350 HERMANN VON HELMHOLTZ 



March 27, and July 10, 1884), his 'Generalization of the 

 Theorems of the Statics of Monocyclic Systems' (ibid. 

 December 18, 1884), and his ' Principles of the Statics of 

 Monocyclic Systems' (Crelle's Journal, 1884), are in the 

 closest connexion with his memoir 'On the Physical Signi- 

 ficance of the Law of Least Action ' (Crelle's Journal, 1886). 

 An important supplement to these articles was given in the Note 

 published in the Berlin Proceedings for March 10, 1887, on ' The 

 History of the Law of Least Action/ and developed in more 

 detail in an address to the General Meeting of the Academy on 

 January 27, 1887, the full publication of which was suppressed, 

 because Helmholtz subsequently learned that Adolph Meyer of 

 Leipzig had already published a complete and fundamental dis- 

 cussion of the Law of Least Action in his Inaugural Address. 

 Helmholtz's lecture, remarkable both for its matter and for its 

 style, was incorporated after his death, with his wife's consent, 

 in the History of the Academy (Vol. II, Documents and Deeds), 

 issued in 1900, on the 2ooth anniversary of its foundation. 



The fundamental researches set out in these memoirs (which 

 gave Hertz the idea and the starting-point for his Principles of 

 Mechanics, and of which the enormous importance, partly from 

 the difficult nature of the problems attacked, partly from the 

 succinct character of their statements, has not yet been widely 

 recognized by scientific men) are entirely mathematical ; at 

 the same time the purely mathematical problems that occur 

 during the generalization of mechanical principles are, according 

 to Helmholtz's invariable practice in his mathematico-physical 

 work, dealt with only in so far as is required for their application 

 to physical questions. Since all mathematical expressions 

 have to be avoided here, it is only possible to give a general 

 outline of these papers. 



'A law which is to comprise the total sum of alterations 

 in Nature must necessarily deal with concepts of the most 

 abstract kind, from which everything has been eliminated that 

 refers to the particular properties of the natural bodies known 

 to us ; for the most part it is necessary, indeed, under such 

 conditions, to form new abstract concepts for the purpose, 

 which, when any one hears them defined for the first time, shall 

 evoke no previous concepts or experiences, that is, in popular 

 parlance, make him think of nothing.' 



