(18) 



260 Mr. A. E. H. Love on the Oscillations of a Rotating 



The motion being oscillatory, we suppose 



a = ao + Qe'"', & = 5o + Re'"^ c = Co+Se^'*'; . (16) 



(■hj ^oj <?o being the values of a, h, c in the steady motion. Then 

 the period is 27r/n ; and, since the volume is constant, we have 



Q/ao + R/&o + S/co=0 (17) 



The values of the constants t^, t'^ are found from (15), by 

 supposing the motion steady, to be 



L % Oq J 



--^(«o + M W+ 6o> ^ 



Now inserting the values (16) for a, b, c in (15) and elimi- 

 nating S by means of (17), we find 



i(aQ-hy (ao + ^of «o^o V °B«o ° ^Cq/ 2 aoM 

 ^ L~ [ao-hX {% + h,y bo^ [ "' B^o ' Bco ^V 



^L («o-M' ("o + ^'o)^ aoH ''B^o '^co V 



-y(^<4)] 



J.T} r 3t^ St'^ irjpf BLo_ BM 



"^ L(«o-^o)' («o + ^'o)' «o^o I ' 'dbo 'hco J 



on eliminating Q : R, we obtain the equation for the fre- 

 quency «/27r. 



6. It is convenient to express the quantities in (19) and 



(20) in terms of three integrals F, G, H, defined by the 



+ 



and 



