406 Mr. Oliver Heaviside on the 
written in the two ways, 
U=2 Hck /8r@=42ZG. 
If there be electrification, we have also another term to add, 
the real electrostatic energy, in terms of the scalar potential 
and electrification. And if there be impressed electric force 
in the dielectric, part of G will be imaginary magnetic cur- 
rent, analogous to the imaginary electric current which may 
replace a system of intrinsic magnetization. 
Plane Wave.—Let there be a plane wave in the medium. 
Tis direction is defined by its normal. Let then N be the 
vector normal of unit length, and < be distance measured 
along the normal. If v be the velocity of the wave-front, the 
rate the disturbance travels along the normal, or the compo- 
nent parallel to the normal of the actual velocity of propagation 
of the disturbance, we have 
H=/(z—2) 
if the wave be a positive one, as we shall suppose, giving 
a @ 
ae) ae = ae ee MOR CR On ee. oO (23) 
applied to H or H. 
Next, examine what the operator VY or curl becomes when, 
as at present, the disturbance is assumed not to change direc- 
tion, but only magnitude, as we pass along the normal. 
Apply the theorem of Version (9) to the elementary rectan- 
gular area bounded by two sides parallel to KE of length a, and 
fe hs Wave fron€ 
two sides of length 6 perpendicular to E and in the same 
plane as E and the normal N. Since its area is ab, and 
6=dz sin 0, and the two sides 6 contribute nothing to the line- 
integral, we find that F 
curl mails Py AS eae eae 
z 
applied to E or H or other vectors, in the case of a plane 
