PROFESSOR IN BERLIN 355 



With regard to this metaphysical assumption of Maupertuis, 

 Helmholtz jestingly remarks in one of his papers, in allusion 

 to the distinction which he had laid down between limiting 

 value and the minimum : ' If inertia is to be personified, as in 

 this formula, it would be proper to make it shortsighted, and 

 concerned with the immediate moment only.' 



The credit of the first, even if it were a wholly indefinite, 

 formulation of the principle is ascribed by Helmholtz to Mauper- 

 tuis, but he justly accuses him of obscurity and want of strict 

 deduction. 



' He grossly neglects the old Socratic demand that every 

 philosopher, i. e. man of science, should be clear in his own 

 mind as to what he knows. He must have been aware that 

 the law which he brought forward as incontrovertible could 

 neither be verified nor clearly applied in many classes of 

 instances. Immersed in self-admiration he held himself justi- 

 fied in merely announcing his discovery like a prophet, a tragic 

 instance of how a mind that was highly gifted at the outset 

 can be led away by vanity and the lax discipline of so-called 

 metaphysical thinking, to border-lands where even the faculty 

 of reasoning becomes dubious. Yet even if he were only 

 guessing at the truth, the truth it was, none the less. And 

 his fixed belief in the possibility of finding a universal law of 

 nature was rooted in a proper confidence in the uniformity of 

 nature, i. e. in the Law of Causation, which is the ultimate basis 

 of our thinking and acting.' 



In his paper ' On the History of the Law of Least Action ', 

 Helmholtz criticizes the evidence given for it by Lagrange, Jacobi, 

 and Hamilton. He shows that if, on comparing the adjacent 

 paths with that actually followed by the system, we assume for 

 the others not only the conservation of energy, but also the 

 same value of the energy constants, then in order to maintain 

 the validity of the law the same initial and final positions may 

 be postulated for the contrasted motions of the system, but not 

 the same period of time. The time must accordingly be taken 

 as a variable factor in the analytic derivation of the principle. 



Jacobi's proof is physically valid for every complete, self- 

 centred material system. Hamilton's form of the law (to be 

 discussed below) allows us, on the contrary, to extend the 

 equations of motion to such imperfectly closed systems as are 



Aa 2 



