182 Mr. A. M c Aulay on a Modification 



where 7 (0) stands for any vector function of which is per- 

 pendicular to k. Similarly 



where cf> and 8(<j>) are functions exactly similar to 0and 7(0). 

 Equations (25) and (26) now give 



'bOfot + (u + vyd0ftz=O, .... (29) 

 30/B* + (M-tO3tf>/a3=O (30) 



These show that if a point move in the direction of k faster 

 by v than the aether, will for it remain constant, and if a 

 point move in the direction of — k faster by v than the aether, 

 <£ will for it remain constant. In other words, and (/> are 

 propagated relatively to the aether with the velocity v in the 

 direction of and that opposite to k. 



11. We may drop the 7 and 8 used above by putting 



*=a(0) ,-dOfa, £=£($). a#a*, . . (3i) 



where u(6) and @(<j>) are vector functions of and <f> which 

 are perpendicular to k. Equations (29), (30), and (31) are 

 exactly equivalent to all the former equations involving a, 0, 

 7, and S. 



On account of the arbitrariness of and <£ they may be 

 chosen so that ~d0fdz and "dtyfdz are each unity, or, again, 

 they may be taken as the angles u and make with i. 



The unknown u may of course be eliminated from equa- 

 tions (29) and (30), leaving but one equation, but clearer 

 ideas seem to be obtained by not effecting this elimination. 



Let us now confine ourselves to propagations in one direc- 

 tion, and therefore put = 0. Take so that '$0/~dz=l, i.e. 

 0=z—Y', where Y x is a function of t only. Substituting this 

 value of in equation (29), 



u =-dY'rdt-v. 



Hence if the aether be oscillating about a mean position 

 dY r fdt=v + Y», 



where Y" is a function of t oscillating about the value zero. 

 It follows that Y'=vt+Y or 



0-z-vt-Y, (32) 



where Y is an oscillatory function of t, whose average value 

 is zero. 



The solution so far is applicable to an isotropic dielectric, 

 for which K' and /// are independent of strain. In this 

 aspect it will be returned to later. 



