1879.] liquid ellipsoid about its mean axis. 235 



therefore 



^^-Kiy-*©' 



dt 



_ , {a' - b') {a' + -m . , , . {o? - b') (3a' + 6-) o • 

 and therefore 



+ hi — ^ + ft) -^^ . .. . j.i,. ' [ y = constant. 



^[a+b {a'+ by j ^ 



The surfaces of equal pressure are therefore the similar cylinders 



(^TTph _ {a^-h')(a' + Sh') \ 

 \ai-b "" {a'+by r 



|4Z[P« . „. K:i&li3aM:Z)U^-constant- 

 + \a + b^'^ {a' + by |2/ -constant, 



and these are similar to the outer surface, and a free surface is 

 therefore possible if 



or 



""{a + b "" {a' + by j 



-^ 1^+6 + '" (^N^6T 1' 



" P {a + by {a' + Qd'b' + W) ' 



More generally, if the cylinder of liquid had been rotating as if 

 rigid with angular velocity ft)', and an additional angular velocity (o 

 had been communicated to the cylinder, then the components u, v 

 of the velocity at the point ict/, the axes of x and y being taken as 

 the axes of the elliptic section, and therefore rotating with angular 

 velocity co + co', are 



a^-b' , ' 



a'-b' ^ , 



V= (O —5 Ta OS + COX, 



a +0 

 the molecular rotation at every point being to. 



