ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID. 491 
But if we equate coefficients of XY in (29) we obtain 


) 9 4 19, , , 19, , 9.91997 
B, (2p? =) ay wt >. [Ai (p? + B’ i) (eC? + 8B) + As (p?-F B’,) (c? ++ B'.)) = — 77070’. 
Hence 
B, (2p? — 0°) +5 — 2p”) = — N°76',0%, 
or 
B, (2p? — 6°) 7? = — N?7?6'50°, 
or 
r20? , 
B,=- ae Pron OS = FPG WGN ID cae saath eh BON 
Again, equating coefficients of XZ, YZ in (29), we have 





ITT PEON a 
B, i 2 1 2 B = h* 26 0) = DGG 
~pia/ (oe? = ce) Nisei? TN? pa/(p? — &) 
Debt USE wtp V(p 2 = 2297 Cn 
(7D) 7 Be Tap * °0 9 9 Q\ 9 
Os 7ip— Bye) tx Be 7ge TVG =P) = 4) 
or, since p® — c? = 7 (p? — ¢”) 
wi 
B, (29* — ¢) — SB, (p? — 0") = NiO | 
(33). 
B, (2p? — b? — c*) + = B, (p? — 2) = — Wr’, ab) | 
Now, as we have seen above, 
Ay (p? + B4)(#? + Bi) (0? + BY) + Aa(p? +B) (x? + B's)? + Bs) 
= ALB (Bi +0) (Bs+e2) +22 (B40) (Bite%) +98 (B +e?) +2°8 (Bi th} 
+ Asf B's (840%) (B40?) +0" (B+0*) (Bote?) +B (Bete) 42°83 (Bat V)} 
which by (30) is equal to 
A, B'?.(B+0")+ AoB’,? (6. + b)4 ac? {A, (B+ 02) +A,(6,+0)} +9 { —_= =F} 
— A, (By ~- b?) f— 2 (Bb? =e ce’) Bi - 1h2¢'2} en A, (8 at b) _ 2 (24 c) B’, a 1P%¢ 2} 
+73 (@—/), 
co 
a] 
bo 
