the problem in hand. In electrodynamic problems however the individual electrons in the element of volume come into consideration, at any rate as regards their main division into positive and negative: and then the Action principle, as being the more universal, must almost of necessity be employed. If further we assume that the material molecule is wholly of aethereal constitution, this general dynamical principle of Action must itself be involved (cf. Appendix B) as a direct consequence of whatever scheme of properties is assigned to the free aether, irrespective of special hypothesis: so that, reasoning back from its truth, we may gain some general knowledge as to the nature of the interactions exerted by the ultimate material atoms across the aether. Its significance would then consist, not in any directly ultimate character such as it was originally supposed to possess, but in its being a derived analytical formulation sufficiently comprehensive to cover by itself the domain of mechanical science, as well as (in a minor degree) in its aptitude for analytical transformation to suit whatever aspect of the phenomena is under discussion, after the manner illustrated for example by the analysis of Chapter VI infra. In the course of such an abstract development of the dynamics of mechanical systems from the Action principle, the idea of force would be introduced through the coefficients in the completed variation of the Action, to which it is necessary for purposes of physical discussions and comparisons to give a name, that name which is in fact suggested from our sensation of muscular effort. It is possible that these considerations are insisted on in various connexions to an extent that will be tedious[1]: but they are at
- ↑ At one time it was customary to appeal to absolute dynamical principles relating to forces, as the fixed unchanging datum of physical science. The interest in fundamental discussions regarding the mode of formulation of dynamics has however revived in recent years, mainly through the writings of James Thomson, and of Hertz and Boltzmann, and of the school of physicists which advocates, restriction to a purely descriptive science of energetics. The conception of the subject that is propounded here is different from the points of view of these writers; while it aims at denning the domain (including all that of steady or very slowly varying states) within which the simpler principles of
