THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



APRIL 1887. 



XXXVI. On the Assumptions necessary for the Theoretical 

 Proof of Avogadro's Law. By Prof. Ludwig Boltzmann 

 {o/Graz).* " 



PROFESSOR TAITf, by making a number of special 

 assumptions, has given a very exact proof of Avogadro's 

 Law — or, rather, of the proposition that in the case of the 

 heat-equilibrium of two mixed gases the mean potential 

 energy of the molecules must be equal. Prof. Tait does not 

 appear to me, however, to have given the least proof that the 

 special assumptions which he makes as the basis of this pro- 

 position are necessary, or even that the more general pro- 

 positions stated by myself { and Maxwell § are incorrect. 



I believe that in my calculations I have stated precisely 

 the assumptions made, and have invariably drawn the logical 

 conclusions from them ; and therefore that I have not 

 deserved the reproach which Prof. Tait makes, that they are 

 " rather of the nature of playing with symbols than of reason- 

 ing by consecutive steps/'' which must also apply to the just- 

 mentioned treatise of Maxwell, when he accepts and further 

 develops the propositions of mine upon which Prof. Tait throws 

 doubt. The contradiction of these propositions by certain expe- 

 rimental facts seems to me to have resulted only from too great 



* Translated from an advance proof, communicated "by the Author, 

 from the Sitzber. d. Wien. Akad. d. Wissensch. vol. xciv., having been 

 read at the Meeting on the 7th October, 1886. 



t Phil. Mag. [5] vol. xxi. p. 343 (1886). 



X Sitzber. d. Wien. Akad. d. Wissensch. vol. lviii. (1868) ; vol. lxiii. 

 March 9 and April 13, 1871 ; vol. lxvi. October 10, 1872. 



§ Camb. Phil. Trans, vol. xii. part 13, p. 547 (1879). 



Phil. Mag. S. 5. Vol. 23. No. 143. April 1887. Y 



