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Philosophical Magazine Series 6
ISSN: 1941-5982 (Print) 1941-5990 (Online) Journal homepage: http://www.tandfonline.com/loi/tphm17
XV. The recent eclipse results and Stokes-Plack's æther
L. Silberstein Ph.D.
To cite this article: L. Silberstein Ph.D. (1920) XV. The recent eclipse results and Stokes-Plack's æther , Philosophical Magazine Series 6, 39:230, 161-170, DOI: 10.1080/14786440208636027 To link to this article: http://dx.doi.org/10.1080/14786440208636027
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Date: 26 June 2016, At: 05:07

THE LONDON, EDINBUROH, ASD DUBLIN
PHI L OSOP HI CA L MAGAZINE
AND
JOURNAL OF SCIENCE.
-
[SIXTH SERIES.]

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I~'EBR UAR Y 1920.

XV. The recent .Eclipse Results and Stokes-Planck's .z~Ether.
By L, SILBERSTEIN,Ph.D., Lecturer in Mathem. Physics
at the University of Rome *

1. ]'T is well known that, in 1845, Stokes proposed a 1_ theory of aberration (Phil. Mag. xxvii, p. 9), which
was based on the assumption that the luminiibrous tether surrounding our planet is dragged along in its annual motion so that the velocity of the tether relative to the Earth is nil at its surface, and, increasing continuously~ becomes equal and opposite to the Earth's velocity at very large distances from the Earth or, to put it short, at infinity. The purpose of this hypothesis, as opposed to that of Fresnel's stagnant tether, was to give a rOorous independence of all purely terrestrial optical experiments from the Earth's annual motion (combined with that of the solar system). In order to account for the semi-terrestrial phenomenon known as astronomical aberration, Stokes had to assume that the motion of the tether, between the Earth and the stars in question, is purely irrotatlonal. But, by a well-known theorem of" hydrodynamics, this assumption was not compatible with the incompressibility of Stokes's tether and, at the same time, with the absence of slipping over the Earth's
surface. 2. In order to overcome this essential difficulty Max
Planck has suggested that the incompressibility could be

9 Communicatedby Sir 0liver Lodge.

_Phil. Maff. S. 6. Vol. 39. No. 230. Feb. 1920.

M

16"2 Dr. L. Silberstein o~ the recent Ecllpse Results

given up * and replaced by the assumpf~ion that the ~ether is condensed round the Earth, and other celestial bodies, as if it were subjected to the force of gravitation and behaved more or less like a perfect gas. Lorentz, in spite of his personal preference for a fixed ~th~r, took up Plauck'h idea and worked out the problem under the special (but by no means the only possible) assumption that the ~ether density p and pressure p obey Boyle's law, p=ap, wher~ ~=const. IFM !)e the E a r t h ' s mass, in astronomical units, this gives

p-~p~e~/~, . . . . . . .

(1)

whore p~ is the density at infinity and r the distance of any exterlml point h'om the Earth's centre. The maximum velocity of slip ;it the Earth's surface ( r = R ) , in the direeti,m opposite to that o[ its motion becomes t

1'

0 -3

), . . . . (2)

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where 0-=~M/R, and v~ is the velocity of ~he rather, relative to the Earth, at infinity.
To account f,)r the astronmnical aberration within the limits of experimental error it is necessary and sufficient to make v=r~,, v~. This gives, by (2), with sufficient approximation (since the required 0- is manifestly so large as to make the second term of the denominator negligible),

a'~- - 0"04 e~,

so that the said requirement is amply satisfied by

= 10"2 . . . . . . . .

(E)

This means, according to (i), a condensation $o[ the rather -unounting at the Earth's surface to little less than

s-- -p = 27000, P~
and gives at the same time for the (lower lilnit of the) coefficient a the value IO'2R/M, to which we may return
9 @ H. A. Lorentz's paper on Stokes's theory of aberration in Amsterdam -Proc.for 1898 99, p. 443, reprinted in vol. i. of his Abhandlungen.
t A short deducdou (,f this formula will be found in Lorentz'~ Theory of Eleetrons~' ]909, p. 314. ++ What is commonly called "condensation." would in our case be
P 1. But it will be convenient to use this as a short name for p/p~, wP~hich will henceforth be denoted by s.

and Stokes-P la~ck's IEther.

163

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later on. In order to reduce the slip to 89per cent. of v| a condensation of about 60000 would be required *
In view of this considerable condensation, required by the theory of Stokes-Planck, Lorentz made in 1909 (' Theory of Electrons,' pp. 173-4) the following characteristic remark:--
"In this department of physics, in which we can make 11o progress without some hypothesis that looks somewhat startling at first sight, we must be careful not rashly to reject a new idea, and in making his suggestion Planck has certainly done a good thing. Yet I dare say that this assumption of "m enormously condensed ether, combined, as it must be, with the h.ypott~esis tl~at the velocit9 of li~jl~t is not in Che least altered bg it, is not very satisfaetor~l." [The las~ words are italicised for our present purpose,]
I n fact, such a condensation, introduced ad hoc and serving only the negative purpose of not upsetting the theory of aberration, did not seem very satisfactory, and the present writer ]ms as recently as 191~ expressed the same opinion i,l his book on Relativity (p. 63), not so much to defend Fresnel's and Lorentz's fixed rather, as to prepare the reader's mind for the complete abolition of the rather and thus tG introduce him to Einstein's "special" relativity of 1905. Such has been the position of things until recently.
3. Now, it so happens that, stimulated by the desire to test Einstein's generalized relativity trod theory of gravitation, the astronomers participating in the last Eclipse Expedition have found an undoubtedly positive effect, the bending of rays passing near the Sun. As I have pointed out on 1)revious occasions, it seems premature to interpret this result ~ls a verification of Einstein's theory, not merely in view of the small outstanding discrepancies, but chiefly in view of the failure of detecting the spectrum shift predicted by the theory, with which the whole theory stands or falls. But the Eclipse result proves at any rate that there is an 9' alteration," a change of ligtlt-velocity ~dl around the Sun, which thus invalidates the words ,)f Lorentz italicized in the quotation above. The condensation claimed by Planck's modification of Stokes's theory, for the Sun as well as for the Earth and for all other material bodies, is no longer devoid of influence on obserw~ble phenomena. It suddenly acquires physical life, so to speak.
9 Notice that the aberration is a first order effect, while such ])henomena as that expected by Michelson-Morley are second order effects (v"/c~'),so that the above condensation suiting the aberration up 9o 1 per cent. will reduce the Michelson-Morley ett~ct to one tenthousandth of its value, and thus practically annihilate it. There is thus no need for making ~ larger than 10'2.
M2

164 Dr. L. Silberstein on the recent Eclipse Results

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In other words, the discovery made at Brazil naturally suggests the idea that the observed deflexion is d~e to tht(~onde~tsation o.f the cether around the Sun r and although on~ has been au implacable enemy of any aether at all, for the last fifteen years, one does not hesitate to point out this possibility--a las~ glimpse of hope, perhaps, for the banished medium.
Let us imagine for the moment that Einsteil~ had never published his debatable, though undoubtedly beautiful, new theory--not even that of 1905. Then it is almost certain that the Eclipse result would readily be acclaimed as an evidence of the condensation of the rather near the Sun, as required by the theory of Stokes-Planck, and would encourage the physicists to work out in detail the optical and ~ssociated consequences of such a condensation. But even thol~gh Einstein's theory h~ls been published, and is being madt, popular in a most sensational way, we cannot help clingii~g to the said idea. I just learn from 'The Observatory' tor August that Mr. Jonckheere suggested some months ago float refractions may, inter alias, be caused by " a hypothetical condensation of ether near the Sun." My point, however, is that such a source of. refraction acquires a particular interest {f it is treated in connexion with the half-forgotten theory of Stokes-Planck, when it ceases to be a detached hypothesis.
It is in this sense and in such an organic connexion that I should like to draw attention to this aspect of the subject.
Of course, the quantitative details of the suitable modification of the optical, or the electromagnetic, properties of the rather due to a radially symmetric~d or any other condensation have to be worked out carefully. It is not the purpose of this Note to give a complete investigation of this kind, but only some hints at its possibility. Such hints, together with some remarks on the possible advantages of the advocated theory, will occupy our attention in the following sections.
4. If, merely to fix the ideas, the Boyle law is still adhered to, the condensation s=p/poo outside a radially symmetrical gravitating mass is given, as in (1), by

log s = -a-M. . . . . . .

(3)

r

l [ we assume, for places near the Earth's surface, not more and not less than what is just needed for the theory of

The lo_~arithmof this condensation ~,ot,ld amount, at the Sun's surface7 by~ and (E), to the enormous figure a=logs--31lO0~ (:f. the fol.lowingfootnote.

and Stokes-Planck' s ~.ther.

165

aberration, i. e. ~----l o g s = 10"2, we shall have at the surface of the Sun, as already m~ntioned in a footnote,

0-= l o g s = 1 0 " 2 1422"8- 104 --31000, .

(S)

which means, no doubt, "m enormous condensation*. The corresponding relative velocity o~ slipping v / v will, by (2), be ahnost ewmescent ; the drag will be almost complete.
On the other hand, at the surface of a hydrogen atom, assumed for the moment to })e a homogeneous sphere (and the only existing body), we shall have log s = 1"7.10 -a4' that is to say,

s = - ~ - - 1 + 1 - 7 . 1 0 -a4, P~
indistinguishable from Ulfitv. Notice that for small 0- the deimminator in (2) reduces"to ~;(r3+ :~o-4+ higher t~rms, so that the relative slip becomes

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For such bodies, therefore, as a hydrogen atom, or in fact any other atom, the ratio in question will be exceedingly nearly equal its limiting wdue 3[2, which is well known to be the maximum relative slipping tbr a sphere moving in an incompressible liquid. In short, for such small bodies there will be practically no drag at all. The more so/'or electrons, if one wished to attribute to them gravitational properties. Thls behaviour will be important in connexion with some such electrodynamic theories of ponderable media, as is that proposed by Lorentz. which require a complete slip. But even a sphere of the mass of 1 kg. and the radius of 10 cm., for which 0-= 1"09.10 -1~, will practically have no " g r i p upon the mther." This will readily be seen to account, among other things, for the negative results of Sir Oliver Lodge's ingenious experiments with the Ether machine, even if its whirling part were made nmch more massive. As a mere curiosity notice that even the Moon would have only a partial, weak grip upon our rehabilitated ~ether. In fact, at the Moon's surface we should have o'=10"2 x 0"094=0"96, and
V
therefore, by (2), v~ ----"1"15, which differs only by 0"35 from
the full slip. Thus the Selenites would obtain with a
* Such fantastically large condensations need not fl-ightenus. They can he reduced if Boyle'slaw is replaced by some other appropriate form of relation between !aressure and density. Boyle's law. which is by no means necessary, is h ~re used only, as the s~mplest one,for the sake of ilhstration.

166 Dr. L. Silberstein on the recent Eclipse Results

Michelson-Morley experiment a pronounced positive effect. But enough has now been said in illustration of the formul~ for the condensation and for the slip.
5. Before passing to consider the Eclipse result it may be well to gelmralize the condensation formula (3) for the case in which Boyle's law is replaced by any relation between the pressure and the density of tile ~ether. The corrcspondlng generalization of the slip-formula (2), not required for our present purposes, may be postponed to a later opportunity.
Let the pressure p be any function of the density p alone, and let there be any distribution of gravitating masses. Introduce the function, familiar from hydrodynamics,

r

!dpp . . . . . .

(5)

Then, in the state of equilibriuub and with dm written for any mass-element in astronomical units,

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9 - 2 7, ' . . . . . .

(6)

where r is the distance of the contemplated point from &~,

and the integral, representing the total gravitational poten-

tial, extends over all material bodies, qb being a known

function of p, formula (6) gives the required relation. It

will be seen from the definition (5) that the dimensions,

of 9 (work per unit mass of rather) are those of a squared

velocity. In order to bring this into evidence, let us recall

that

-./V ......

(7)

is the velocity of propagation of longitudinal waves in any compressible non-viscous fluid '~. This velocity is, in genera], a function of p, and becomes a constant for the special case of Boyle's law, namely, our previous l/v/~. Using (7) and
writing, as before, d___p= d log s, we have P
9 = y v 2 . d l o g s, . . . . (5a)

the required form. The integral is to be extended from
9 This result, known as theformula of Zaplace, holds alsofor the most characteristic kind of waves--to wit, for a wave of longitudinal discontinuity (Hugoniot, :Hadamard),for which it follows directly, without integration, from the hydrodynamical equations of motion. See, for
instance, my ' Vectorial Mechanics,' p. 169.

and Sto~es-.Pla~wt.'s~'Etl~er.

167

s = 1 (or log s -= O) to the actual value o[ ~he condensation.

Thus the condensation tbrmul~ (6) becomes

j'v d l o g s = El, i

(8)

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where Et has been Wl'itteu/'or tlle total gra~'ita~ional potential at the place under consideration. For constant v (Boyle's law), and for a single spherical body, the pre~ious formula (3) reappears.
Itwitl be kept in mind that althouah the mtheris assumed to behave in this way (say, like a gas) with respect to slow processes, it can still propagate rapid transversal lightdisturbances as it' it were an elastic solid (like the famous cobbler's wax o~ Lord Kelvin) ; but it will be best to think of light as o~ electromagnetic distm'bances. The normal velocity c of propagating them is another property of the ~ther, independent of that which is represented by t~, and subjected only to slight variations with condensation, as will appear presently. The ratio of v to c will be of importance, but as to the longitudinal waves themselves, they are o[ no physical interest for the present and, on the other hand, are not likely to become a nuisance. For it is not in our power to produce them to any relevant extent, and even i[ theyare generated and maintained by some gig~mlic natured processes, their only effect would be to alter very slightly, here and there, the normal velocity of light-propagation.
If we wish to form an idea of the numerical value of v, or at least of' its upper limit, for the case of Boyle's law~.say, it is enough to take the value of" o" given ,hove for the Sun,
and to remember that .M]c'~=1"5 kin., and, in round figures,
R = 7 . 1 0 ' k m . Then the result will be vc = 8 " 2 . 1 0 -s, that is to say, v equal to about 2"5 kin. per second *. This is quoted by the way only. But the ratio of these two velocities wili be seen to acquire a particular interest in connexion with the recent astronomical discovery.
6. Let c, as before, stand for the propagation velocity of light in uncondensed rather, i. e. in absence of, or far away from, gravitating masses, and let cr be the light velocity at a place where the rather has undergone a condensation s." The questio'n is: How are we to correlate c~ with s? In other words : On what are we to base the optical behaviour of the ~ether modified by a condensatiou? The only reasonable
* If so~then the condensational disturbances due to the Earth and other planets, whose velocities exceed V, will be confined to conical regions as in Mach's famous experiments.

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168 l)r. L. Silberstein on the receipt Lh:lipse Results

answer is: On experience. For, clearly, we cannot deduce a relation, which is essentially electro-mechanical, from mechanical principles ;lhm~, or from electromagnetism alone. Nor can we imitate tile usual dispersion theory (wlfich makes rise of both kinds of principles), for we are interested in ~hose portions ef the rather in which there are no atoms and no e!ectrons.
In short, as was announced in section 3, let us write down the required relation by utilizing the observational result obtained by the Eclipse Expedition. In other words, let us see what that relation must be like in order to give the observed effect.
Now, if we disregard the small discrepancies (which may be eithm" due to accidental errors or, t)e.rhat)s, due to a superposed slight ordinary refraction), the observed total deflexions of the rays passing near the Sun are represented by Einstein's tbr,nula (quite apart from his theory)

1 4M A0--
7'0 C2

where r0 is the minimum distance of the (undeflected) ray from the Sun's c(,ntre, and it can easily be shown that such will be the case* if the refractive index "n=e/c' at an)" distance r>_R f,'om the Sun's centre be determined by

9~.2 ~

4M
~ -4- - - 9 C2~

or, denoting the potential by ~2, and generalizing to any distribution of gravitational matter,

n 2 = 1 + 4j&- .2 . . . . . .

(9)

[This, in fact, is the formula which would follow at once from Einstein's approximate liue-eloment

d.~ =

c~Zt~(1 --

2~ -~)-

( & ' + @ ~ + & ' ) (i + 2~E)~,

for a "static" fiehl.] In order to obtain the required relation, that is to say the
assumption to be made (,n the optical behaviour of the condensed ~ether, it is enough to combine equation (9) with our last equation (8), which gives

,z~ - 1 = c , 2 . d l o g s . . . . . (10) * Approximately, that is, for smM1 AO, and consequently for a refractive index but little differing from unity.

and Stokes-Planck' s .~!Ether.

169

Such, then, would be the required refractivity of the condensed rather, obeying any law p=J'(p). In particular, if it obeys Boylo's law, we have

n 2 ---- 1 + 4 ~ . l o g s , . . . . (10a)

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which is of a surprisingly simple form, and reads: n~--l equal tc four times the log~,rithm oa{condensation multiplied hi!! the squared ratio of the two velocities of propagation characterizi~9 the (ether.
Notwithstanding this temptingly simple form of the relation, I shall not try to " deduce" it from things more familiar. I prefer to regard it as an assumption, dictated by observation.
If the reader so desires, he can write n2 - 1 = 4 w / c ~, where w is the work, per unit mass of matter, done by the gravitational f9ieht I" n condensi" ngo t" he tether. The r "1 small t.racti9on n~--i being known from the Eclipse results (tbr troy ~'), the numerical value of this work is determined without any further assumptions. If we agree to the lowest estimate of log s at tbe Sun's surface, as required by the aberration theory, we can also evaluate separately the ratio v/c, as already mentioned. This, however, is only a secondary matter.
7. Some. details and further implications of the StokesPlanck ~ether theory, supplemented by assumption (10), must be postponed to a later opportunity. Here it will he enouoh to add only a few more general remarks. It will be kept in mind that the proposed theory would account not only for the observed astronomical aberration and for the older terrestrial opti~;al nil-effects, but manifestly also for the nileffect of the Michelson-Morley experiment. The bending of rays round the more massive celestial bodies would be only a by-product of the theory. Again, in view of the exceedingly small condensation of the ~ether round single atoms or corpuscles there will be no difficulty in working out a satisfactory electromagnetic theory of ponderable media. The proposed theory would ~lso have the advantage of not predicting the obstinately absent gravitational shift ef the spectrum lines. It might also react, in part at least, Ul)On the 1905 relativity, .depriving it of its indispensability in most cases, but by no means banishing it from the whole domain of physicomathematical investigations. Finally, the just objections raised by the advocates of the physical principle of causality against the fixed and homogeneous rather of Fresnel-Lorent~z would not apply to Stokes's modified rather. For this

170

Sir Oliver Lodge ou a Possible

latter wouhl by no means be a mere framework of reference axes and, as such, illegitimately privileged. For in referring a class o[ phenomena to the tedler here advocated we would ultimately refer them to assignable physical things, namely those most massive gigantic bodies which, so to speak, have the ~trongest grip upon that medium. It is, among other things, this latter remark that I hope to make par.~icularly clear at an early opportunity.

London, December 22~ 1919.

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XVI..Yote on a Possible Str,lcttt~'e for the Ether. B y Sir OLIVER LODGE~.
D R. S I L B E R S T E I N ' S communication gives me ;m opportunity for calling attention to a paper of ,nine on many points in connexion with the ether which must surely be of interest even to those who are contemplating the abandomnent of that medium. In that paper an estimate is made of etherial density, and an attelnpt to measure experimentally its louver limit is described ; there are also comments of interest from Sir Joseph Larmor and Sir J. J. Thomson. The paper is in tt'e PLdl. )/fag. ser. 6, vol. xiii. pp. 488-506, and is of date April 1907 ; though among other things it relates experiments conducted in and about 1893.
The transinission of transverse vibraSons like light shows that the ether cannot be a mere structureless fluid; and if it is to be treated dynamically, which at first is surely a legitimate attempt, it must have properties akin to what we call, in ma~ter, Rigidity and Inertia. Its inertia must be something fundamenfal, which underlies and accounts for the inertia we perceive in matter, possibly in a way having some analogy with a motion of a solid through a perfect fluid. For when an electric charge is nmved, a magnetic field in the shape of an ether vortex-ring" is generated (witll an energy of circulation per unit volume equal to tt(eusinO):/8Trr'), and this confers upon the charge its observed momentum if the medium has the requisite density (see Phil. Mag., April 1907, vol. xiii. p. 492). The rigidity may be explicable hydrodynamically by a vortex circulation~a turbulent motion having a circulatory velocity of" the same order as that of the waves which the medium is able to transmit.
In Lord Kelvin's laminar vortex arrangement the velocity
* Communicated by the Author.