482 
PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD. 
Coefficient of Magnetic Induction (g). 
(60) Let g be the ratio of the magnetic induction in a given medium to that in air 
under an equal magnetizing force, then the number of lines of force in unit of area 
perpendicular to x will be goc (g is a quantity depending on the nature of the medium, 
its temperature, the amount of magnetization already produced, and in crystalline bodies 
varying with the direction). 
(61) Expressing the electric momentum of small circuits perpendicular to the three 
axes in this notation, we obtain the following 
liquations of Magnetic Force. 
dR dR 
~ _ dF dR 
~ dz dx 5 
dG dY 
(B) 
Equations of Currents. 
(62) It is known from experiment that the motion of a magnetic pole in the electro- 
magnetic field in a closed circuit cannot generate work unless the circuit which the pole 
describes passes round an electric current. Hence, except in the space occupied by* the 
electric currents, 
udx+fidy-\- ydz=d<p (31) 
a complete differential of <p, the magnetic potential. 
The quantity <p may be susceptible of an indefinite number of distinct values, according 
to the number of times that the exploring point passes round electric currents in its 
course, the difference between successive values of <p corresponding to a passage com- 
pletely round a current of strength c being 4src. 
Hence if there is no electric current, 
but if there is a current 
Similarly, 
— ^—0 • 
dy dz - u ’ 
dy d$ . . 
!-s= 4 *y'- 
da. dy . , 
d/3 dx . 
7U-Ty= 
We may call these the Equations of Currents. 
(C) 
