40 Mr M¢Connel, On the Mechanical Force acting [Nov. 22, 
We may put (10) into the form 
d (4—4,) d (a —4,) d (a — a,) 
A ae Smee ap +C AE 
dx, dp, dy, 
Now Ap — VW; i = 27rw, =: => 270, by (8), 
and d(a,+4,+4,) _@(8,+8,+B,) 
dy da 
by the definition of 5, 
wer Get meee 
We can treat the third term of (10) in the same way, so (10) is 
equal to 
ae ae pee + ce — B2aw + C2n0......-.. (11). 
dx dx i 
Let us now consider (9). 
§, is indefinitely small throughout the element, 
H, =— 275,, if S, be the transverse part of the magnetisation, 
§, is parallel to the current, so that vy, — w@, is zero ; 
therefore (9) = vy — wB + (v27C, — w27B,) 
_ =vy—we+ 270 —w2rB, 
since the rest of the magnetisation is parallel to the current. 
Adding a we find that the total force has the components 
A= Ae Sal a0! + (y+ 470) —w(68 + 47rB), &e. 
The couple has the components 
L=B(y,+%.+%,) — C (8, +8, + 8) 
= By — CB, &c. 
and these are Maxwell’s expressions for the total force and couple. 
This completes the proof; but there is one point of considerable 
interest, which occurs in the course of it, and demands some further 
remarks. In Art. 490, as we have said, Maxwell shows that the 
mechanical force acting on a conductor is V.@,, using Quaternion 
notation. Where there is no magnetisation this is the same as 
V.G%, and Maxwell adopts this latter form and retains it even 
