210 Mr Greenhill, On the Rotation of a [March 20, 



neglecting the inertia of the case which contains the liquid. 

 Also JJ?L + VjL+ W^=0, 



and L- -I 2 — -I - — = () • 



a 2 b 2 + c 2 + b 2 c 2 + a 2 + c 2 a 2 + 6 2 ' 



and therefore the relative lines of flow are the similar ellipses made 

 by the intersection of the similar ellipsoids 



x 2 ij l z 2 



~i + 72 + "a = COnst., 



a b c 2 

 with the system of parallel planes 



x A , y n » . * °3 _ const 



<?&' + c * + tf <? + a * + C 2 fl2 + j. - const. 

 In a state of steady motion we must have 



rf« ritf eft 



leading to the conditions (from the preceding paper) 



fe 2 + c 2 ' ? c 2 + a 2 " ^ a 8 + 6 2 " & ' 



or fl= £ 12 = 77,12=- f; 



1 /"- At /* 



where //, is some constant, hereafter determined. 



The relative stream lines or lines of flow now lie on the 

 parallel planes 



Px riy tz 



planes which are conjugate to (£, 77, £). 



For steady motion we must have in addition 



or 



dt dt dt 





