174 G. EF. Firzceratp.— Wave Disturbances in Ether by means of Electric Forces. 
simple periodic V=V,, cos nt, we see that the periods of maximum and minimum 
occur simultaneously everywhere so that it need not be of the nature of a wave 
propagation like light. 
e er V Kp nv) O 5 
Now if r=”z2@+y—B242—-y) then Va= cos” Ker) satisfies the equation 
z 
A2V,,=17KpV, 
and we may get a more general form for V,, by taking it 
sin = 
Vi =f f (aBy) mC, dadBdy 
ae BT a 
and we can make it have given limiting values by determining / (« P y) rightly. 
This value of V, vanishes for r= ~. 
We thus see that as 
a2V sin 
de ZV, 1 cos (nt) 
sin 
and A?V = —- Kp XV, nr’, ae (nt) 
: PV 
we get that V satisfies the given equation 4°V + Kp Ga—0. 
We thus see, generally, that if V contain a part depending on the time, and a 
part independent of it then it must be of the form just determined, in order to 
satisfy this equation. 
We have then that V satisfies the given equation if it is expressible thus :—. 
sin — 
V=3 f/f f (aby) 608 (VKyur) re (nt) dadBdy. 
This, of course, may represent a wave propagation, but a simply periodic variation 
of V in one curve in space would produce simultaneous maxima and minima 
values throughout space, and so would not originate wave disturbances at all. 
There is another method by which we may arrive at this same distribution of 
displacement currents near a varying current, 
Assume an initial distribution of currents (U) in conductors only, and calculate 
the electromagnetic potential at each point due to them, and then in terms of the 
initial acceleration of current ({j) calculate the initial displacement current (w) 
throughout space. We may not assume this to be the total initial displacement 
current, for we must go on and calculate the acceleration (w) of this, and find the 
resultant displacement currents and soon. Then by summing up the resultant 
infinite number of these partial initial currents, we may assume that the resultant 
is the actual initial current at each point. 
As we may deal with each element of current separately, I shall confine myself 
