292 Ji?' Greenhill, On Green's function [Nov. 10, 



therefore 



d'U d'U d^U 

 dx^ dy^ dz^ 





x^K-ir'" 





xiUA'rrK.^W 



X ^, TT 



26 



z — z 



2c 



,1 



-^3(-^^so 



-^.(-4fS0 



2c 



M-^-|?'0} 



26 



which is zero, except when x^ y, z are the co-ordinates of an image, 

 when it becomes infinite. 



For a single source of incompressible liquid of delivery 47r at 

 the point x^y^z^, under the condition that there is no flux across 

 the faces of the parallelepiped, we must suppose the images to be 

 all sources, and therefore the velocity function (^^ 



= 2 1 



^J[[^ma+{-l)^'x-xY■\■[^nh+{-lfy-yY+[^c + {-l)^'z~zY'\ 



Jtv Jo 



dt 



[e- (^-*.)^^ 6'3 {2ai {x - x^)t, q] + e" (^+^>)'^ e^{'2ai {x + x^ t, gj] 

 [c- ^y-y^)'t e, {2hi (y - 2/J t, q,] + e' (^+^')=^ 6, [m {y + y,)t, q,]] 

 [-g- {z-z,)H 0^ |2ct {z - z^ t, q^] + e- (^+-.)=^ 6^ {2ci (z + z^) t, gj]. 



