THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
257 
them.'^’^ If, however, the medium were crystalline, the stress would be of a more 
complex type than this, being related to the crystalline axes as well as the axis of 
polarization. When the interface is the surface of a conductor, the forcive on the 
charge of free electrons which pervades the layer of transition adds nothing to this 
effect beyond what has been already set down ; for the electric force due to a volume- 
distribution of single poles or electrons has no finite j^art depending solely on the 
element of volume at which its value is expressed, that is, it involves no molecular 
term, 
44. The analysis here given is not however numerically applicable to a case in which 
the effective distance between the poles of a molecule is comparable to the distance 
between neighbouring molecules. The system formed by a bundle of iron nails 
suspended from the pole of a magnet and hanging on to each other against gravity, 
which has been used as an illustration of the molecular part of the forcive in the 
previous papers, does not come under these formulm. That system may however be 
employed with advantage as a real illustration of the general principles, especially if 
we imagine the magnetized iron nails to be connected by springs or imbedded in an 
elastic matrix. When no extraneous forces such as gravity act on this model of a 
molecular medium, it adjusts itself into a condition of internal equilibrium, in which 
attractions between the magnetic nails are locally balanced by repulsions exerted by 
the springs. The various local molecular forcives, typified here by these attractions 
between magnets and forces exerted by springs, precisely compensate each other in 
each portion of the medium. If an additional magnetic field is introduced, which 
alters the magnetic polarities of the nails, the parts of the medium will change their 
shapes and volumes until compensation again supervenes : there will thus occur an 
intrinsic deformation of the medium, and there may be also intrinsic changes of its 
physical properties, associated with the polarization and proportional in simple cases 
to its square. Suppose now that an extraneous force like gravity, or the magnetic 
field arising from the medium as a whole, begins to act, that is, a regular mechanical 
force on the medium in bulk so that it is in the aggregate proportional to the volume 
on which it acts ; this will produce a further deformation, but one proportional to 
the first power of the exciting force. The local internal molecular forcive will again 
no longer be exactly balanced ; but the unbalanced part will possess at each point 
the characteristics of an elastic stress system, because when the element of volume 
is small enough the tractions thus arising over its surface must equilibrate without 
any assistance from the then negligibly small extraneous bodily forcive. Even then 
however this elastic stress excited by an external field cannot be specified in terms 
of surface tractions unless the dimensions of the smallest element of volume which 
the circumstances require us to consider are large compared with the range of the 
intermolecular forces. Unless that is the case, the energy of elastic strain of the 
element of the medium, expressed in Green’s manner, will involve higher fluxions of 
* This is an example of Maxwell’s theorem, ^ 40 supra. 
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VOL. CXO.—A. 
