AND ON THE ELECTROMAGNETIC THEORY OF LIGHT. 
655 
If we divide by b and differentiate with respect to z , we find 
f=-^ < 14 ) 
Let us next consider a parallelogram in the plane of x z , two of whose sides are a along 
the axis of x, and z along the axis of z. 
If P is the electromotive force per unit of length in the direction of x, then the total 
electromotive force round this parallelogram is «(P — P 0 ). 
If p is the coefficient of magnetic induction, then the number of lines of force embraced 
by this parallelogram will be 
f* ayjfldz, 
and since by (B) the total electromotive force is equal to the rate of diminution of the 
number of lines in unit of time, 
«ip-Po)=-f t s;^dz. 
Dividing by a and differentiating with respect to z, we find 
dV_ dp 
dz—^dt 
(15) 
Let the nature of the dielectric be such that an electric displacement/' is produced by 
an electromotive force P, 
r=¥> (16) 
where Jc is a quantity depending on the particular dielectric, which may be called its 
“ electric elasticity.” 
Finally, let the current j), already considered, be supposed entirely due to the varia- 
tion off, the electric displacement, then 
p=% ('"» 
We have now four equations, (14), (15), (16), (17), between the four quantities (3,_p, 
P, and f. If we eliminate p, P, and/, we find 
If we put 
d *[ 3 k_ cPp 
dt 2 4 ny. dz 2 ‘ 
the well-known solution of this equation is 
(3=(p.(z— V£)+<p 2 (z+V£), . 
showing that the disturbance is propagated with the velocity V. 
The other quantities p, P, and /can be deduced from (3. 
(18) 
(19) 
( 20 ) 
