732 
MR. A. McAULAY ON THE MATHEMATICAL 
In these, D', n have been substituted for Maxwell’s e , m, as the latter symbols 
already have, in the present paper, a different meaning. “ When the magnetic force 
can be derived from a potential ” 
H' = ~ Vn .(16). 
[There is no risk of this scalar being confused with the H of §§ 9, 10, 54 of the 
present paper.] In addition to these, he gives in § 613 the surface equation corre¬ 
sponding to equation (14), viz., 
D/ = [SUffd']„ + /) .(K) (17), 
where D/ has been put for his cr. 
61. Equation (5) is the same as equation (22), § 26, above, (7) as (23) § 26, (8) as 
(14) § 25. We can now show that equations (6), (9), (10), (11) all follow if we 
assume that there is no external force other than that due to friction. 
By the last paragraph of § 50 above, we see that what Maxwell calls E is not 
likely to be what on the present theory we call E'. To compare with ordinary 
theories, then, it is convenient to introduce a new intensity E 0 defined by 
E 0 = RK.(18). 
Since E 0 and RK (§ 10, Prop. VI, above) are both intensities, equation (10) 
follows. To prove (9), note that 
c V.r = — K Vx = — RK = — E 0 
d V£ = — 4rrK ~ 1 d, 
so that putting e of equation (28), § 50, equal to zero, 
d = KEo/477% 
from which equation (9) follows by Prop. VI, § 10. Again, 
B = 47t h VZ = /a H -f- 47 tI 0 
and therefore 
B = /PH' + Anl 0 ' .(19), 
which implies that the part of B' “induced” by magnetic force, is /x’H'. This is 
equation (11). 
62. To prove equation (6), note first that putting E = 0, equation (29) of § 50 
[modified by equation (39) of § 50] gives 
E 0 = — A — Vf 
(20). 
