102-103] MOTION OF AN OVARY ELLIPSOID. 149 



whilst (to avoid imaginaries) we write 



and 0. (f) = ( f._i)j, .................. (5). 



It may be shewn that 



As examples we may take the case of an ovary ellipsoid 

 moving parallel to an equatorial axis, say that of y, or rotating 

 about this axis. 



In the former case, the surface-condition is 



d<l> _ dy 

 df " V d' 



for f = f , where v is the velocity of translation, or 



This is satisfied by putting n = 1, 5 = 1, in (2), viz. 



cos...(8), 



the constant J. being given by 



In the case of rotation about Oy, if q be the angular velocity, 

 we must have 



d(f> ( dec 



(10). 



, 

 Putting n = 2, 5= 1, in the formula (2) we find 



= Ap (1 - /) (? - 1)1 f flog - 3 - sin ... (11), 



being determined by comparison with (10). 



