330 Mr 8. H. Burbury, On the application of [Jan. 28, 
From this equation we cannot deduce the laws of induction 
in the circuit due to variation of the magnetic field. Maxwell’s 
method would therefore fail if applied to the system of circuit and 
magnet. In order to justify it as a logical process, it becomes 
necessary to show how the case of circuit and shell is logically 
distinguishable from that of two circuits, so as to admit of the 
employment of Lagrange’s equation in the one case and not in 
the other. Maxwell gives no explanation directly. It appears to 
me that the distinction lies in the reciprocal property mentioned 
by him as proved by Felici [Maxwell, § 536 (2)], namely, that the 
induction of circuit A on circuit X is equal to that of X on A; 
or as we may otherwise express it, if F’,, F, be the electromotive 
forces of induction in the two circuits respectively, ¥,, 7, the cur- 
rents, then 
dF. dF, 
dy 2 Re: dy 1 : 
‘ dF, dF, 
ae dij, dij,” 
This property, though true for two circuits, is not true for circuit 
and shell, and that is the reason why Lagrange’s equations are 
inapplicable in the latter case, and why Maxwell did not attempt 
to apply them to it. 
In case of any purely mechanical system the energy is given by 
pl d\n (LUNG ZNe 
OY == S70 \(@e) + a a5 a | 
over the whole system. 
If q,.-.q, be the generalized coordinates defining the system, 
p,---p, the corresponding momenta, then 
ram (t=O) +a 
sim (#2 & 5 du ay 4 de dey, 
- (ai, dq," dq, dg," dq, dq,) 
+ &e. 
And therefore dp, = ap, : 
dq, dq, 
aT 
and p= ae 
Lagrange’s equations are proved only for these values of the 
ps. If the space coordinates be invariable, we shall have 
dp 
i= ae 
