284 
MR. J. LAR^rOR ON A DYNAMICAL THEORY OF 
magnetic elongation and the pressure corresponding to the strength of the 
part of the field in Avhich it is undamped. This is on the supposition that the bar is 
long, so that there are no free magnetic poles near together which would diminish Q 
l)y their mutual attraction. The work done per unit volume by the magnetic forces 
during the removal of the bar is — |(/f + I H dH. The resultant work in 
the cycle being null, we have dKjciq . |QH aTT = - = - ^Qp7'M, where M is 
Young’s elastic modulus. This can only be satisfied if Q is of the form XH-, 
where X is a constant, and it then gives d/c/dQ = — 2X/M, and the elongation I is 
^d/f/c7Q . H^, that is ^ dK~^ldQ ,. I^, or — ^d log /c/c/Q . HI; while the corresponding- 
stress Q is — ^dKjdl. This result is of course valid only in the absence of 
hysteresis. A similar process applies where the field is transverse to the bar; and 
thus Kirchho.ff’s complete insults may be obtained. A more complete enumeration 
of possible physical changes would also take cognizance of alteration of the elastic 
constants of the material due to the magnetic excitation ; but this cause {cf. § 83) 
will not add terms of the first order to the energy-changes unless the bar is under 
extraneous stress, not merely constraint, while the cycle is being performed. 
For dielectrics, direct experiments have not found any sensible dependence of 
inductive capacity on the pressure in the case of licpiids ; while the experimental 
discrepancies,which these terms were introduced by von Helmholtz to reconcile, 
have since been cleared up. 
68. In the paper above referred to, KrncHHOEF remarks (§ 3) that an expression 
for the traction across an ideal interface in a uniform polarized medium might be 
arrived at by supposing a very thin film of air introduced along the interface, and 
computing Ihe attraction between the two layers of opposed poles thus separated, a 
jmocess which had been employed by Boltzmann. He concludes that this process 
must be at fault, on the ground that the specification of stress thus obtained does not 
satisfy a necessary property of mechanical stress-systems, namely that the tractions 
exerted over the surface of an infinitesimal element of volume of any form must 
balance each other; and he gives this as the reason for having to fall back on an 
energy-method in order to obtain a specification free from objection. The preceding 
considerations (§§ 44-48) indicate the direct reason of the illegitimacy of that process, 
while they also exhibit the logical basis of the application of the method of mechanical 
energy in problems of molecular ])hysics. 
* [In these clitferentiations I is constant; see § 83.] 
4 Namely, the differences in tlie values of K at first found by Quincke, bv use of three different 
expeiimental methods (§ 78), which it is easy to see wonld on the usual theory involve perpetual 
motions. 
