354 HERMANN VON HELMHOLTZ 



bodies. The validity of the law appears to Helmholtz to be 

 limited in the so-called irreversible processes of conduction of 

 heat, production of heat by friction, electrical resistance, and 

 so on, only because we are unable either to follow the 

 unorganized motions of the individual atoms or to bring them 

 together practically in any congruent direction. He tried, 

 in his work on monocyclic systems to show that the most 

 diversified classes of internal motions are subordinated to the 

 law of least action. 



The hypothesis that Helmholtz here puts forward and is 

 constantly elucidating, to the effect that all phenomena come 

 about uniformly through the action of concealed masses, by con- 

 cealed motions and rigid combinations, was subsequently stated 

 by Hertz (as a corollary to this fundamental idea of Helmholtz, 

 which stands for the most significant advance that has been 

 made by modern mechanics) in correct language in the some- 

 what wider assumption : ' that the complexity of the real world 

 is greater than that of the world that lies open to our senses ; 

 we admit that an unknown agent is at work, but we deny that 

 this agent has a specific character, like the concepts of force 

 and energy; the unknown must still be Motion and Mass, 

 distinguished from the visible not by its own nature, but simply 

 in relation to us, and to our normal modes of perception. . . . 

 Force and Energy are no more than effects of Mass and Motion 

 which are not always perceptible to our senses.' 



In his Address to the Academy, Helmholtz gave a striking 

 account of the historical development of the law of least 

 action, tracing it back more particularly to the works of 

 Maupertuis, who was ' essentially what we term a genius, with 

 all the qualities and failings which that implies '. He indicates 

 what is indefinite and obscure in the views of Maupertuis, who 

 holds that this law satisfies the demand of metaphysics, that 

 Nature should invariably employ the simplest means to produce 

 her effects, and thinks himself called upon to ascertain what 

 quantities are minimal in natural processes, since these will be 

 those which Nature tries to economize ; so that we can discover 

 the objects which Nature pursues. Maupertuis even goes so far 

 as to assert that the law of least action, as discovered by 

 himself, is the first binding and incontrovertible proof of the 

 existence of God, as an Intelligent Governor of the Universe. 



