398 Mr. Oliver Heaviside on the 
tric displacement to magnetic induction. The three principal 
velocities will be (cu,)—?, (cue)—?, and (cu3)—?, if ¢ is the con- 
stant value of the capacity, and p41, (2, “3 are the three principal 
permeabilities. The wave-surface will be of the same character, 
only differing in the constants. 
But a dielectric may be eolotropic both as regards capacity 
and permeability. The electric displacement is then a linear 
function of the electric force, and the magnetic induction 
another linear function of the magnetic force. The principal 
axes of capacity, or lines of parallelism of electric force and 
displacement, cannot, in the general case, be assumed to have 
any necessary relation to the principal axes of permeability, 
or lines of parallelism of magnetic force and induction. 
Disconnecting the matter altogether from the hypothesis that 
light consists of electromagnetic vibrations, we shall inquire 
into the conditions of propagation of plane electromagnetic 
waves in a dielectric which is eolotropic as regards both 
capacity and permeability, and determine the equation to the 
wave-surface. 7 
For any direction of the normal (to the wave-front, under- 
stood) there are in general two normal velocities, 2. e. there 
are two rays differently inclined to the normal whose ray- 
velocities and normal wave-velocities are different. And for 
any direction of ray there are in general two ray-velocities, 
i. e. two parallel rays having different velocities and wave- 
fronts. 
In any wave (plane) the electric displacement and the 
magnetic induction must be always in the wave-front, 1. e. 
perpendicular to the normal. But they are only exceptionally 
perpendicular to one another. 
In any ray the electric force and the magnetic force are 
both perpendicular to the direction of the ray. But they are 
only exceptionally perpendicular to one another. 
The magnetic force is always perpendicular to the electric 
displacement, and the electric force perpendicular to the mag- 
netic induction. This of course applies to either wave. If 
we have to rotate the plane through the normal and the mag- 
netic force through an angle @ to bring it to coincide with the 
magnetic induction, we must rotate the plane through the 
normal and the electric displacement through the same angle 
§ in the same direction to bring it to coincide with the electric 
force, the axis of rotation being the normal itself. 
In the two waves having a common wave-normal, the dis- 
placement of either is parallel to the induction of the other. 
And in the two rays having a common direction, the magnetic 
force of either is parallel to the electric force of the other. 
