330 Mr. G. U. Yule on the Passage of Oscillator 



K _ c*f*.coT C (l-g 4 )sec % 



%~" i 9 (seox-cos X ) Ul-2| 2 cos2S + f)(l-o> 2 J 2 ) 



(l_f){cos(0-2^)-a> 2 f 2 cos(<£ + 2^)} 

 (l-2o) 2 | 2 cos4^ + ft) 4 f 4 ) 



^fsin (2g-4^){sin(<^-2^)-a)^ 2 sin (0 + 2^)} 

 (l-2J 2 cos(2S-4^) + f) 



an expression very similar to that for l t /l given in equation 

 (49). Reverting now to the terms containing Y in (58), let 

 us evaluate 



} ,(65) 



! S Y.yndt. 



Rationalizing (55) we have 



Y=A&.e-ft'sin(p 2 *— ^). • - • (66) 



The expression for y n is given in (56) : multiplying up 



Yy n =-iA 2 c/ft) 2 ^-W[cos (2n8-«-^)-cos (2p 2 t-\-u-f-2nB)]. 

 Integrating from 2nt 2 to infinity, and writing for brevity 



A = *-t + X, (67) 



we get 



C J 



JTy.*=-A^.f 



2nt, 



x [sec x- cos (2nS — a — ^r)— cos {2?i(p 2 t 2 — ^r) + A}]. 

 Summing this from « = lton = co, and multiplying by two, 



[sec % {cos (28 — a— ^) — f 2 cos (^ + a)} 

 l-2Pcos2S + f 



cos(A + 2g-4^)-^ cosA -| 

 l-2f 2 cos(28-4^)+f* J* ' [b } 



Calling this l ry and dividing through by I we get 



5 b -2c/. g 2 |s ec % {cos(^ + a-2g)-g 2 cos(i/r + a)} 

 I " sec %— cos % t " 1 — 2f 2 cos 2S + f 4 



cos(A + 28-4^)-g 2 cosA -) 

 1 -2? 2 cos (26-4^) +£ 4 J" * ^ ' 



