ii6 HERMANN VON HELMHOLTZ 



with such success that any doubt as to the correctness of 

 his statements was henceforth impossible. 



This assault might have been prejudicial to Helmholtz, 

 inasmuch as it conveyed the impression to non-mathematical 

 physicists that his conclusions were erroneous, and as he was 

 not a professed mathematician, the allegations of Clausius 

 might have been accepted. At the time when Helmholtz 

 published 'The Conservation of Energy ', he had already 

 done a great deal of work in the direction of a mechanical 

 theory of heat, but in the printed essay omitted everything that 

 savoured of hypothesis, ' in order to facilitate the reception of 

 the work by the physicists.' At a later period he had entirely 

 left the matter aside, in the belief that the mechanical theory 

 of heat could only be promoted by avoiding all presumptions 

 as to the constitution of the molecules, and examining generally 

 how the motions within the complex molecules affected the 

 position of adjacent molecules. But he had been engaged 

 on far wider problems prior to the publication of * The 

 Conservation of Energy '. When Carnot (on the presumption 

 that heat was material, and as such could neither be destroyed 

 nor added to) investigated the processes by which heat is 

 able to perform mechanical work, he found that this can 

 occur only when heat is passing from a warmer to a colder 

 body. Perpetual motion would then be an impossibility 

 only if the return of heat from the colder to the warmer 

 body required an amount of work to be performed equal to 

 that done by the previous and opposite process, besides which 

 this expenditure of energy would have to be independent of the 

 nature of the transmitting substance. Subsequent work upon 

 the conservation of energy, however, made it impossible to 

 maintain the material nature of heat, which had been an 

 essential postulate in Carnot's deduction. Helmholtz had 

 already attempted to formulate proofs, based on mechanical 

 principles, for certain of Carnot's conclusions which seemed 

 to him to hold good in the theory of heat, but he was forced 

 for the time to leave over any decision as to the validity of 

 these propositions. He had, therefore, gone much farther 

 than Clausius had detected from the published memoir on the 

 Conservation of Energy ; farther indeed than Clausius himself 

 had advanced at a much later period. 



