

Density of the Mther. 503 



of the fluid through that aperture divided by 4tt. The resultant 

 electro-magnetic force at any point will be numerically equal to the 

 resultant fluid velocity at the corresponding point ia the hydro- 

 kinetic system.'' 



Appendix B. 



Considerations respecting a rotatioxally elastic jdther. 



On showing proof-sheets of the above to Prof. Larmor, he 

 favoured me, just before leaving for America, with a communi- 

 cation concerning the outstanding difficulties which had been felt 

 by some mathematicians concerning the dynamical theory of the 

 aether considered as a rotationally elastic medium ; mentioning 

 especially a critical remark of Lord Rayleigh, quoted by him in 

 Phil. Trans. 1897 A. p. 230, concerning what would happen if a 

 set of electrons were to circulate continually round a ring fixed in 

 space, so as always to affect and keep in rotation the same identical 

 portion of aether, instead of constantly operating on fresh and fresh 

 portions. I quote his letter : — 



"If we imagine a permanent magnet fixed in cether (through 

 which it is to be observed that the earth is moving at something 

 like 20 miles per second), then the circulation of the aether round 

 it which represents its magnetic field, though it is at each instant 

 differentially irrotational, would ultimately bring each element of 

 aether round again to its original position, yet with a finite re- 

 sultant rotation acquired by it. This would mean that the circu- 

 lation iu the aether, considered as an elastic medium with simple 

 rotational reaction stress, would in such a case ultimately choke 

 itself by becoming gradually held up against an accumulated rota- 

 tional reaction. It would seem, therefore, that a magnet fixed in 

 czther could not exist in absolute permanence. It is pointed out 

 (Joe. cit.) that this ultimate elastic choking can be delayed in time 

 indefinitely by taking the inertia of the aether very great, a hypo- 

 thesis which there was no reason for excluding and which was 

 accordingly then adopted. 



" If the inertia of the aether were no greater than your own 

 (itself immense) estimate, then the statement of the fourth section 

 of your § II would seem at first sight to hasten up this time of a 

 complete circulation of the aether, close around the moving electron 

 there considered, and on the theory of a purely rotational aether 

 the region very close around the electron would not be amenable to 

 the ordinary circuital relations of electrodynamic theory, but would 

 be governed by modified relations of form which might perhaps be 

 worked out. There does not seem to be anything definitely known 

 that would absolutely exclude this way out of the difficulty ; for, 

 needless to say, the representation of an electron as a small con- 

 ducting sphere surrounded by free aether and with a charge on it, 

 deformable or not, is merely an illustration ; and the interesting 

 calculations that can be made about it must not obscure the 

 fundamental fact that it implies a reversal of the order of ideas, 



