and its Application to the Molecular Motions of Gases. 195 



when the system passes from the one state to the other. If SL 

 denote this work, the equation will be 



8L=fTSlogtt (101) 



If in equation (98) the last term of the right-hand member be 

 transposed to the left-hand side, besides the previously dis- 

 cussed quantities of work, there also occurs here, contained in 

 SE, the quantity 6T, which represents the increment of the vis 

 viva, and in the equations of the theory of heat signifies the in- 

 crement of the heat present in the body. Now, as the increment 

 of the heat present and the work done (for which also heat must 

 have been expended) are together equal to the total heat com- 

 municated (which we will designate by SQ), we have 



SQ=fTSlog(£ (102) 



The above equations are in accord with those derived in my 

 earlier memoir*, except in one point, which is one of those in 

 which mine agreed with those previously advanced by Boltz- 

 mannf. I have already alluded to this point: in correcting an 

 article, in which I made clear the difference between Boltzmann's 

 treatment of the subject and my own{, I added the following 

 note : — " Since sending this article to the printer, I have found 

 in pursuing my investigations that the expressions in question 

 need, in order to be universally valid, a further alteration, which 

 will make them still more different from Boltzmann's." It is 

 through this change that my new equations differ from my pre- 

 vious ones. 



The equation which I formerly advanced § for the determina- 

 tion of SL can, by some slight transformations, be brought into 

 the following form, 



8L=2TSlog% 



where $1 denotes a quantity very nearly proportional to the mean 

 length of path of the molecules. Now, as we have seen, the 

 mean length of path is nearly proportional to the volume of a 

 given quantum of gas ; hence #t is also approximately propor- 

 tional to the volume. Accordingly the variation 8 log $t and 

 the variation in (101), 8 log It, may be regarded as answering to 

 one another. The factors, however, of these variations do not 

 correspond, the former variation having the factor 2T, while the 

 latter has for its factor §T. 



* Sitzungsberichte der Niederrkein. Ges. fur Natur- und Heilkunde y 

 1870; Pogg. Ann. vol. cxlii. ; Phil. Mag. S. 4. vol. xlii. 



t Sitzungsberichte der Wiener Akademie, 1866, vol. liii. 



X Pogg. Ann. vol. cxliv. p. 265. 



§ Sitzungsberichte der Niederrhein. Ges. 18/0 ; Pogg. Ann. vol. cxlii. 

 p. 45S; Phil. Mag S. 4. vol. xlii. p. 179. 



2 



