( 404 ) 



would llieu bo piisscd llii-oiiuli lor llii' second liiiio w illi llie xelocilv ul'd'i' 

 impact is tlunii;lit lo he Itinied ovei' along- AIL Now llic ])<>iiil pursues its 

 course unintei-i-ui)ted. A following' collision \villi^>/j now becomes collision 

 with BC: now we may pi'oceed again in the same way. The [)encil 

 then goes on without any disturbance, but we must take into account 

 that the elements of surface, whicii in this way proceed from each 

 other, represent the same placing of the two molecules. Tiie conti- 

 mially extending figure of the representing points will linally contain 

 a very large lunnber of element^; of surface of every kind coming 

 to the same thing, or a vei-y large nuud)er of lui-ned over triangles, 

 so that tinally the j)oints will be unifoi'udy distributed over the sums 

 of the elements of surface. So e\'ery situation of the two molecules 

 represented by a point in ABO, occurs eipially freipiently. A point 

 of BD( f, however, is never reached : so every situation in \vhich 

 the 2"*^ molecule is on the right of the l*"' is e(pially j)i-obable, but 

 the 2"^^ cannot get to the left side of the {^^ . 



Now we should have to extend this i-easoning to the case of more 

 than two dimensions. The retlection against the walls does not 

 affect our reasoning. The sti-iking of the molecules against each 

 other, however, is now represented by sti-iking against a cylindrical 

 surface. Though this obstructs the way, it no longer shuts off a part of 

 the space. The case may be compared with that of lig, 3^ if the line 

 OB is re})laced by a circle. I have not succeeded in solving the 

 problem for this general case. However, it seems very plausible that 

 the finite number of cylindres will not be able to prexent that tiie 

 uniform distribiilion of the representing points over the sums of the 

 elements of volume which come to the same thing, which distribution 

 would finally come about as we saw in § 3 if there was no collision, 

 will be established also now. So all the combinations of place of 

 the molecules would then occur equally fre(piently. 



§ 5. Finally it may still be shown that when all the combinations 

 of place and all the combinations of velocity occur with equal fi'e(|uency, 

 it follows from this that for the great majority of the systems the 

 molecules are distributed about nniforndy over the vessel, .and have 

 jMa\wklt/s distribution of velocities. So far we have alwavs distinguished 

 between the indi\'idual molecules, now we shall have to take into 

 consideration, that exchange of the molecules does not affect the 

 distribution of place or xelocity, so far as we can know it. So all 

 tjie combinations which arise from each other by excliange of 

 molecules, now come to the same thing. Hence if of .v molecules 

 .Vj are in the first element of volume, s, in the 2"^' etc., there arQ 



