218 
MR. J. LARMOR ON A DYNAMICAL THEORY OF 
material bodies on one another, and the material stresses and physical changes 
thereby produced. As in the preceding papers, the quantitative results are to a 
large extent independent of any special theory of the constitution of matter, such as 
is here employed to bind together and harmonize the separate groups of phenomena, 
and to form a mental picture of their mutual relations; so far as they are electric 
they may be based directly on Maxwell’s equations of the electric field in free 
space, which form a sufficient description of the free aether, and have been verified by 
experiment. In the Faeaday-Maxwell theory, however, as usually expounded, an 
explanation of these equations is found, explicitly or tacitly, in an assumption that the 
aether is itself polarizable in the same manner as a material medium, and aether is in 
fact virtually considered to be matter ; on the present theory the equations for free 
space are an analytical statement of the ultimate dynamical definition of the 
continuous a^thereal medium, and the polarization of material bodies with the 
resulting forcive are deduced from the relation of their molecules to this medium in 
which they have their being. 
10. In the modern treatment of material dynamics, as based on the principle 
of energy, the notion of configuration is, as above explained, fundamental. The 
potential energy, from which the forces are derived, is a lunction of the mutual 
configurations of the parts of the material system. In the case of forces of elasticity 
the internal energy is primarily a function of the mutual configurations of the 
individual molecules, from which a regular or organised part (§ 49 infra) is separated 
which is expressible in terms of the change of configuration of the differential 
element of volume containing a great number of molecules, and from which alone 
is derived the stress that is mechanically transmitted. In connexion with the 
discussion of contact action in § 6 above, the mode of this derivation and trans¬ 
mission becomes a subject of interest.* In the first place the primary notion of a 
force as acting from one point to another in a straight line, has to be generalized 
into a forcive in Lagrange’s manner on the basis of the principle of virtual work : 
then the forcive arising from the internal strain-energy of the element of volume of 
the material is derived by variation of this organized energy, and appears primarily 
as made up of definite complex bodily forcives resisting the various types of strain 
that occur in the element ; then these forcives are rearranged, by the process of 
integration by parts, into a uniform translator^ force acting throughout the element 
of volume of the material (wdiich must compensate the extraneous applied bodily 
forcive) together with tractions acting over its surface. When this is done also for 
adjacent elements of volume, other tractions arise which must compensate the 
* It is here assumed that the direct action between the molecules is sensible only at moleculai 
distances, which would not be the case if the material were electrically polarized. The statement also 
refers solely to transmitted mechanical stress of the ordinaiy kind : more complicated tj pes, not 
expressible by surface tractions alone, are put aside, as well as molecular conceptions like the Laplaciax 
intrinsic pressure in fluids. Cf- §§ 44-6 infra. 
