804 



Prof. W. B. Morton on the Discontinuous 



a] oner the infinitely extended free surfaces, introduced ex- 

 plicitly to keep the dimensions right, as Greenhill does in 

 his li Report." The diagrams are not drawn to scale. The 



Fisr. 2. 



Hr—-—C 



r i 



TT 



a 



= C 



c- 



CJ 



f 



LL 



values — 1, +1, go aie chosen for the points H, B, G, 

 leaving A, D, F, G to be fixed by the conditions of the 

 problem. Indicate the corresponding values of u by small 

 letters, then d,f, g are negative and a of doubtful sign, and 

 the transformations are given by 



du 



= (u-f)(v>-I)-i(u-d)-i(u-gy 



W 



It will be seen that the analysis applies to a more general 

 case than that with which we started, for there is in it 

 nothing to imply that the second plane passes through D, 

 the upstream edge of the first. What we really have is the 



