48 HERMANN VON HELMHOLTZ 



empirical facts must be investigated/ Unlike Helmholtz, he 

 did not test the accuracy of the law (conceived as it were 

 by inspiration, and by a certain creative activity of his brain), 

 or rather its consequences, upon all the natural processes 

 known at that time: the recognition of the principle in fact 

 involved other, and deeper mathematical, knowledge than any 

 Mayer could command. 



Helmholtz by his discovery gave an impulse to the whole 

 later development of mathematical physics, and showed by 

 rigid mathematical proof that whenever natural bodies act 

 upon each other by attractive or repulsive forces, which are 

 independent of time and velocity, the sum of their vires vivae 

 and 'tensional forces' must be constant; but if these forces 

 depend upon time and velocity, or act in other directions than 

 the straight lines which unite the two active material points, 

 then (provided the action and reaction are equal) combinations 

 of such bodies will be possible in which energy may be either 

 lost or gained ad infinitum. When in this sense the above 

 forces are described as ' conservative ', the Law of the Conser- 

 vation of Energy says no more than that all elementary natural 

 forces are conservative. 



The work which the great French mathematicians had done 

 in mechanics was familiar to Helmholtz, and to him it was 

 no new induction, but merely the definite statement and 

 complete generalization of an established conviction, to say 

 that all elementary forces are conservative. In Helmholtz's 

 opinion those great thinkers must have made the same con- 

 jecture, but did not state it in terms, since they could not 

 prove it, having ' set themselves the particular task of educating 

 men from the false rationalism of scholasticism to the strict 

 appreciation of experimental data*. Helmholtz termed his 

 theorem the law of the 'Conservation of Energy' (Erhaltung 

 der Kraft), to mark that it was an extension of the already 

 known law of the ' Conservation of Vis Viva ' (Erhaltung 

 der lebendigen Kraft], and to make its relation clear with the 

 old question of the possibility of a perpetuum mobile. 



Mayer, by trying to get rid of the conception of force in 

 mechanics, and defining as Kraft (force) what had previously 

 been defined as work, i. e. the product of force into the dis- 

 tance through which it acts, obscured the meaning of the 



