M?' Basset, Reply to a Paper by Mr Bryan. 329 



small motions of a viscous rotating mass of liquid cannot always 

 be expressed by terms of this character. Perhaps not ; and 

 whenever this is the case the system will be ordinarily unstable, 

 but nothing can be asserted with regard to its secular stability 

 without further investigation. It is however possible that for 

 certain types of displacement the liquid may perform finite oscilla- 

 tions about the spheroidal form ; whilst for other types the liquid 

 may continue to deviate further and further from this form until 

 it breaks up into two or more detached masses. When the dis- 

 turbed motion is of the former kind, I consider that the steady 

 motion may properly be termed secularly stable for these par- 

 ticular types of displacement; and it is in this sense that I 

 employ this phrase. When motion is secularly stable accord- 

 ing to the above definition, the approximate solution which 

 gives the state of things in the beginning of the disturbed 

 motion will certainly not be of the form 6"'^+'^^, a negative ; but 

 since the particular kind of disturbed motion we are considering 

 is periodic, the complete solution of the equations of motion will 

 necessarily be expressed by periodic terms. 



October 6, 1895. 



