324 
MR. J. J. THOMSON ON SOME APPLICATIONS OF 
— B and k will differ widely. According to equation (32) the force acting on a piece 
of soft iron placed in a magnetic field is 
{IX} 
(39) 
if I be the intensity of magnetisation, but according to the ordinary formula it is 
equal to the differential coefficient with respect to X of the energy per unit volume 
(40) 
Now we have just seen that B and k differ widely when I approaches the value 
which it has when the iron is magnetised to saturation, so that if our view be correct 
the ordinary formula will not give correct results in this case. 
[zz] cannot be a function of the heat coordinates a, as these are kinosthenic. 
Joule’s discovery that a bar of soft iron lengthens when magnetised in the longi¬ 
tudinal direction, and that the increment in length is proportional to the square of the 
intensity of the magnetisation, shows that {zz} is a function of the strain coordinates w. 
We shall consider in some detail a few of the consequences of this result. Let us 
suppose that we longitudinally magnetise a soft iron bar, whose length is in the 
direction of the axis of x ; let e, f g be the dilatations at any point of the bar parallel 
to the axes of x, y, z respectively. 
Then neglecting for the present any torsion there may be in the bar the potential 
energy V of the strained bar will in the usual notation be 
\m{e +f+gY J r\n(e l +p+g 9 '-2ef-2eg-2fg) ..... (41) 
But if T' has the same meaning as in equation (22) 
T '=terms not depending on the magnetic coordinate — J — 
— (42) 
if I be the intensity of magnetisation. Joule’s discovery shows that B is a function of 
the strain coordinates e,f g. If there is no external force tending to strain the bar, 
the modified Lagrangian equation gives, when things are in a steady state, 
dJF dY 
de de 
(43) 
with similar equations for J’and g. 
