.
oe rp aN
aS ae
FIFTH SERIES. » \~ sey |
N° 38.—NOVEMBER 18738: ~ ee “an
WITH THREE PLATES.
MIlustrative of Mr. T. Gray’s Paper on the Experimenta] Deterniination’
of inencite Moments in Absolute Measure, and Prof. 8.:P. THOMP
son’s on Magnetic Figures illustrating Electrodynamic Relations.
LONDON:
PRINTED BY TAYLOR. AND FRANCIS, RED LION. COURT,, BLEET. BIRERT,
Sold by Longmans, Green, Reader and Dyer; Kent and Co.; Simpkin, Marshall and
NOVEMBER 1878. No. 38.
A on emeetrrar er eerernetliiey egy Nea RrB FS eee i ot ee ew ern
5
|
Co. ; and Whittaker and Co. ;—and by A. and C. Black, and Thomas. Clark, Edin-
burgh; Smith and Son, Glasgow : :—Hodges, Foster, and Co., Dublin: ‘Putnam,
New York: —and ee and Co., Berlin.
ee
FOREIGN BOOKS AT FOREIGN PRICES.
WILLIAMS AND NORGATE’S NATURAL HISTORY CATALOGUE :—
Anthropology, Zoology, Physiology, Botany, Geology, Palseontology, &c., in
French, German, and other Foreign Languages. Post free, ld.
WILLIAMS AND NORGATE’S NATURAL SCIENCE CATALOGUE :—
Mathematics, Astronomy, Meteorology, Physics, Electricity, Chemistry, Micro-
scopy, Optics, Mechanics, Engineering, Technology, &c. Post free, 1d.
14 Henrietta Street, Covent Garden, London ; and
20 South Frederick Street, Edinburgh.
THE GEOLOGICAL RECORD
Describes or notices works on Geology, Mineralogy, and Paleontology.
Volume for 1874, price 15s; for 1875, price 16s. Price to Subscribers 10s. 6d.
per volume.
The Volume for 1876 is now ready, price 16s.
Subscribers’ names and remittances should be sent to the publishers, Messrs.
Taylor and Francis, Red Lion Court, Fleet Street, London, H.C.
Price 2s. 6d., post-free 3s.
THE UNIVERSITY COLLEGE CALENDAR.
The CALENDAR for 1878-79, containing the Bye-laws, Regulations, Me-
morials, List of Students, Exhibitioners, &c., together with much useful infor-
mation respecting the College and School.
TAYLOR and Francis, Red Lion Court, Fleet Street, B.C.
THE GEOLOGY AND FOSSILS OF THE TERTIARY AND
CRETACEOUS FORRIATIONS OF SUSSEX.
By the late FREDERICK DIXON, Esq., F.G.S.
NEW EDITION.
Revised and augmented by
T. RUPERT JONES, F.B.S., F.G.S.,
Professor of Geology, Staff College, Sandhurst.
Aided by the Surviving Contributors to the First Edition—Professor Owen, ©.B.,
LL.D., F.R.S., F.LS., F.G.8.; Sir P. de M. Grey-Egerton, Bart., M.P., F.R.S., F.G.S.;
and Professor T. Bell, F.R.S., F.L.S., F.G.S.: and by W. Carruthers, Hsq., F.R.S.,
¥.L.S., F.G.8.; T. Davidson, Esq., F.R.S., F.G.S.; R. Etheridge, Hsq., F.R.S., F.G.S.;
John Evans, Esq., D.C.L., F.R.S., F.G.S.; Professor John Morris, F.G.S.; E. YT.
Newton, Esq., F.G.8.; W. J. Sollas, Esq., F.G.S.; W. Topley, Esq., F.G.S.; Ernest
H. Willett, Hsq., F.S.A.; Henry Willett, Esq., F.G.S.; Henry Woodward, Esq., LL.D.
F.RS., F.G.S.; T. Wright, M.D., F.R.S., F.G.8. ; and other Scientific Friends.
‘The descriptions and lists of Sussex Fossils are carefully revised in this New Edition,
vome of Mantell’s plates being added, and a full account given of the Subwealden
Joring and its results, of the Warren Farm Well, and the Archeological Discoveries
at Cissbury and elsewhere in Sussex.
‘The work forms an clegant quarto volume of 500 pages, with many woodcuts, and
upwards of Sixty Plates, some coloured ; also a Geological Map of the County by W.
‘Topley, Esq., and a section of the Subwealden Borings.
‘The price to Subscribers is £2 2s.; and, as the number is limited to 250 copies, early
zpplication is respectfully solicited. :
Brighton: W. J. Surry, 41, 42, and 43 North Street.
[ADVERTISEMENTS continued on 3rd page of Cover.
i. ; "Publis hed the First Day of every Month.—Price 2s. 6d.
f -
THE
LONDON, EDINBURGH, ann DUBLIN
| PHILOSOPHICAL MAGAZINE,
— AND Fee ;
|} #JOURNAL OF SCIENCE.
i ie Being a Continuation of Tilloch’s ‘Philosophical Magazine,’
- Nicholson’s ‘Journal, and Thomson’s ‘Annals of Philosophy.’
CONDUCTED BY
ԤIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.G.S. |
SIR WILLIAM THOMSON, Kxr. LL.D. F.RS. &.
iar AND
WILLIAM FRANCIS, Pu.D. F.L.S. F.RAS. F.C.
FIFTH SERIES.
\ N° 39. DECEMBER 1878.
| phe
a | LONDON:
: 2 PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STRERT,
: ¢ Sold by Longmans, Green, Reader and Dyer; Kent and Co.; Simpkin, Marshall and
4} —s-: Go. and Whittaker and Co. ;—and by A. and CO, Black, and Thomas Clark, Edin-
4 sc burgh; Smith and Son, Glasgow :—Hodges, Foster, and Co., Dublin :—Putnam,
~ i ——New York :—and Asher and Oo., Berlin.
at : Sa
aS | DECEMBER 1878. No. 39. ™~
|
}
|
|
|
|
|
|
ROYAL INSTITUTION OF GREAT BRITAIN,
ALBEMARLE STREET, PICCADILLY, W.
LECTURE ARRANGEMENTS BEFORE EASTER 1879.
(Lecture Hour, THREE 0’CLOCK.) .
CHRISTMAS LECTURES.
Professor Dewar, M.A., F.R.S.—Six Lectures on a Soap Bubble; on De-
h cember 28 (Saturday), 31, 1878; January 2, 4, 7, 9, 1879.
BEFORE EASTER, 1879. |
Professor Epwarp A. Scuarer, F.R.S., Fullerian Professor of Physiology,
R.1.—Twelve Lectures on Animal Development; on Tuesdays, Jan. 14 to April 1.
J. H. Gorpon, Esq.—Four Lectures on Electric Induction; on Thursdays,
January 16 to February 6. |
Professor TynDALL, D.C.L., F.R.S., &.—Eight Lectures on Sound, including
its Recent Applications and Methods of Reproduction; on Thursdays, Feb. 13
to April 3.
Paseo H. G. Srrry, F.L.S., F.G.S.—Three Lectures on Reptilian Life ;
on Saturdays, January 18, 25, February 1.
RreinaLD W. Macan, Esq. (Ch. Ch. Oxford).—Four Lectures on Lessing ;
on Saturdays, February 8 to March 1.
Water H. Poutock, Esq., M.A.—Two Lectures on Richelieu and Colbert ;
on Saturdays, March 8, 15.
“. Seymour HapeEn, Esq.—Three Lectures on Etching; on Saturdays,
March 22 to April 5.
Professor DEwAR will give a Course of Lectures after Easter.
Subscription to all the Courses in the Season, Two Guineas; to a Single
Course, according to length, One Guinea, or Half-a-Guinea; to the Christmas
Course, Children under Sixteen, Half-a-Guinea. Tickets now issued daily.
The Friday Evening Meetings will begin on January 17, at 8 p.m. Pro-
fessor Tyndall will give a Discourse on the Electric Light, at9 p.m. Succeeding -
Discourses will probably be given by Professor W. E. Ayrton, Mr. H.H. Statham,
Rev. R. Haweis, Professors Roscoe and Huxley, Mr. I. B. Tylor, Professor Abel,
Sir Henry C. Rawlinson, and Dr. Warren De la Rue. To these Meetings Mem-
bers and their Friends only are admitted.
Persons desirous of becoming Members are requested to apply to the Secre-
tary. When proposed, they are admitted to all the Lectures, to the Friday Even-
ing Meetings, and to the Library and Reading Rooms; and their Families are
admitted to the Lectures at a reduced charge. Payment:—First Year, Ten
Guineas; afterwards, Five Guineasa Year; ora composition of Sixty Guineas.
FOREIGN BOOKS AT FOREIGN PRICES.
WILLIAMS AND NORGATEH’S NATURAL HISTORY CATALOGUE:—
Anthropology, Zoology, Physiology, Botany, Geology, Paleontology, &c., in
French, German, and other Foreign Languages. Post free, ld.
WILLIAMS AND NORGATE’S NATURAL SCIENCE CATALOGUE :—
Mathematics, Astronomy, Meteorology, Physics, Electricity, Chemistry, Micro-
scopy, Optics, Mechanics, Engineering, Technology, &c. Post free, la.
14 Henrietta Street, Covent Garden, Londen; and
20 South Frederick Street, Edinburgh.
THE GEOLOGICAL RECORD
Describes or notices works on Geology, Mineralogy, and Paleontology.
Volume for 1874, price 15s; forr Pe pre 16s., Price to Subscribers 10s. 62.
2! ;
por volume. F735
The Volume for 1876 is now ready, price’F6s.
Subscribers’ names and remittances should be sent to the publishers, Messrs.
Taylor and Francis, Red Lion Court, Fleet Street, London, E.C.
Ban 6 i ahr,
ne hal \
ITHSONIAN INSTITUTION LIBRARIES
VIN
3 9088 0
1202 4204
Live Music Archive
Librivox Free Audio
Metropolitan Museum
Cleveland Museum of Art
Internet Arcade
Console Living Room
Books to Borrow
Open Library
TV News
Understanding 9/11