( 671 ) 

 Now, if an electron willi ('l)ai-p;e e, is in O al the tiin<^ /, and lias 



(III, (hi, I (hi- 

 nt that instant tlie accelerations , ', ", it will produce at the 



(It (It (It ' 



pomt /*, at the time ^ -| , a dielectric displacement, whose com- 



c, 



ponents aix' ^) 



e dii , e (In 



(I 



4rrc^- (It ' \:ic^r dt ^*'^ 



On account of tlie .ureat len,i;th of (}l\ tliese expressions m;i\ also 

 he ap})lied to an electron situated, not in (> hut in an\- oilier point 

 of the ])art of the plate correspon<lin,u- to the ai-ea o>. The whole 

 dielectric displacement in I* in the «lirection of ,r (it is onh this 

 component that will he considered in \\iQ next paragraphs) at the 



r 

 time t -\ will therefore he 



c 



1 (III r 



^:ic'i' (It ^ ' 



if the sum is extended to all electrons |)reseiit in the Nolnme (oL 

 at the time f. 



There will also he a magnetic force of the same jnimei'ical \alne, 

 and hv PovNTiN(i's theorem a flow of eneruv aci-oss the element o>', 

 iji the direction from the jdate towards /'. The anujnnt of this How 

 per njiit of time is given Iw 



(' t>/ .io' (8) 



§ 5. It will he )iecessarv for our purpose to decom[)ose the whole 

 emission into rays of dilfereiil wa\ e-lengtlis and to examine^ the part 

 of (<S) corresponding- to the rays that liaxc their wa\e-lengllis within 

 cei'tain limits. This may he done hy means of Foi IvMkh's series. 



Let ns consider a rcz-i/ Ioikj time, e\len<ling from / = (I to I z= iy. 

 During this interval the value of ^ at the point /' will eojitinnally 

 change in a very ii-regular way ; it jiiay howexer in every case he 

 ex|>ande<l in the series 



'" = * mjtt 



b, = 2l ((,n Kili — - , ^ . (0) 



m := 1 



iy 



whose cocfllicients are gixen hy 



2 /• in:it 

 — _ , I sla \i,(lf (1 



0) 



') Tiic proot of IJiis will be tuiiiid in onv of tlu' iiexl pails of my "(lonlriitii- 

 lions to the theory of eleclfuus.' 



