582 EQUILIBRIUM OF ROTATING MASSES OF LIQUID. [CHAP. XII 



which leads to 



...... (15). 



The case of an infinitely long elliptic cylinder may also be 

 noticed. Putting c = oo in (5), we find 



26 2a 



The energy per unit length of the cylinder is 



F 1 = ^yaMog^)! ............... (17), 



if a 2 = ab. 



314. If the ellipsoid rotate in relative equilibrium about the 

 axis of z t with angular velocity n t the component accelerations 

 of the particle (a?, y, z) are n 2 x, - n*y, 0, so that the dynamical 

 equations reduce to 



1 dp cm I dp dO, 1 dp dn 



n z x = -- -f- ~j , n*y = -- -f -j- , = f ~j- 



p dx dx p dy dy p dz dz 



............... (1). 



Hence ^ = J n* (x 2 + f) - O + const ................ (2). 



The surfaces of equal pressure are therefore given by 



= const ........ - 



In order that one of these may coincide with the external 

 surface 



we must have 



In the case of an ellipsoid of revolution (a = b), these con- 

 ditions reduce to one : 



