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



There is one other matter I should like to mention to the 

 Society. By our Bye-Laws (chap, xii.) it is laid down that " the 

 common seal, charter and deeds of the Society shall be kept in an 

 iron chest with two locks and two different keys, the one to be 

 kept by the President, and the other by the Treasurer." We 

 have the chest : the Treasurer and I hold the keys prescribed by 

 the law, and the Society's seal and certain documents are safely 

 kept therein : but our charter is not forthcoming, and no one of 

 the present or former officers with whom I have been able to 

 confer can throw any light upon what is become of it. This an- 

 nouncement I make to the Society, not merely to exonerate myself 

 and your present officers from responsibility, but rather in the 

 hope that one result thereof may be the recovery of this instru- 

 ment, which is interesting and valuable to us, and of no use to 

 any one else. 



The following communications were made to the Society : 



(1) On the general motion of a liquid ellipsoid under the 

 gravitation of its own parts; continuation of a paper on the 

 rotation of a liquid ellipsoid (Vol. in. pp. 289 — 293). By A. G. 

 Greenhill, M.A., Fellow of Emmanuel College. 



The following paper contains a new method of solving the 

 problem, by means of moving axes, which has already been at- 

 tacked by Lejeune-Dirichlet and Biemann, in the Abhandlungen 

 der Konigl. Gesellschaft der Wissenschaften zu Gottingen, in the 

 8th and 9th volumes respectively. 



x 2 v 2 z 2 

 Suppose the ellipsoid ^ + ^ + -2 = 1 to be filled with liquid, 



and suppose the liquid frozen, and the ellipsoid to have component 

 angular velocities £, rj, £ 



Then if u, v, w denote the component velocities at xyz, parallel 

 to the axes, 



U = — y% + Z7), V = — Z% + X%, W = — XT) + y%. 



If the liquid now be melted, and additional angular velocities 

 O x , £1 2 , H 3 communicated to the ellipsoid about its axes, then 



„ c 2 — a 2 „ a 2 — b 2 i 



u^-yt+zv + ^j^z + ^^-^y, | 



c c ^ a~ — o 2 „ 6 2 — c 2 ... 



„ _. 6 2 — c 2 . _. c 2 —a^ 



w = _ x v + y% + n l ^- c2 y + n 2 c ^- ? x ; 



