6 GWYTHER, Velocity-Potential across a Channel. 



If we write \ for the angle the bisector makes with 

 the axis of x, and \i for the semi-angle at the apex. These 

 expressions become 



f{{x-\-iy)e~'^] and/{j^±^>} 

 respectively, and X and \jl as representatives of such 

 quantities as /3i — 7, j32 — 7, may freely enter the function 

 f^x^iy). 



It is easy to verify that the known cases of transverse 

 oscillations in such a space (Lamb's Hydrodynamics^ 



p. 426) where X = - and u = - or -, are in accordance with 

 ^ 2 '^ 4 3' 



the expressions here given. 



The main difficulty in finding solutions to suit actual 



cases of fluid motion is the condition, not here dealt with, 



relating to the pressure at the surface of the fluid, and no 



new solution is here offered. The very suggestive form 



arrived at in the expression f {{^x + iy)e - i"^} is perhaps 



worthy of notice. 



