MR. G. F. C. SEARLE ON PROBLEMS IN ELECTRIC CONVECTION. 
711 
equilibrium distribution, ^ is constant throughout the interior of B, and hence the 
field between A and B and inside A is the same as if A alone were present. The 
restriction that the charge on A should be rigidly fixed may therefore be removed. 
There is no disburbance inside A since there both and Tq are constant. 
We now see at once that if the distribution on B be changed in sign and that on A 
O o 
be removed, then at all points outside B the field is exactly the same as that due 
to A. We have now only to substitute another equilibrium surface C for B in order 
to complete the proof of the proposition. 
The electric force just outside B is, of course, the same whether it is produced 
either by the charge on B or by that on A. Thus, if E„ be the normal component 
reckoned outwards of that part of the electric force which is not derived from 12, then 
_ K 
ct -s e -' 
Energy of a system of Moving Charges. 
22. If it be allowed that there is energy stored in the ether when it sustains 
electric and magnetic stresses, and that the amount of energy per unit volume does 
not depend upon the manner in which those stresses are produced, but only upon the 
values of the stresses themselves, then, as is well known, it follows that if U be the 
total energy due to electric stress, and T the total energy due to magnetic stress, the 
values of U and T are 
U = MJ [******■ . . . 
.... (90), 
T = s x - |(j gWdxdydz . . . . 
.... (91), 
the integration extending through all space, or, what is equivalent, throughout the 
whole of those regions where E and H do not vanish. 
If W be the total energy of the system, then 
W = U + T.. . (92). 
When 12 = Q, and the electricity is distributed over surfaces which form the 
boundaries of regions of no disturbance, the expression for the energy admits of an 
important transformation. I have not succeeded in effecting any simplification in the 
case in which both 12 and exist. 
If we take the values of E and IT given by (26) to (31) in terms of V P when 12 = 0, 
and remember that K/jlv 2 = 1, we find that 
