A POCKET GALVANOMETEE. 283 



gives the lines of force. Fig. 6 shows a special case of such a field. 



Ï0 determine the best arrangement of the magnets so as to 

 minimize the error due to the eccentric position of the current 

 (which is the same thing as that due to the deflected position of the 

 magnets) we may proceed to find the electro-magnetic forces acting 

 upon the system of magnets, when the current is placed in any 

 position X, y. Putting F for this force and expanding it in terms of 

 eccentric displacement "bx, "by, we have, 



+ 



where Fq is the force at the origin. On account of the symmetry of 

 configuration, the terms containing odd powers of either Ix or ly 

 vanish when taken for all the four magnets. The equation then 

 reduces to 



^^'=^^0 + l{-l^(^^')-^ + ^w + 4^(^-)^ + } (2) 



where _i<= =^ 2 2. 



tan 



V 



Lut since 



cSx' "ex ^ 



x=a- ^ ] 

 y = h - 7) > 



