MR G. F. C. SEARLE ON PROBLEMS IN ELECTRIC CONVECTION. 
685 
where we have used 
Thus, 
But, 
Again, by (35), 
E + pYu (R - KVEu) = F, 
YHu = - YuH. 
E + ijlYvlR • —~ YuYEu — F 
v i 
VuYEu = ESuu — uSuE = E — uSuE. 
SuE — pSuYHu = SuF. 
(37). 
But \ r Hu is at right angles to u (and also to H), and hence the “ scalar product ” of 
u and YHu vanishes. Thus SuE = SuF, and therefore (37) becomes 
E + pYuR - ~ E - 4 SuF = F, 
V ir 
so that 
/ 2 \ 
E i I - |j = F - ^ SuF “ /^VuR.(38). 
Similarly, 
H (1 — ~) = R - iL SuR + KYuF.(39). 
The last pair of equations are easily seen to be equivalent to the set of six typified 
by (22) and (23). 
The forms which E and H assume when u is parallel to x, are given in equations 
(76) and (77) below. 
Motion of a Point-Charge. 
6. The problem of a moving point-charge has been solved by Mr. Heaviside and 
Professor J. J. Thomson, but as the solution will often be needed in other parts of 
the work, it will be useful to put it down. 
If, in the ordinary case of electrostatics, there is a point-charge q at the origin, the 
electrostatic potential is q [x 2 -f- r + * 2 ] *• 
Guided by this, let us put 
M' = A |——[- y 2 -f 
Since these values satisfy equations (33), (34), they form the solution of some 
problem in the case of motion. We have now to find what that problem is. 
