MR. G-. F. 0. SEARLE ON PROBLEMS IN ELECTRIC CONVECTION. 
G81 
lead to two important results, for if the divergence of each of these equations be 
taken we have 
div curl H = 4a- (div D) -f- 477 div (pu).(6), 
(LO 
div curl E =- jr (div B).(7). 
CIL 
But div curl H and div curl E both vanish identically, so that 
Y t ( div D) = - div (pn) .(8). 
lit (d^ B) — 0 
(9) 
But div D = p, so that (8) becomes 
dp/dt = — div (pn) 
( 10 ). 
Thus the density of electrification at any point can only be changed by the convec¬ 
tion of electrification to or from the place. If a body has a charge q. no change in q 
can be produced by the motion of other charged bodies or of magnets in its neigh¬ 
bourhood. In the ordinary parts of the field p is zero initially, and therefore 
continues zero. 
From equation (9) we find that div B = constant. But we already know that 
div B = 0. 
If K and p, are constant, then at all points of the field we have, 
div E = 
47rp 
~K 
(ii). 
div H = 0 
( 12 ). 
Application to Steady Motion. 
4. I shall now apply the principles already stated to the case of the steady motion 
of any system through the field. The coordinates x, y, z will be supposed measured 
from a system of axes moving forwards with the system, without rotation. The 
motion of the axes will introduce no difficulty, for the values of the line and surface 
integrals are the same whether the axes are at rest or in motion. 
mdcccxcyi.—a. 4 s 
