178 Mr. S. H. Burbury. [Nov. 19, 



in which R is a function of v l ---- v and the coordinates, and the 

 integration includes all values of p r+ \ . . v n -\ and R. 



We will suppose now (see 13, post} that the number F is not in- 

 creased or diminished by any ireans except by collision with systems 

 m. If that be so, 



= J| . . . . (F'/-F/) R dp, . . . . dpn-i ctoi . . . . dvn-i dR 

 and 



= JJ ____ (F'/ F/) R log F dpi ---- dpn-i dv l ---- <Zv_i dR. 

 By symmetry, 



= JJ . . . . (F'/-F/) R lofsfdpi ---- op_i dvi ---- dv tl -i dR. 



Now if 

 H = JJ . . . . F (log F-l) dpi ---- dv r + JJ ./Og/-l) dp r+ i .... dv H 



and therefore 



^ = JJ . . . . (F/-F/) R log (F/) dp lt ... dp n dvi .... dv n . 

 By symmetry, as we may interchange the accents, 



^ = JJ . . . . (F/-F/) R log (F'/) d Pl .... dp H dvi .... dv 

 and therefore 



which is necessarily negative, if not zero, and then only zero when 



F'/' = F/, that is, when the Maxwell-Boltzmann distribution prevails. 



13. It can be shown in the case of riid elastic bodies that F is not 



