and Electric Waces upon Small Obstacles. 31 



the volume, so that 



T = ±Trahc, (9) 



we have 



A^=-AT, B 2 r=-BT, C,w=-CT, . (10) 



whe 



re 



KU 7> KV ri KIV . . 



A = IT^' B= l+3' C =T+rfJ' • (11 > 



L=2 ™' ,C J„ («F+X)l(i£w+*)" ' ( 12) 



with similar expressions for M and N. 



In (11) k denotes the susceptibility to magnetization. In 

 terms of the permeability jjl, analogous to conductivity in the 

 allied problems, we have, if fj/ relate to the ellipsoid and fi to 

 the surrounding medium, 



l+4flI7B = f*7/*, (13) 



so that 



(n' — fi)u 

 47r,u +(/*'-,.) L' • • ' • W 



with similar equations for B and C. 



Two extreme cases are worthy of especial notice. If 

 fi'/fL=:o , the general equation for ty becomes 



l 3 yjr _ ux vi/ wz 

 ~~Y ~L + M + ¥' * ' • ^ 



On the otlier hand, if /*////, = (), 



r z -yjr _ ux vy wz 



~ ^T ~ L-4tt + M^r + N^i^' * • (16 ) 



In the case of the sphere (a) 



L = M = N = 4tt; (17) 



so that (15) becomes 



a 8 

 yjr = ~ (ux + vy + wz), .... (18) 



giving, when r=a, </> + i/r = 0. This is the case of the perfect 

 conductor. 



In like manner for the non-conducting sphere (16) gives 



. a z , 

 Y= 2^3 {ux + vy + wz) (19) 



