750 
MR. A. McAULAY OR THE MATHEMATICAL 
At the surface of the soft iron H' is tangential, and therefore continuous. From this 
it easily follows that 
[{f} Uv'l + V = Q. 
Hence, due to Maxwell’s stress, there is in this case no superficial force and no 
bodily force in the air, but there is a bodily force in the iron directed towards the 
axis. The iron will therefore be compressed. 
77. For the other case, notice that the force per unit surface due to the electro¬ 
magnetic part of Maxwell’s stress is — [{</}UV] ft + 6 and by equation (27), §67, 
- 8tt [{</>' }XJv'] a + b = [B'SH'UV + H'SB'UV - UFH' 3 ]„ +6 . 
This can be put in several different forms, of which, perhaps, the following are the 
most useful 
- 8tt [{</>/U/] 0+6 = 4tt [I'SUfH'] s+i + (H/ + B/)[SU^rul 
= (47rT + H/ + B/) [SUVH'] a + 6 -f- 47? [rSUFH'] a + 6 J * 1 } ’ 
where the bar indicates the mean value for the two regions bounded by the surface, 
and the suflixes n and t denote normal and tangential components respectively. Thus 
B/ and H/ have the same value on both sides of the surface. When B' is parallel to 
H', B' = ,x H' where /x' is a scalar, not necessarily constant. (But if not constant it 
lias here a different meaning from what it has in the rest of this paper.) In this 
case the tangential component of — 87 t[{<//}UV] C(+ 6 is zero. For the first expression 
of equation (36) gives for the component in question 
[(477-1/ + H/) SUFH'] tt + 6 H/[/SUfH'] a + c = H/ [SLVB'], + 6 = 0. 
So long then as we deal with magnetically isotropic media this surface traction is 
normal. 
Consider a magnetically isotropic body surrounded by a non-magnetic medium, and 
let the magnetic region be denoted by the suffix a, so that 1/ = 0. In accordance 
with what has been just proved we consider only the normal part of the traction. 
Thus, 
- 8ir[{f} U./]. + 6 = 4 7 r[IbSWH / ] a + , + B/ [SIVH'] a + i . 
Let now = HUV„. Thus 
to [I'„]„ = (y - 1) HTV„ B', = n'HU»'„ 
[S WH'i = - h, [surH']„ +i = (y — 1) H, 
the last coming from the fact that H',,], = E „ Thus 
