io6 



PROPERTIES OF CIRCULAR CURRENTS. 



for all the windings, but this arrangement presents great practical 

 difficulties in coiling the wire and centering the needle. It is more 

 advantageous to arrange the coils in a rectangular section so as to 

 produce a field which is very nearly uniform. 



749. VON HELMHOLTZ'S ARRANGEMENT. If we consider two 

 circumferences, Bj and B 2 (Fig. 139) of the same radius <?, having the 

 same axis O x O 2 , and traversed by parallel currents, we readily 

 see that at the point O, half way between O l O 2 , the component X 

 parallel to the axis is a minimum, or a maximum relative to points 

 on the axis, or in a plane perpendicular to the axis ; and that the 

 component Y is zero in the plane perpendicular to the axis, which 

 passes through the point O. The field is sensibly uniform near the 



o. 



Fig. 139 



point O, and the moment of the action produced by these two 

 currents on a magnetised needle situate in this region is sensibly the 

 same as if the needle were exactly in the centre ; a difficulty of 

 adjustment is thus easily got rid of. 



Moreover, if the distance of the frames is equal to the radius a, 

 the first term of the correction in the value of X given by equation 

 (33) vanishes, and we have 



L 



54/ 





This is the arrangement devised by Von Helmholtz.* The con- 

 dition of the magnetic field is represented by Fig. 140, taken from 



WIEDEMANN. Ekctricitdt, Vol. III., p. 250. 



