488 MR. 8S. S. HOUGH ON THE OSCILLATIONS OF A 
Eliminating B, the values of 6 are given by 
IP +2P+eAYB+R O=0....... . ap 
Let us now apply the formule (16), (18), to the different forms of R’; take first 
RB = pl/(p? —B). 
At the surface 
WN! = p'/ (un? — B). 0. / (8 — v2) = eo, xy = Dee’ ,/ (c? — B). XY. 
Therefore, when y, = RMN’, 

from (16) 
ots cos « + 2 = cos 8’ ave os TCOStyA==ae es b?c’ ,/ (ce? —b*). xy | 
| 
from (18) + (24). 
Be cos of — VF cos f= PP /(c®—V) (| 
Similarly, when R’ = p’,/ (p” — c”), 
M’N’ = __ be? ,/(c? — b?) XZ_ at the surface, 
and 
a cos a’ + a cos [sy a os cos y = fp’ es be! 4/ (62 ah 0?) XZ, 
| 
op (25) ; 
cos! — SP cos p= P A/& —3(— YZ) | 
and when R’ = V/ (p? — b”) (p? — c?), 


M'N’ = be’ (c? — 6?) YZ, 



MH eos a! + WP cos pi + PICOSLy a= eae 2iphiio Oier 1a a’ (c? — 0°) YZ, | 
VF — BF) (e — (26) 
Bp cos a! — SP cos p= PME) (c’? — b*) XZ i 
Take, now, the form (22). 
When 
=(p*+ 8), RMN = (p? + B) (x + B)(’ + 8); 
