490 MR. S. S. HOUGH ON THE OSCILLATIONS OF A 
yy, = Ay (p® SIF By)(e° ate By)(v? + 8) + Ay (p” a B's) (p? = B's) (v? + B's) 
+ nO V0? Ba! (uw? — BM — 9") 
B, / ph hp) , yp) f LO fh) 
eee J (p? — 6”). pw! / (6? — pe”). (ce? — v”) 


F be’ (ce ar ) V(e" Ne =e): V (pu? b*) (c” — p”). J (% —v"’)c*® —y"), 
From equations (24) . . . (28), we see that (19) now takes the form 
2A, {8 (8 + ¢%)(Y? — X*) + 61 (B1 + 8) (2 — &)} ‘ 
y.| + 2A2 (Ba (Bs + 07) (Y? — a + Bs (6, + 2) Gs > X2)} 
2p? 
i Be NOt Ie 




YZ 

ae a DGaH 
~ 2A,(B +o) (p+ BY)KY—2A3 (B's + 6?)(p? +.B) XY 
+ Bipv p? — b? (XK? — Y’) — B.pV/p?— e2 YZ 
u +B, V(p?— 8) (pe =e) XZ_ 
Bagi GNy e—b - (ny. ; P | 
= Ol) 5 YZ + Os Fag ZK + Op ee XY] (29), 
pa 
2o1 
~ pa/(p? — B) 




§ 6. Calculation of Coefficients in ,. 
Equating coeflicients of Y? — X*, Z? — X? in the two members of (29) 
A,B) (By + ©”) + A2B’, (B'2 +c”) + B, =0 | (30) 
A,B’, (B', + 0) + AsB's (B's +P) =0| 
Multiply the first of these by 2 and add to the second. Reducing by means of 
(23) we obtain 
62 = Aui(e2-b Ba) Aa(eo-b Bees 3 = =0. (31). 
Multiply by = and subtract from the first of equations (30) ; then 
A (p+ Bi) (C7 + Bi) + As (p° +.B) (? +83) + F(1-F)B =o. 

