(o6%\") 
IlL—ON THE QUANTITY OF ENERGY TRANSFERRED TO THE ETHER BY A 
VARIABLE CURRENT. By GEORGE F. FITZGERALD, M.A., F.R.S. 
[ Read, November 19, 1883. ] 
I rake the simple case of a small circular current varying according to the simple 
periodic pendulum law. 
If the current be a small circle of radius a round the origin in the plane zy, then 
the direction of the electro-magnetic potential (9) at any point is evidently in the 
circumference of a circle through the point parallel to the current, and whose centre 
is on the axis of z, and its amount is 
b) 
oy! pal" wes 
when @ is the angle between the element of current ad@ and the plane through the 
axis of z and the point, and 7 the intensity of the current. 
This value is not the complete value when 7 varies, because there are then dis- 
placement currents due to the variations of electric displacement which produce 
electro-magnetic potentials of their own. The complete value of % must, however, 
be such as to satisfy the equation 
Aa + Keil = 0, 
for all points outside the current, and must vanish at infinity. 
Now, if 7 be simply periodic we may assume 
; t 
7 = | COS 27 - 
and if we take 
(cos e- Vv Ky.r) 
A= par, J cos 66, 
’ 
it, as a function of 7, satisfies the required conditions, and for small values of 7 and 
large values of 7’ is the same as if we neglected the displacement currents. 
In order to get the energy of the ether due to the displacement currents in it 
we must calculate : 
T=1\{\(Fut Go + Hw)drdy dz =} § {| S(t) dady dz. 
TRANS. ROY. DUB. SOC., N.S. VOL. III. I 
