of Sound by Spheroids and Disks, 367 



To the second order of », 



H» = l-^ (8) 



which can only be finite at all points if ei = f , leading to 



E,0u) = -g, H 1 (^)= /i -^. . . (9) 



Further, 

 ™ M f" ^ /9 7 9e 2 + 6 B , l + 6e 2 3 



and if 1 — ytt 2 is a factor of the numerator, e 2 = ~yj 



whence h 2<>)= i ( 3^_ 1) + ^(27^- 9/»»-8). . (10) 



In the same manner, 



_23 



63 ~45 



H,(/i) = K5a* 3 -3aO- ^(125^-75^ -24*0- (11) 



In order to obtain higher approximations, it is only neces- 

 sary to write, in the differential equation for the harmonics, 



H„/P„ = 1 + t» 2 E n + o) 4 F n + co*G n + q,»K w + 



and X=n.n.+ l-{- e n co 2 + 8 ;i co 4 + *: ;i a> 6 + 0n(o 8 + . . . (12) 



The following results are readily obtained : 



Q.=J" i-^ P .» y5? z vg--g.Bi,-*ji > . f ^ 



K»=fV4o^ r^^ G »- 8 „ F »-^E, ,-^)P>, (13) 



and so on, the mode of formation being now obvious. 



The higher approximations to \ n are obtained by making 

 these expressions finite for all values of fi. 



2 C2 



