THE ELECTEIC AND LUMINIFEEODS MEDIIJH. 
283 
various types of strain that it can sustain. Their vationctle is best seen by the more 
elementary procedure of Korteweg, who first introduced them. He considered the 
following cycle; (i) move up a piece of the dielectric material from an infinite 
distance into an electric field, (ii) strain it and so alter its inductive capacity and 
therefore the electric energy, (iii) move it back to an infinite distance in the strained 
state, (iv) restore it In its original condition by removing the strain. In order to 
evade perpetual motions, the mechanical work done by electric attractions as it 
approaches must exceed the work absorbed as it recedes, by the loss of available 
electrical energy due to strain ; and this leads Korteweg to terms in the mechanical 
forcive which depend on the rate of variation of inductive capacity with strain. 
The process is analytically developed for fluids by vox Helmholtz, by adding on to 
8K, the variation of K, a part arising from the compression of the material which the 
virtual displacement involves, namely by adding — dK/d log 5 . {d Sx/dx -f d Si//dy 
+ d Szjdz), where s denotes the material density: and Kirchhoff formulates it for iso¬ 
tropic solid media, replacing c/K/rHogsby Korteweg’s two coefficients which express 
the actual rates of change of K due to elongations along the line of polarization and at 
right angles to it. But here again a process of integration by parts comes in, which 
removes part of the bodily forcive from the element of volume at which it is directly 
applied to the boundary, and so vitiates the result regarded as a specification of the 
forcive which produces the actual mechanical strain in the material. 
G7. Moreover, phenomena of this latter kind are more appropriately investigated 
as intrinsic changes of the equilibrium configuration of the material arising from 
molecular actions produced by the polarization, the forcive of the above argument 
being simply what would he originated if these changes were prevented by constraint. 
Such deformations of the elements of volume of the material, the result of electro- 
striction or magnetostriction, may not fit in with each other, and the strain thence 
arising will originate secondary mechanical stresses: but it appears preferable to keep 
these distinct from the regular stress which is the effect of the direct electric or 
magnetic action of different finite portions of the material on each other. 
This separate procedure may be illustrated by an investigation of the change of 
intrinsic length of a bar of magnetic material, caused by its introduction into a 
magnetic field. Clamp the bar to its natural length when at a great distance ; then 
introduce it into the magnetic field so as to lie along the lines of force; then unclamjo 
in such way that it may do as much work as possible in pushing away resistances to 
its magnetic elongation ; finally remove the undamped bar again to a great distance. 
If this cycle is performed at a uniform temperature, it follows from Carnot’s principle 
that there can be no resultant work done in it. Now the work done by the magnetic 
forces in introducing the bar is |Ir/H, that is J(/c-f qdK/dQ+ IrMI)Hr/H, per 
unit volume, where k is the magnetic susceptibility which is presumably a function of 
the internal longitudinal pressure Q in the bar and of its intensity of magnetization I. 
The work done in unclamping is per unit volume, where is the intrinsic 
2 0 2 
