182 Mr. G. A. Schott on the 
where K, U, V have the same meanings as before (§ 4), 
and 
i=.n-il ni t Ljri l= !lZ l ~L ,iri iri . Zkni 
H= y 7 cosec— sin 2 - — , M= y -cot — cosec — sin , 
^ 4 n n o n n n 
N= S l^cosec 3 -cosec— sm 2 — , 
W=T(* + |)cot^±^ ) - !r [^J 2s+ i{(2^+l)^}-rJ 2s+ i|(2 S +l).^^]. 
s=0 ^ ' ^ ° 
A, A, ... are functions of /3, g, and & defined by the 
equations 
A=n 7 2 «|2&+2>, (2k+2jn+^)j3y, 
A= j" cot- (2 ^ 1)7r a^ + 2^+l, ^+2« + l+^)^j., 
with similar expressions for B, B, C, C, D, Z>., where 
^ *^ 
c (m, M) = ^ ' WW« + ^ ' W» G» 
+ (l + ^)(^ + W-4 m ^-3-/3^p jm(? . t , )& , - 
rf(m, ft) = -^-Vj'„(W + ^f V-G/8) 
(15) 
A , -4 , ... are the values of A, J, ... in the particular case 
when & = and q = 0. 
The expressions (14) and (15) remain true for a complex 
frequency, q, corresponding to finite damping. 
§ 16. The functions a, ... all vanish when the argument 1/3 
vanishes. When //5 is not zero, they diminish rapidly as the 
order m increases. 
In the particular case of vibrations stationary in space, for 
which q-\-hco vanishes, as in our present problem, we have 
