PROFESSOR IN BERLIN 359 



by Maxwell's theory of electrodynamics. In this the velocities 

 of electricity appear in a function of the second degree, the 

 coefficients of which are not, however, constants, as are the 

 masses in the value of the vis viva of ponderable systems, while 

 linear functions of the velocities moreover come into play, so 

 soon as permanent magnets are introduced. Since the pheno- 

 mena of light can essentially be explained on the hypothesis 

 that the ether is a medium of similar properties to the solid 

 elastic ponderable bodies, and as the law of least action must in 

 any case be held valid for the motion of light, Helmholtz even 

 at this stage regarded the validity of the principle of least action as 

 far transcending the limits of the mechanics of ponderable bodies, 

 and held it to be highly probable that it was the universal law 

 of all reversible natural processes. 



In this connexion it must be mentioned that Boltzmann had, 

 as early as 1866 (in a memoir, ' On the Mechanical Significance 

 of the Second Law of Thermodynamics/ that remained 

 comparatively unnoticed and was unknown even to Clausius), 

 formulated a law for the mechanics of ponderable masses, which 

 is as analogous to the Second Law of Thermodynamics as the 

 Law of Vis Viva is to the First, and that, as Boltzmann wrote to 

 Konigsberger in 1896, he had, as early as 1867, been presented 

 by Stefan to his colleague Loschmidt as ' Herr Boltzmann, the 

 discoverer of the physical significance of the law of least action '. 

 The scope and weight which Helmholtz attributed to this 

 principle in every department of physics, and actually established 

 by rigid mathematical deductions, appear with increasing clear- 

 ness from his earlier as well as from his subsequent papers ; the 

 almost simultaneous work of J. J. Thomson was directed to the 

 same object. 



Helmholtz was led to these universal investigations, which 

 aimed at the widening of the principles of mechanics, by special 

 cases, whence he had shortly before obtained a similar though 

 less extensive generalization, published in 1884 in the above- 

 mentioned memoirs on the principles of the statics of monocyclic 

 systems. By monocyclic systems he understands mechanical 

 systems which exhibit internally one or more stationary motions 

 returning upon themselves, but which, supposing there to be 

 several, depend in their velocity upon one parameter only, while 

 systems with several independent parameters are termed poly- 



