418 THE ELECTROMAGNETIC FIELD. [PT. III. CH, XI. 



Consequently the dimensions of the product of the electric 

 and magnetic inductivities must in any system be those of the 

 square of the reciprocal of a velocity. The absolute dimensions 

 of either factor are arbitrary. Attempts have been made to settle 

 the absolute dimensions of e or //,, but they are evidently based 

 upon misconceptions of the theory of dimensions. The two 

 common assumptions are, that 



This gives the electrostatic system. Secondly we may assume 



= 1 = - 



P' ~ V 2 ' 



This gives the electromagnetic system. We shall, when 

 dealing principally with the magnetic properties of currents, use 

 the electromagnetic system, but when dealing equally with elec- 

 trical and magnetic phenomena, to avoid ambiguity, we shall, 

 following Helmholtz and Hertz, use the Gaussian system, 

 measuring all electrical quantities in the electrostatic system, 

 all magnetic quantities in the magnetic system, and introducing 

 the factor A, with the numerical value 1/v. A complete table 

 of dimensions of the various units is given at the end of 

 Chapter XIII. 



215. Potential due to Circular Current. The potential 

 at P due to a current being H = /&>, where a> is the solid angle 

 subtended at P by the current circuit, if P is situated at a dis- 

 tance so from the center of a circular current of radius R, on 

 the line through its center perpendicular to its plane, we 

 have for the area of the segment of the sphere of unit radius 

 about P cut off by the right cone whose vertex is P, and base 

 the current, 



(l) ft> = 2?r I sin 6dO = 27r(l cos a) 



Jo 



' 27T (l - 



This may also be obtained, according to 123, by differen- 

 tiating the expression for the potential of a disc at a point on the 

 axis. 



