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470 W. B. BOYCE GIBSON : is significant that where names have been judiciously given, as e.g., the law of Conservation of Areas, the principle of virtual velocities, D'Alembert's principle, names which all agree in suggesting nothing psychical, there has been no tendency to extend their application outside the realm of the Science they represent. How could one apply the Law of Least Squares to the facts of mental life? The principle of Least Action has been peculiarly unfor- tunate in this respect. Maupertuis, who first publicly enunciated it, proclaimed it as a universal teleological principle, and in this he was supported by Euler, its real discoverer, 1 who first presented the principle in a serviceable form. Lagrange was the first to see clearly that far from being a principle from which the designs of the Creator could be inferred, it could itself be deduced as a necessary conse- quence from the ordinary laws of motion. 2 The principle is now a century and a half old, but has in that time been expressed in so many different ways that it is not easy to say in a few words what is exactly meant by it. Its general meaning is simply the expression of the fact that in moving from one point to another a body will follow the path which involves the least sum total of action, the Action of a body during any time being a term adopted by Leibnitz to express the continued product of the mass, velo- city and space traversed by the body during that time. What then is the significance of this mechanical principle ? We may say that the value of a mechanical principle depends on three considerations: (1) On its generality, i.e., on the number of other mechanical principles deducible from it ; (2) on its being a good working principle, a principle easily applied to the solution of mechanical problems 3 ; (3) on the simplicity of its physical import. Now, the principle of Least Action possesses great generality, and two great mathemati- cians, Lagrange 4 and Helmholtz, 6 have made it the funda- 1 ('/'. Herr Adolph Mayer, Oeschiehte de,s Principe der Action, Leipzig, 1877. 2 Mecanique Analytique, p. 246. 3 In this respect the Principle of Least Action is found wanting : <;/'. Bartholomew Price, Infinitesimal Calculus, vol. iv., p. 150. 4 Lagrange, (CEuvres, ed. Serret, vol. i., p. 365), in a sequel to a paper of his Ensai d'une nouvelle methods pour determiner lea maxima < / /< x minima des form-vies inte'f/rales indefinws. 5 H. v. Hehnholtz, " Uber die physikalische Bedentung des Princips der Kleinsten Wirkung," Journal fur die reine und angewandtr. Matheinfttik (usually known as Crelle'ss Journal), Berlin 1886. Hundertster Band, Zweites Heft, pages 137-166, cf. especially pages 142, 143. For a good general review of the various treatises in which Helmholtz attempts to