216 
I^IR. J. LARMOR OX A DYXAMICAL THEORY OF 
act on each other from a distance with forcives obeying definite laws, derivable from 
the formula for the energy. It is only in electromagnetic phenomena and molecular 
theory that non-vibrational movements of the rether are involved. The tether not 
being matter, it need not obey the laws of the dynamics of matter, provided it obey 
another scheme of dynamical laws consistent among themselves ; these laws must 
however be such that we can construct in the sether an atomic system of matter 
which itself obeys the actual material laws. The sole spacial relations of the aether 
itself, on which its dynamics depend, those namely of incompressibility and rotational 
elasticity, are thus to be classed along with the existing Euclideax relations of 
measurements in space (which also might a 'priori be difierent from what they are) 
as part of tlie ultimate scheme of mental representation of the actual physical world. 
The elastic and other characteristics of ordinary matter, including its viscous rela¬ 
tions, are on the other hand a direct consequence of its molecular constitution, in 
combination with the law of material energy which is itself a consequence of the 
fiict that the energies of the atoms are wholly located in the surrounding simple 
continuous aether and are thus functions of their mutual configurations. In this way 
we come round again to an order of procedure similar to that by which Cauchy 
and Poisson originally based the elastic relations of material bodies on the mutual 
actions of their constituent molecules. 
Consider any two portions of matter which have a potential-energy function 
depending, as above explained, on their mutual configuration alone, the material 
movements being thus comparatively slow compared with the velocity of radiation ; 
any displacement of them as a single rigid system, whether translational or rota¬ 
tional, can involve no expenditure of work ; hence the resultant forcive exerted by 
the first system on the second must statically equilibrate that exerted by the second 
system on the first, these forcives must in fact be equal and opposite wrenches on a 
common axis; and the energy princijile thus involves the principle of the balance of 
action and reaction, in its most general form. This stress, between two molecules, 
is usually sensible only at molecular range ; hence the action of the surrounding 
parts on a portion of a solid body is practically made up of tractions exerted over 
the interface between them. Further, since rotation of the body without deformation 
cannot alter the potential energy of mutual configuration of the molecules, it follows 
that for a rectangular element of ordinary solid matter the tangential components of 
these tractions must* be self-conjugate, as they are taken to be in the ordinary 
theory of elasticity. On the other hand, for a medium not molecularly constituted 
we can hardly treat at all of mutual configuration of parts, and the self-conjugate 
stress-relation will not be a necessary one. 
A certain similarity may be traced with the view of Faraday, who was disin¬ 
clined to allow that ray-vibrations are transmitted by any medium of the molecular 
character of ordinaiy matter, but considered them rather as affections of the lines 
which represent electric force, the propagation being influenced by the material 
