692 
MR. G. F. FITZGERALD ON THE ELECTROMAGNETIC THEORY 
consequently P, Q, 1\ linear functions of f, g, h, so that we may write in Quaternion 
notation 
<£=<£$> 
and if we call U the general symmetrical quadratic function of f g, h we may assume 
L =P/+Q<7+RA 
and consequently 
. dxdydz =^( [[if dxdydz 
As the medium is magnetically isotropic we have 
^ — or a=fjL<x, b=y/3, C—yy 
where y is the coefficient of magnetic inductive capacity, and consequently the electro- 
kinetic energy may be written 
T= -^ f f j \^.dxdydz=^ \\\(od+P+f)dxdydz 
Now I shall assume the mediums to be nonconductors, and although this limits to 
some extent the applicability of my results, and notably their relation to metallic 
reflection, yet it is a necessity, for otherwise the problem would be beyond my present 
• 8 doc 
powers of solution. With this assumption, and using Newton’s notation of x for —, 
we have the following equations (see ‘Elect, and Mag.,’ vol. ii., § 619) 
using V for the operation 
47r < j) = V V 
. d . d d 
dx J dy dz 
or the same in terms of its components, namely, 
