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



Also the kinetic energy 



T = \ Xm {u 2 + v 5 + w 2 ) 



, rr f(6 2 -c 2 ) 2 , , (c 2 -a s ) 2 2 , (a 2 -Z> 2 ) 2 . 



I 6" + c 2 x c" + a 2 



45V 2 _4c 2 a 2 _ 

 + & 2 + c 9 * + c 2 + a 2 



t 2 + 6 2 



^ + 



a constant. 



The hydro dynamical equations with moving axes are 



1 dp v , du , . JT du 17 du w du - 



p cfa; a£ - dec dy dz 



1 dp ^ dv , 77 dv dv , -rfrdv 



-^--Y + - Tl -WG> l + ua> s +U -j- + V-j-+ W-j- = 0, 

 p dy dt 1 3 dx dy dz 



1 dp r? , dw , jjdw T/ dio w dw I 



pdz dt 2 ] dx dy dz J 



and by the elimination of the pressure and the potential, supposing 

 one to exist, 



df; . y . jjd£ . ir djj . -rrrd^ t du du du -\ 



i-^ + ^ +U Tx + V dy +W Tz = ^dx +V dy + ^dz > 

 dt] 

 dt 



„ rrdri Tr dn -rrrdri -. dv dv dv 



dx 



dy 



dz dx 



dy 



M* 1 ) 



dx 2 l dx dy dz ? dx dy 



dz 



dx dy dz dx 



where (f, 77 and £ have their usual meaning. 



With our values of u, v and w, these equations (F) reduce to 



d% 2a 2 



2a 2 



dt'a' + b 2 ^'^^^' 



d v 26 2 



a x z- 



c' + a' 



26 2 

 a 2 + 6' 



n 3 £, 



d* 6 2 + c a 



d? 2c 2 2c 2 



(0) 



three equations, similar to equations (B) ; £, y, £ having the same 

 values as in equations (A). 







