222 Mr Greenhill, On the Rotation of a Liquid, &c. [March 20, 

 There is therefore a point saillant on the curve when x=l, 



2 



and then y = S4<, and ^— = '1871; and the curve has the asymp- 

 tote y — 1. 



As x increases from to 1, y increases from to '34, 



2 



- decreases from 1 to '34, and ^— increases from to '1871. 



X 27T/0 



As x increases from 1 to <x> , y increases from "34 to 1, 



co 2 



- decreases from '34 to 0, and s — decreases from -1871 to 0. 



X *7F/0 



Throughout the present and the preceding articles the inverse 

 method to that of Lejeune-Dirichlet and Riemann has been em- 

 ployed. 



These writers start by assuming the existence of surfaces of 

 equal pressure similar to the ellipsoidal surface, and proceed to 

 determine the motion of the liquid necessary for the existence 

 of these surfaces of equal pressure ; whereas in these articles a 

 certain motion is supposed to have been set up in the liquid by 

 mechanical processes, and the pressure at any point is investi- 

 gated, the liquid being supposed contained in a rigid case or shell. 

 Afterwards the conditions are investigated that are requisite for 

 the ellipsoidal shell to be a surface of equal pressure, and that 

 a free surface can exist. 



Some algebraical errors on page 11, Vol. IV. Part I., must be 

 corrected : line 3 should be 



U t +I2 a - M +2c 2 (a 2 -c 2 ) g ' 



and then 



(d^_ 4c* F f (a 2 + c 2 , 2 a 2 #«• + <?) » 



[dt) - (aJTJ)i LM + I 2c* {a 2 - c 2 ) M c 2 



(« a + c 2 )- a (9a 2 -c a ) ' 



16c 4 (a 2 -c 2 ) *. 



and therefore £ is an elliptic function of t, which becomes a circular 

 function when c 2 = 9a 2 or LM = N 2 . 



