THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FOURTH SERIES.] 



SEPTEMBER 1871. 



XX . On the Reduction of the Second Axiom of the Mechanical Theory 

 of Heat to general Mechanical Principles. By R. Clausius *. 



1. TN a memoir recently communicated and published f, I 

 J- have advanced the' following theorem, valid for every 

 stationary motion of any system of material points : — The mean 

 vis viva of the system is equal to its virial. This theorem may be 

 regarded as one of dynamical equilibrium, since it gives a rela- 

 tion which must subsist between the forces and the motions 

 called forth by them in order that the latter may continue with 

 their vis viva, on the average, neither increased by positive work 

 of the forces nor diminished by negative, but, amid passing fluc- 

 tuations, maintaining a constant mean value. 



As the magnitude which I have denoted by the name virial is, 

 with equal coordinates of the material points, proportional to the 

 forces operating upon them, the vis viva of stationary motion is, 

 cceteris paribus, proportional to the forces which it balances. If, 

 then, we regard heat as a stationary motion of the smallest par- 

 ticles of bodies, and absolute temperature as the measure of the 

 vis viva, we shall find no difficulty in recognizing the agreement 

 of the above-mentioned mechanical theorem with the law ad- 

 vanced by me in an earlier memoir J : — The effective force of 

 heat is proportional to the absolute temperature. 



* Translated from a separate impression communicated by the Author, 

 having been read before the Niederrheinische Gesellschaft fur Natur- und 

 Heilkunde, on November 7, 1870. 



f Sitzungsberichte der Niederrheinischen Gesellschaft f. Nat. u. Heilk. 

 June 1870; Pogg. Ann. vol. cxli. p. 124; Phil. Mag. S. 4. vol. xl. p. 122. 



X Pogg. Ann. vol. cxvi. p. 73; Abhandlungen uber die mechanischen 

 Warmetheorie, vol. i. p. 242. 



Phil. May. S. 4. Vol. 42. No. 279. Sept, 1871. M 



