62 Mr. Gwyther on a 



is directed along the axis of/, in order that it may satisfy 

 the condition of admitting of resolution, the displacements 

 must take the form 



'i=fx{cc.r)y 



l=-i^lx.r)yz. 

 Making use of a form of solution of the equations of light 

 given by the author in a previous paper quoted, I show 

 that we may write these 



s^=-2-^^^;,niT^sin-(^/-r) + etc. 



77 = S ^-^1 Sin— (6^ - r) + etc. 



^=-S--^^sin-(^/-r) + etc. 



where a^ and b^ are any constants. 



Without proceeding further we may notice that this 

 agrees in form with the solution found on dynamical 

 grounds by Professor Stokes. We shall obtain his solution 



if we put ;^ = 2 or 3, ^2 = ^3 = ^2 = <^3=^, and accelerate the 



phase by - . Before going further it may be well to explain 



4 

 that the difficulty I find about this form of displacement 

 consists in this fact and its consequences. 



If we consider a point immediately in front of the point 

 of origin of the secondary wave for which j = 0, s = 0, x=r 

 we should have 



n = — sin ~ {bt - r), 

 ' r A 



and if we consider the point for which ,r - 0, j = 0, ^ = r, we 



should have 



^a . 27r , 



giving a displacement one-half of that immediately in front 

 of the aperture. And if, instead of considering an element 



