THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
261 
matter, mechanical forces, in the ordinary sense, would not exist. The actual 
interactions between the molecules are however necessarilj^ presented to us divided 
into various statistical groups, which are the subjects of perception by different 
senses; and it is the business of physical theory to follow out the relations of these 
different groupings to each other, and to trace them all back into the ultimate unity. 
The total energy of the molecules of a material body, corresponding to any kind of 
excitation or polarization, is thus for us made up of various parts. There is a part 
involving the interaction, with any molecule under consideration, of other molecules 
at finite distances, which integrates into an energy function of applied mechanical 
forces of the system, such for example as gravitational or magnetic forces. Of the 
remainder of the energy, which arises from the mutual actions of neighbouring 
molecules, a regular or organized part can be separated out which represents the 
energy of elastic stress, and is a function of the deformation of the element of 
volume treated as a whole : this stress arising from the immediate surroundings in 
part compensates, for the element of mass under consideration, the applied mechanical 
forces aforesaid. The remaining, usually wholly irregular, parts of the local inter- 
molecular forces and motions compensate themselves mutually on the spot,—or at 
any rate can be considered as thus compensated by other such forces, of different 
origins, that are not at present under consideration.* The temperature depends in 
fact on this irregular residuum of forces, and so do the density and the other 
physical properties of the medium, which are thus affected when, owing to 
polarization or other excitation, this local part of the molecular forces and motions 
is altered. If we adhere to these principles, it will not be allowable, in deriving the 
applied bodily forces of a polarized material system from its organized energy of 
polarization, to vary such physical constants of the element of mass as occur in the 
expression for the energy ; for we should thereby be trenching on that part of the 
energy whose variation is compensated molecularly without directly originating 
transmitted bodily forcive, c/i § 63. 
49. It seems desirable to have names for the two parts into which the total energy 
of the molecules of a material medium is thus divided. If we agree to maintain the 
original precise meaning of the term mechanical (as above employed), viz. that a 
mechanical force is one which we can actually control for doing work for our purposes 
on matter in bulk, in contrast with a molecular force which we can reason about but 
not directly employ, we may call the regular part the mechanical energy, and the 
remaining wholly irregular part the non-mechanical; we may also use (as above) the 
* The principle of D Alembeet, which is the basis of the dynamics of finite material bodies, 
necessarily involves this order of ideas. That part of the ag'gregate forcive on the molecules in the 
element of volume which is spent in accelerating the motion of that element as a lohole, is written ofl"; 
and the regular part of the remainder must mechanically ec|uilibrate. But the wholly irregular parts 
of the molecular motions and forces are left to take care of themselves ; which they are knov,'n to do 
for the simple reason that the constitution of the material body is observed to remain permanent. 
