QS Proceedings of the Royal Irish Academy. 



c^h'H'^ whicli has been supposed large ; if the supposition, made early in the 

 investigation, that c^r'^s'"^ is large, should not hold up to the outer boundary 

 r = a, the discussion yet suffices to show that the relative kinetic energy 

 throughout the region for which the supposition does hold will be much 

 increased ; the fact that r*/a* and h^l7^ cannot both be small close to a boundary 

 does not, however, sensibly affect the result if s be sufficiently large. 



If, instead of taking s large, as in the preceding, we consider the case in 

 which s is unity, we may show that if a/r, r/h, c^/r'^ are each large, then at the 

 critical time the radial velocity bears to its initial value a ratio of order cV"*, 

 at that time the radial and circumferential (relative) velocities are of the 

 same order of magnitude, and the resultant (relative] velocity bears to its 

 initial value a ratio of order cV"^. 



The single type of disturbance, which is investigated above, appears 

 sufficient to illustrate the possibility of instability. 



