1880.] 



under the gravitation of its own parts. 



and if U, V, W denote the component velocities of the liquid rela- 

 tive to the ellipsoid, then 



U = u+yco 3 — z(o 2 = 



2a* 



2ft2 o 1 

 c'+a' 2 



1 3 b +c* 1 a' + b 1 \ 



2c 2 2c 2 



(B) 



c'+ar 



b* + c % 



where a> 1 , a> 2 , io 3 are the component angular velocities of the ellip- 

 soid about its axes, and therefore 



We see that Z7-^ + V^ + W- 2 = 0, and therefore a liquid par- 

 ticle always remains on a similar ellipsoid. 



If h lf h 2 , h 3 denote the components of angular momentum about 

 the axes, 



Aj = %m (ivy — vz) 



- Q x ^ 2m (2/ 2 - s 2 ) + ££m (f + z>) 

 = iJf{^^- 2 fl 1 + (6 2 + c 2 )^ 



M denoting the mass of the liquid. 



If no external forces act, the dynamical equations are 



•(C), 



dk 

 dt 



a\ 

 dt 



1 -K^ + K a 2=°> 



-h^+h^^O-, 



(■*>) 



and therefore h* + h* + h* = G 2 , a constant. 





