Permeability of Iron and Steel. 87 
assume a factor in the permeability which vanishes for the 
saturation-value, namely (%3,, —%), where %_ isthe saturation- 
value of the induction. The resistance will then be propor- 
tional to the reduced length divided by this factor, so that 
resistance es 
jo 
A l 
ON (GB. — B)cos 6, 
or p=A(B, — B) cos 8. 
We may give some further account of the factor (%, —B) 
based on an analogy between the lines of magnetic force and 
solid wires. Ifa number of thin wires had to be packed into 
a cylindrical tube, by the time there were a certain number of 
them the hollow of the tube would be full, and no more could 
be got in. Also, if there were a less number, the space avail- 
able in the tube would be measured by the number of wires 
that could still be added. 
Now if our axis of transmission in the molecule represent 
the hollow tube, and the lines of force the wires, it is reason- 
able to assume that the permeability is proportional to the 
portion of the channel left open and unoccupied. And this 
is precisely given by (@,— %). It is only an analogy, but it 
seems to me not destitute of force. We may call (B, — B) 
“defect of saturation.” 
Let us return to the consideration of the equilibrium of 
the molecule. On the one hand we have the couple exerted 
by the lines of force ; on the other that arising from molecular 
attachments, which tends in the opposite direction. 
The simplest law of molecular attachments is the law of 
torsion ; and in considering a single molecule I assume that 
the couple tending to restore it to its place is proportional 
to the angular rotation from the position of rest. (The dis- 
placements of subpermanent and permanent magnetism are 
at first left out of the question.) If therefore 
p be the diameter of the molecule, 
k the torsion per degree, 
@ displacement from rest, 
@ inclination to direction of magnetization in disturbed 
position, 
%* psin 0=kad 
* J assume that the tension along the lines of force is proportional to 
35 instead of to %, according to Maxwell. I shall return to the point ; but 
‘may say here that the assumption of force proportional to 3§, led to 
formulz which failed to represent the experiments. 
