( 4()() ) 



u^ 1 , 



n - ^ 2s 



s-\- ~ " 2s »» 



(l/2jr.)"-ij 1/XJ 



o 



Very soon, however, this value is very large, when u, is only a 



few times -\^%^ as vet; then // or the mean ,r, however, is still 

 n 



small compared to -, the mean numher of molecules per volume 

 n 



element. 



In a similar way the [)rohlem of the distril)ution of velocities may 



s! 

 be treated. Here the denominatoi- of the expression — , 



may be reduced to Cc ' ' , in which / (^»is) i-epresents 



the function of distribution of the [)oints of velocity. The integral is 

 minimum, taking into consideration that ^r'' is constant, when 

 ƒ (g)j^) r=: a/'— -^ 5-'+'-+?-). Now it remai]is to investigate what is the 

 chance to a given deviation from tins distril)ution. We may deiine 

 this deviation by the ligures j\, .\\ . . . d\^, ,v^ . . etc. indicating the 

 relative sui'pbis of points of velocity in the elements of volume, respec- 

 tively with the velocities i\, r., etc. In the tirst element is then the 

 quantity .Vj ^ a('—'"'^'\\. -f .''i)'), in tlie second .v., = ae~''''^'{;i +'t'i') etc., 

 so that the number of coiid)inations to be taken together: 



s! 



L„g-6.V^ (1 +.rO] ! [ar-h^^" (1 +,r/)] .' . . . [a^-^"'/- (1 + .t,)^ ! ... 

 The lirst factor of the denominator is c(pial to (by approximation!: 



If we nudtiply by the other factors, the latter part \anishes, as 

 ^ae~^''i"" .i'-j = 0. So we keej) : 



C{ae-^^-i-) '(1+.^) -^''^- X ('"'-"■'") 



If we take the Nep. log. tiie former j>art \anishes, as also 

 ^ a/'- '""1- ,rj . r,- = u, 80 that log. denominator: 



== ^ [<7. /-r(I-[-.rJ + i| Av/(l + .»g f C. 



!_) This a in equal to the above one iiuiUiplcd by d^d/,d^. 



