6S Mr. Gwyther ou a 



and to show the relation to the nature of his solution and 

 the differences from it, I will compare equation (39) page 27 

 of his reprinted papers (with his notation). 



■'%-;;^/('-3*iSi/('-;)-S^A<'-'''- 



each term of which he explains on page 279. 



Write /(/) = <:sin27r(^//X, replace Lm.n by xir.ylr.z\r, com- 

 plete the integration and separate into two parts, we then 



get 



Kt x(l'x + 7n'y^n'z)\ .277.. . 



f ^xjl'x 4- my + n'z) /'\ 



+ (^ y, • - ^3j 



(xil'x + 7ny + n'z) . 2Trb, ^ . 



^i' — v^ — -^'"^('''-'■> 



(T^xil'x + 7ny + n'z) t \ 

 V (\ra 2Trb , . f ^(^\' . 27r^, , --|1 / .-. , 



the wave length in the two waves being in the ratio d/a. 

 Each of these expansions separately is of the form that I 

 have used, the first being without condensation, the second 

 without rotation. 



If we now make a = ^, the second expansion gives 

 a single term only, representing a wave of infinite wave 

 length, which would be sensible only near the point of 

 origin of the wave, 7V-cr .• — 



r /' 3^^^'^r + m'y 4- ;/.)! / ^ Y.in'"^^^ / 



^TzDb 



ax 



d (l'x + m'y + n'z^ / X V • ^tt/^/ / ^ .„ 



