683 



the firsl case we have (o take IVon» the canonical ensemble an 

 easily defined sub-ensemble M^, in which u.. has equally often equal 

 and opposite values (and therefore is "independent" with respect to 

 u^). For the second demand a more closely limited snb-ensemble J/i^ 

 has to be selected from the mentioned ensemble Ji,. It is however 

 • hardly possible to determine J/,,. Still this should be done in order 

 to decide whether the distribution of the values of ii^ in it does or 

 does not agree with Einstein's assumption. 



APPENDIX. 



m, + m^ = M , 



.... («) 



Then : 



4 {m^u,'' + m,»,') = 19,' >i i- q,' M + 2 q, q^ (m, — "^i)! . 



Let p^, p^ be the momentum corresponding to the coordinates 

 ^i, q^, then we have 



c¥^ ^ . 



M^ . . . 



and because of the equipartition theorem the mean values with respect 



to time of {^) and (7) are both equal to kT, so that their difference 



i¥» -. r-~ 



9/1 = 0. {(f) 



érWjWj 



On the other hand («) gives 



M'- 



u,u^ = {q,- — q^-) (e) 



From (ff) and {e) combined we find : u^ u^ = (q.e.d.). 



