144 Mr. G. F. C. Scarle on the 



It is easily found that tan ty has a maximum value (24) —$ or 

 0*20412, corresponding to i|r = ll° 32 x , when sin 2 = 2/5 or 

 = 39° 14'. 



For a sphere with a surface-charge where the surface- 

 density is o- cos 6, we have, by § 22, when u/v is very small, 



T = 2ii 2 ~UJ5v\ ' . 



Hence, by (47), 



d S = w 2 UoA«? '- JT - 4^ 2 U /5t- 2 = 2T 



For a prolate ellipsoid, when n is very small, we may put 

 7 = c, and then we find, by § 25, that 



m ' 1{2 Q 2 fa 2 + e 2 , a-\-c a "1 

 Hence 



w 2 Q 2 f3c 2 — a 2 , a -he , a "1 



where c 2 = a 2 — lj 2 . 



For a very slender ellipsoid, where a/6 is very great, we 

 may put (a + c)j(a — c) = 4a 2 /^ 2 , and need retain only the 

 logarithmic terms. We then find 



T=.M«U /t-*, S=JT. 



§ 31. Hitherto we have supposed that the speed is im- 

 pulsively changed front to u or from u to 0. But the 

 principle of § 3 is easily extended to the case when the velocity 

 of a point charge is impulsively changed from u to u', where 

 u and u' may be inclined at any angle. We have, as Dr. 

 Heaviside* has indicated, only to destroy the velocity u and 

 then instantly restart the charge with the velocity u/. By 

 (8) we obtain a vector expression for e in the form 



Jir 



■r^iir!)— u/ ri(uri)— u 



•1 J 



Writing u' — u = w and putting v — u cos = v—Tir 1 = v h we 



easily find 



j_ r w (jt 1 -u>pcqs7 -| ™ 



~ Kr L vli — io cos 7 vh(yh—w cos 7 J * 



Here 6 is the angle between r and u while 7 is the angle 



between r and w. 



* ' Nature/ Nov. 6, 1902. 



