252 REPORT—1885. 
while the electromotive force at any point is also determined in terms of 
this same quantity F, G, H by the equations 
a¥ dv 
P= = ‘ ‘ f 
dt de | , (6) 
etc., ¥ being the electrostatic potential. From this it follows that 
d/a¥ ,@¥) -_op, dd 
Oe ae tae) OP Egg? ge a 
etc., and the vector F travels through the medium with velocity 1// Kp. 
Now, the value of this quantity can be determined by experiment, and 
agrees very closely indeed with the velocity of light. Thus the vector 
potential, and in the same way the electric displacement and the magnetic 
induction, travel through the medium with a velocity, as nearly as we can 
say, identical with that of light. 
Moreover, the electric displacement corresponding to this is in the wave 
front, and the same is the case with the magnetic induction a, b,c. By 
this motion energy is conveyed through the medium, the electrostatic 
energy depending on the electric displacement, the electro-kinetic on the 
magnetic induction, and the two can be shown to be equal. Thus the 
theory agrees with the undulatory theory of light in assuming the exist- 
ence of a medium capable of becoming a receptacle of two forms of 
energy. Electric displacement and magnetic induction are, then, changes 
of condition which can be propagated in waves of transverse disturb- 
ances through the medium with a velocity practically identical with that 
of light. Maxwell’s theory supposes that there is an intimate connection 
between the vibrations which constitute light and electric displacement ; 
according to some of his followers the two are identical, though, so far 
as I can judge, that is not necessary to the theory as he left it. 
Now, experiment shows that the value of is nearly the same for all 
media, so that it follows that on this theory the specific inductive capa- 
city of a medium—the ratio of its inductive capacity to that of air— 
should be equal to the square of the refractiveindex. Experiments have 
shown that while this law is by no means true for all substances, it is suffi- 
ciently nearly so for many to render it probable that ./ K gives the most 
important term of the index. 
In estimating the value of the comparisons we must remember that 
while K is determined by observations lasting over an appreciable time, 
the refractive index depends on vibrations of great frequency ; to compare 
the two, then, we have to adopt some dispersion formula, and find the 
value of the index for waves of infinite period, and this alone is a source 
of error. 
Again, the equations for a crystalline medium are obtained by Maxwell, 
and he shows that the velocity of wave propagation is given by Fresnel’s 
construction, while the electric displacement is in the wave front, and its 
direction is that of the axis of the ellipse which determines the velocity. 
The theory is not burdened with a wave of normal vibrations, and 
accounts quite simply for all the phenomena of double refraction. 
§ 2. The theory of reflexion and refraction of electro-magnetic waves 
was first given by H. A. Lorentz,! who follows a method of attacking the 
1 Lorentz, Schlimilch. Zeitschrift, t. xxii. 
