40 Mr Basset, On Maclaurin's Liquid Spheroid. [Nov. 28. 



given mass of liquid by natural forces or by any operations per- 

 formed on the boundary, it is usually possible to alter the value of 

 the resultant molecular rotation as well as the configuration of the 

 vortex lines. If the liquid is rotating as a rigid body in steady 

 motion about the axis of z, the vortex lines will be parallel to that 

 axis, and the molecular rotation will be constant throughout the 

 whole mass of liquid ; but it is quite possible that certain disturb- 

 ances may twist the vortex lines into slightly sinuous forms, 

 which differ from straight lines by small quantities depending on 

 the disturbed motion, and also that the new value of the molecular 

 rotation at any point of the liquid may be a function of the 

 position of that point. Whenever this is the case, the velocities 

 during the disturbed motion will not be expressible by means of 

 (1), and the method explained in the last section for calculating ^ 

 will not be applicable. Under these circumstances the method 

 of Poincare and Mr Bryaii*, for calculating the disturbed motion 

 would enable us to find the value of ^ in the form of a series, and 

 the discussion of this series combined with the one for V would 

 lead to the conditions of stability. 



* Phil. Trans., 1889, p. 187. 



