1879.] liquid ellipsoid about its mean axis. 239 



and therefore if M denote the mass of the liquid, the kinetic 

 energy 



and the liquid is therefore kinetically equivalent to a mass M of 

 principal moments of inertia 



^(6^_-0^ ^il-^'_ ^ {c^'-hj 



Consequently, if no external forces act, and the inertia of the 

 case be neglected, Euler's equations of motion of the ellipsoid 

 become 



(c^-g^)^ (a' -by 



c' + a' a' + h" 

 *«. = (6--C7 • '"^'"3 



b'+c" 



b' + c'{ 4a* 



with two similar equations. 



If p denote the pressure of the liquid at any point xyz, p the 

 density, q the velocity, and V the gravitation potential of the 

 ellipsoid, then we have 



-—V+ ^ + 12^ = ff, a constant. 



dd> . h^-c" b'-c%. .. 



^^^ ' '^"'^'b^T?^^'^'^'¥T?^^^^^^'^"' 



52 — gZ 

 C2_(^2 



+ ;^:jr^ [- < (^' - ^') - ^i'"^^^ + «.«3««/} 



(j2_ ^2 



