280 



Mr. L. de la Rive on the 



Inchon 

 Differentiating (6) with respect to t, we obtain 

 ,'dD 1 d 2 A 1 d<h 



hence, using (2) and (8), 



1 _ 1 d' 2 A 1 \/d6 . /n . 



andb y( 7) lrf2A 



A similar equation may be obtained for <p ; and so we 

 arrive at tbe system of equations : — 



I d-A. 

 -— _ V 2 A = 4*r^ ..... (I.) 



7?-V 2 ^V- (H.) 



H = curl A, (III.) 



^ 1 (I A 1 „, /T TT N 



D= ; 2 -j.— A — ^V0. • • . (IV.) 

 4?rtr at •±7rr r v ' 



Consider the point P of the field at the instant t , and 

 suppose that the values of <£ and A have been propagated to 

 it from the electron with the velocity of light v. They have 

 therefore been emitted by the electron at an instant t such 

 that the radius vector at that instant has the value 



r-v(t -t) (6) 



Let now t be regarded as constant, and let <j> and A 

 be expressed as functions of r by means of equation (6). 



d 2 q> _ , d 2 (f) <PA _ 2 cPA . 

 dt' 2 ~ '' dr 2 ' W ~ V dr 2 ' 



and equations (I.) and (II.) become 



^_ V 2 A=r ^pu, .... (La) 

 dr 



^lf_V 2 </> =±<irpv\ .... (II. a) 



A theorem of Beltrami's gives for a function <p of r at a 

 point P , 



4 ^° = ;©-v 2 4>Wr, 



