1891.] Fluid Motions in two dimensions. 185 



This relation must hold among the constants of Mr Michell's 

 problem. In his paper c is only determined in the case of 

 symmetry for which it is obviously zero. 



I do not propose to proceed further with this problem at 

 present. (See Art. 13 below.) 



6. Problem (ii). Liquid flowing against a disc with an elevated 



rim. 



Suppose that in an infinite mass of fluid moving from infinity 

 in the negative direction of the axis of y there is a vessel bounded 

 by three sides of a rectangle the missing side being parallel to 

 the axis of x. The fluid will enter the vessel — one stream-line 

 will divide at the middle point of the base, and there will be two 

 free stream-lines starting out from the edges of the vessel, behind 

 which there will be dead water. 



The boundary in the z plane will be as in the figure, and we 

 shall suppose the points u = ± 1 to correspond to the edges of 

 the vessel, u = ± a to the corners of the vessel, and u = to the 

 point where the stream-line divides. 



The boundary in the w plane will consist of the two sides of 

 the line ty = from the origin to + oo , thus 



oC 



-1 



This can be transformed into the real axis in the u plane by 



taking 



dw 1 , 1A v 



S=2" (10) ' 



and then the u boundary is 



