THE PRINCIPLE OF LEAST ACTION, KTC. The fact that the principle of Least Action can he deduced from the principle of Virtual Velocities with strict logical necessity suffices, as Hertz ingeniously points out, 1 to dispose of the fiction that the action in question involves any occult economic activity on the part of the body concerned. The most deanimistic physicist will not grudge to a material body any tendency to control its own motion economically, which can be shown to be a necessary consequence of the fact that motion can never take place except where work can be performed. We may take it then, provisionally, that the principle of Least Action owes its importance as a mechanical principle merely to this, that it is one of the many mutually deducible forms for expressing some funda- mental, obvious, instinctively understood physical fact. ' In the case of all principles.' writes Mach, 2 'we have to deal merely with the ascertainment and establishment of a fact.' 3 This one main result of our inquiry into the meaning of the mechanical principle of Least Action will serve us as a clue in the further inquiry with which we are now confronted as to the validity of the principle as a psychological principle. We put the question to ourselves as follows : What is the mam fact or facts with which the Science of Psychology has to deal? What are the principles that embody this fact or facts in the most general and appropriate form ? Can some principle of Least Action be said to be among these principles ? If so, what is the psychological import of the principle ? If not, can such a principle be allowed a secondary place in psychological theory, or must it be banished alto- gether from Psychology ? II. THE PRINCIPLES OF PSYCHOLOGY. The main fact with which the Science of Psychology deals is, as I take it, the activity of the individual Consciousness. The aim of Psychology is to analyse and mentally reconstruct in an intelligible way the incessant change which character- iuiport. Jacobi's form of the Hainiltonian principle of Least Action abounds in square roots to which it is impossible to give a direct physical meaning. It is mainly the simplicity of Killer's form of the principle which has led physicists to inquire so persistently into its physical import.
- /v//i r/'/'/Vn der Mechanik, p. 178, cf. also p. 272.
- Mach, Xcit'iice, of Mechanic*, p. 7<i. " Throughout this inquiry I use the word ' fact ' as a fact of Physics or Psychology, as the case may be, not as a fact in the eyes of Metaphysics.
