12 Mr Greenhill, On the motion of a liquid ellipsoid [Oct. 25, 



and therefore cp will be expressed by elliptic integrals of the third 

 kind. 



Put £ = co cos y^r, 7] = — co sin ty, 



then co 2 = L-^?, 



a 2 + c 2 

 also co£l cos (cf> — i/r) = N-\ — o-2-f 8 ; 



, dg f.drj 2 dty 



and W^Tt^dt 



1 (o^+n^r, 



a*+c 



7y.i. a +c >-2 

 ° r eft a 2 + c 2 "7 ^TT" 



and therefore ty will also be expressed by elliptic integrals of the 

 third kind. 



In a state of steady motion, £ is constant, and therefore 



dt ' 



or -zr = — - . 



£ *? 



Also -^- and -^ are constant, and equal to n suppose. 



Therefore if 



£l 1 = £1 cos nt, 2 = — XI sin nt, 



a t 2a 2 £ n 2a 2 £ n . 



then t = s « - il cos wr. « = -= „ - 12 sin nt, 



* a 2 + c l n ' a? + c i n 



so that &) = — 5 = - 12. 



a' + c 2 w 



Then the equation (K) leads to 



