( 407 ) 



This is by approximation : 



a<?-^^'r .V, + ^'-^ 4- . 



-\- aL'~^"r \ ./•/ 



1.2 



+ etc. + C 



01' 



1.2 ^ 



1.2 



so that the whole form may be represented by 



Ce 



-6iv- : 



2,v •' 



1.2 



j- (U 



1.2 ^ 



or it' we denote the most probable quantities per element by rtj, a, etc. : 



Ce 



1.2 



r + ^*ï 



1.2 



+ • 



Tiiis exponent agrees perfectly with that obtained for the pre- 

 ceding- problem. We may reduce the latter to the form — 2 



and the former to the foi'm — ^^ 



(ü^O 



[/2a/ 



; now the}' represent 



the negative sum of the squares of the absoluttï deviations divided 

 by the root from twice the normal number. Just as in the pre- 

 ceding problem the chance to a combination of deviations for which 

 the root from this latter sum does not amount to more than a 

 ÏQW times unity is no^v very large. If we now take as measure 



for the deviation the mean relative deviation or I X -:r— , we see 



that this value is very small compared to 



i: 



a.v 



T 



A' 



so (hat this 



mean deviation will be very slight^). 



To conclude we ma}- still remark that in order to get in the end 

 both uniform distril)ution of the molecules over the vessel and Maxwell's 

 distribution of velocities, originally both a unite part of the space 

 of velocities and of the space of coordinates must have been occu- 

 pied. Or there must be such an uncertainty as to the original 

 situation and velocities of the molecules that we must consider possible 

 a unite whole of combinations with regard to l)oth. This linile whole 

 of possil)le combi)iations constitutes the ensemble, which we follow 

 in its course instead of the svstem uidcnown within certain limits. 



') It 1 laving been assumed in the calculation that a considerable num])er of 

 points of velocity sliU occur in every element, we must not think of the whole 

 of Ihe space of velocities when estimating tlie number of elements i\^. 



