32 Lord Rayleigh on the Incidence of Aerial 



If the conductivity of the sphere be finite (yu/j, 



M 



which includes (18) and (10) as particular cases. 



If the ellipsoid has two axes equal, and is of the planetary 

 or flattened form, 



h = c =-^-y T=f7r C V(l-. 2 ); * (21) 



L=4 7 r[i-^^5.sin-i,},. . . (22) 



= N=2.{^lsin- 1 ,-^ 2 }. . (23) 



In the extreme case of a disk, when e=l nearly, 



L = 47r-27rV(l-e 2 ), .... (24) 

 M = N = 7rV(l-tf 2 ) (25) 



Thus in the limit from (14), (21) TA = 0, unless fi'=0 ; 

 and when /•*•' = (), 



TA = -~ (26) 



In like manner the limiting values of TB, TC are zero, 

 unless /x.' = go , and then 



TB = ^, TC=^. . . . (27) 



In all cases 



t= _T(A., + B, y + C) _ _ m 



gives the disturbance due to the ellipsoid. 



If the ellipsoid of revolution be of the ovary or elongated 

 form, 



a = /, = cv(l-^); (29) 



L = M = 2 7 r|^- 1 ^ 2 log^j, . . (30) 



N=4.{^-l}{ilog^-l}.(31) 



* There are slight errors in the values of L, M, N recorded for this 

 case in both the works cited. 



