the Theory of Electrons. 277 



From this result and the previous equation we deduce that 

 the pressure is constant through each separate homogeneous 

 region, which taken in conjunction with the surface condition 

 shows that it is constant everywhere. 



The equations satisfied by (/, g, h) now lead to 



a V(/; 9i ft) = — {d/dx, d/dy, d/dz)V, 

 where V is some function of position. But we cannot deduce 

 that V 2 V should be zero. 



The equilibrium conditions thus admit of far more general 

 solutions than the equations of equilibrium in an actual 

 dielectric. They are, however, satisfied by any solutions of 

 the latter. And they are satisfied without it being necessary 

 to apply any extraneous forces to the surfaces of discontinuity, 

 i. e. the surfaces of the electron-nuclei ; that is. to say, the 

 assumptions made do not account for attractions or repulsions 

 between electrons, on the present hypotheses which do not 

 include " free mobility." 



If, adopting the other alternative as to the exact form 

 of the rotational potential-energy, we suppose it to be 

 i/yz 2 (/' 2 + <7 2 + /i 2 ) per unit volume, the effect on the equations 

 of equilibrium is merely to replace throughout 



p(f,9, h ) h J P (f>9> h) 

 and 



10. It should be stated that the above remarks are the out- 

 come of a discussion with Larmor, in which the views I at 

 first expressed were shown by him to be in many respects 

 mistaken, and in others have been considerably modified. In 

 particular, the above analysis was put forward in an erroneous 

 form to explain the transmission of mechanical force without 

 postulating " free mobility," by showing a supposed incompa- 

 tibility among the complete equations of equilibrium in the 

 absence of extraneous forces on the electron-nuclei. 



[ July 23. — Mr. Larmor sends me the following rejoinder: — 



In the rotatioTially elastic model which your paper consi- 

 ders, the gradient of the translatory displacement (£, 77, £) is 

 proportional to magnetic force ; but your argument, § 4 and 

 § i>, tacitly takes it to be also continuous with the velocity of 

 the matter : such a scheme cannot be wide enough, as in fact 

 you say. 1 should thus reply to § 9 that virtual variation of 

 the aether-strain and virtual displacement of the material system 

 are independent operations : you do not introduce the latter, so 



