A POCKET GALVANOMETEE. 291 



Let ^, V) ^ be the co-ordinates of any corner of the coils referred 

 to any point x, y, z as origin, so that 



^ + x = a, T] + y = h, Ç + s=z c. 



Then the potential at any point due to unit current is the sum of the 

 solid angles subtended by the coils, or 



- - ^ --"-^ '^ ' = 2Q say 



2 meaning the summation for 8 corners, there being four to each coil. 



Now, 



-^^=(-1)"^^; ^^=(-1)"-^; -ï^^^-'^y^^' 



Hence ^. = _ IL =. ^ ^(A. + M 



where p, = V^'' + i\' + t ; p^ = ^^^ + 7/' ; p., = V^' + ^' 



The force at the center of the coils will be given by making 



i,, Î), ^ = a, b, c respectively and multiplying the result by n, if 



n be the number of turns of wire in the coil. 



The increment of force at any displaced point Ix, ly, Iz, is given 



by the equation (odd terms disappearing as before). 



— èl^!-)' + f^(^*"-^^(-H+^ 



but, since 



}ix Ix^ Ix ly^ Ix Iz^ Zx 



it is necessary and sufficient that any two of IW/Tix^, ^F/ly^, IWJlz' 

 should vanish simultaneously, in order that they all may vanish at 

 the same time. 



Thus we have 



^'f -^ pA pA pV\pt + Pi)^ Pt ~1ÎpF~~^\-^\ 

 î>2- "^ pA p'i\ pV\pi pi) P'i p!pi pi ^ ) 



(A) 



