108 Prof. J. Y. Jones on the Magnetic Field 



the current is passing through it, and the electromotive force 

 between the points of contact of the brushes on a radius 

 of the rotating disk when the same current is passing through 

 the standard coil ; and this balance gives us, in the general 

 case, the formula 



p-Hrfr, (A) 



R = 2i 



where a Q and a x are the distances from the centre of the disk 

 of the points at which the internal and external brushes are 

 applied, and H is the magnetic-field intensity at a point 

 on the radius through these points of contact at a distance r 

 from the centre when unit current is passing through the 

 standard coil. [If the coil is circular and coaxial with the 

 disk, this formula simplifies into the formula first mentioned.] 



§ 2. In the case of the coil used in my observations, the 

 dimensions of which are given below, the excentricity of the 

 elliptical section is so small that the value of the integral (A) 

 differs only by a small quantity from the value it would have 

 for a coil otherwise similar but of circular section with radius 

 equal to the arithmetic mean of the semiaxes of the elliptical 

 section ; and to a first approximation we may assume that the 

 percentage correction to be applied to the value of the integral 

 for the circular coil to obtain its value for the elliptical coil is 

 the same as the percentage correction to be applied to its 

 value for the circle in which the mean plane cuts the circular 

 coil to obtain its value for the ellipse in which the mean plane 

 cuts the elliptical coil. It will be sufficient for our purpose, 

 therefore, to calculate the latter percentage correction. 



§ 3. Let H e be the value of the field intensity at a given 

 point in the disk due to unit current in the ellipse, and H c the 

 value of the field intensity at the same point due to unit 

 current in the circle coplanar and concentric with the ellipse 

 and of radius c equal to the arithmetic mean of its major and 

 minor semiaxes. 



Then we have, in this case, 



A= 2«rn( rH.rfr 



= 2-G7 n \ r H c dr + 2'gt a 1 r (H # — H c ) dr 



J a Q Ja 



= n M, + 2-5T n I radr 



= »(Hc+B), 



