1892.] and Stability of Dynamical Systems. 357 



where R is the radius of a sphere of equal volume ; whence 

 £/c must be constant throughout the motion, and we may there- 

 fore treat this quantity, as one which is in the nature of a 

 generalized component of momentum. 



The angular momentum h about the axis is also constant ; 

 and if we introduce two new constants r, t, such that 



J/ c = ( T ' - r)/2abc, h = \M <Y + r) ; 



it follows, that since the volume is constant, we may regard 

 t', t as quantities in the nature of generalized components of 

 momentum, and employ them in the place of £/c and h. Whence 

 the expression for $ is 



{(a-by^(a + bf 

 and 



accordingly the steady motion is determined by the equations 



in which c must be regarded as a function of a and b. See 

 Hydrodynamics, vol. II. §§ 363—367. 



