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THK 1'lilNCII'l.!. o] i.| ST CTI()N. BTO. 471 mental principle from which they Inive attempted to deduce all others. It is still a vexed question whether the principle of Least Action has a right to this supreme position in the hierarchy of mechanical principles, Mach contending that no general mechanical principle has any claim to priority over any other, inasmuch as they are all different forms or as] of one and the same fundamental physical fact the only true prior and can all he deduced one from the other ; and Hertz, contending that in addition to the presence of certain refractory facts which in his opinion argued strongly against Helmholtz's apotheosis of the principle of Least Action, the principle had not a sufficiently simple physical import to justify its standing at the head of an entirely deductive Mechanical Science. In his own attempt at elaborating the principles of mechanics into a single deductive system Hertz has enunciated a principle a composite of the principle of Inertia and of Gauss' law of Least Constraint which has apparently the double merit of possessing supreme generality and a relatively intelligible physical import. 1 As regards the physical import of the principle of L ;i>t Action, I cannot see that anything at once certain and satis- factory can be said at present. Lagrauge speaks of it as expressing ' a remarkable property of the movements of bodies,' 2 but does not attempt to make its import really clear. Helmholtz has a whole treatise on ' The Physical Meaning of the Principle of Least Action,' but he does not succeed in displaying this remarkable property as a natural consequence of properties less remarkable but more intelligible. This most desirable reduction of the remarkable to the obvious is definitely attempted by Mach, but alas ! with a similar result. The same writer, however, gives casually, in other parts of the same work, certain indications of the direction in which the solution must be sought. He most tantalisingly points out in the first place that all mechanical principles, being de- ducible each from the other, are only different forms of one and the same physical fact, but leaves us uncertain as to what this interesting fact may be. Probably if Mach were pressed to state it in a word, he would answer 'Work,' work being, as he puts it, the factor that determines motion, motion taking place only where there is work to be done. found the Science of Mechanics on the principle of Least Action see III rui'iit. fun lli'ltnholtz'x I'/iti rxni-lii'itj/i'ii i'llii-r itif Cfiiiiitliiiii Mntlti-,,ntti/; ii.nl Mi i-Iunti '/.-. von. Dr. Leo Kii'iiiijsherfjer, especially *. "'!>. 1 Gesammflii' ~i-rkr von lli'/nrii-h Hertz, Band iii., l>ii- /'//'/< :/'/'. Mi'i-liiiiiik ' with a preface by Helinholtx himself). 2 Lagran.nc, Mi'i-iiiiii/m- A/Ktlitiijw. p. 299.