290 Mr Greenhill, On Greens function [Nov. 10, 



be the lengths of the edges, and x^, y^, z^ the co-ordinates of the 

 influencing point. 



Then the co-ordinates of an image will be 



2ma-l-(-l)'«'£c,, 2nh+{-lYy^, 2pc+{-iy z^, 

 and the sign of the image will be (—V)'m''+n'+p'.^ and all integral 

 values from — oo to oo must be given to m, n, p to obtain all the 

 images. 



Therefore Green's function, U suppose, 



= % 



1 If 



Now -^ = -r """" 



and therefore 



X % (_!)«' e-{2«&+(-i)""2/,-2/}=< X X (- i)p'e-{2i)c+(-irzi-2W^ 



[N'ow 2 (— 1)"^' e-{2ma+(-ir'a;i-a;}2i 



_. SQ-^m,a+Xi-x)H ^q- {'ima- x^- x)"t 



— Q-[x-xd"t Vg-4mV«+4ma(a;-a-,)< _ Q-(x+Xi)-t 2g-4mV«+4ma(a:+^iK 



Now 6*3 {x, q) = tq'^'e^^^^ 



and therefore 



^Q-(.x-x,y-t 0^ \2ai{x - x^ t, e-*«'«} - e-('«+^^)'^ 6^ {2ai (a; + x^ t, e"^^'^}] 

 [e-f^i-y.y't 0^ ^2M {y - y^) t, e-^^"-'] - e-(2'+2'>)=^ 0^ {2U {y + y,) t, e-^^^'j] 

 [e-(z-z,n 0^ ^2ci {z - z^) t, e-^'''] - e-(^+^'>'' 6^ {2c^ (z + z^) t, e-^'^% 

 the expression given in Kotteritzsch's Electrostatik. 



=1 / 



2a V 



(f).--"^.(-^'.e-«) 



