of an Electrified Ellipsoid. 341 



that as far as terms in n 2 /v' 2 the electric part of the energy is 

 unaltered by the motion. 



(C) Energy of a very slender Ellipsoid. "When the ellip- 

 soid is so slender that b q /a 9 may be neglected in comparison 

 with unity we have 



V l - ? 



When w/v is small, this becomes 



W =2LU 1+ ^) l0g T + 2^)' 



(D) Energy of a Disk. 



When a" 2 < a& 2 the ellipsoid is more oblate than Heaviside's, 

 and P becomes negative. In this case let us write 



a 



so that r is the radius of the disk which is the " image " of 

 the ellipsoid a, b. Then writing V — 1 = 2 we have from (23) 



r/t 



~ 4Ki>Va \ »Va r° g l_,Var/a 2KbW 



t 



1 l + «2 / # 3 «■ \ _ 



-r log^j .=2(x— o-+ ^... )=2tan- 1 #, 



e & 1— xi \ 3 5 / 



so that (23) becomes 



W=-^{(l-^)tan-lV^ + ^=). (27) 

 2KWa IV »V«/ a v*rV a ) V ' 



When a=0 we find for the energy of a disk of radius r 

 moving along its axis 



tit < f" Tr 



w =it^ < 28 > 



In all these cases it will be found that when u = v the 

 energy becomes infinite, so that it would seem to be impossible 

 to make a charged body move at a greater speed than that 

 of light. 



Phil. Mag. S. 5. Vol. 44. No. 269. Oct. 1897. 2 B 



