316 
MR. J. J. THOMSON ON SOME APPLICATIONS OF 
energy of a charged sphere is e 2 /2c, where c is the capacity of the sphere, we see 
from equation (9) that the motion of the sphere will alter the coefficient of e 2 in the 
expression for the energy, and will therefore alter the capacity. To find this altera¬ 
tion let us suppose that the charge on the sphere is increased by Se, and that Q is the 
external electromotive force acting on the sphere, the energy of the system is 
m 2 ju,c 2 \ 0 1 e 3 
5 + 15 a ’ r+ 2Ka’ 
• (10) 
if K be the specific inductive capacity of the medium surrounding the sphere, if the 
increment in v he Sv, and in e oe, the increment in the energy 
ffl+ r5 
i e ^ e 
cSc+— 
a K« 
flV 
( 11 ) 
but by the conservation of energy this must equal 
QSe 
Now since the momentum of the sphere is not altered 
—W+zy — vSe=0.(12) 
\ 15 a / 15 a 
eliminating Sc between these equations we find 
so that the capacity of the sphere is increased in the ratio of 1 to 1 — ^ _/xIvn 2 ; or since 
by the electromagnetic theory of light /xK = 1 ju 2 where u is the velocity of light, the 
fit f $ > 
capacity of the sphere is increased in the ratio of 1 to 1 ———, and thus the altera- 
tion depends on the square of the ratio of the velocity of the sphere to the velocity 
of light, and will consequently be very small. If the earth does not carry the ether 
with it, the alteration in velocity which occurs at a point on the earth’s surface will 
produce a diurnal variation in the capacity of a condenser at that point. If the 
condenser is a sphere, the maximum diurnal variation in its capacity, which wall be 
when the direction of motion of the solar system, is parallel to the direction of motion 
of the earth in its orbit: is about 4 X 10 -8 per cent, of the capacity of the condenser. 
This is much too small to observe, but it is remarkable that the capacity of a condenser 
should depend upon its velocity. 
There seems nothing to show that (xxj is a function of the magnetic coordinates z, 
