( "92 ) 



From this general formuhi Clausius crnild easily determine 7^ and / 

 also for our case. He has only lo take into account that in a 

 collision the centre of a molecule nnist necessarily be on the surface 

 of the distance sphere of the other. If ^ve. tlierefore, want to delei-mine 

 tlie numl)er of collisions of the former, we need only see how great 

 the chance is that this molecule will strike against the surface formed 

 by the distance spheres. 



We get then: 



/= -^ P — r 



Clausius observes, however, that not all surface elements can be 

 struck Ity the moving point, viz. not those which are found within 

 distance spheres. In the same way we must subtract from the 

 Aolume V the volume lying within the distance spheres. By deter- 

 mining the area of these surface elements by first a}»proximation, 

 Clausius obtains: 



11 h 

 1 



7t )is^ - 8 r 

 P=- r .... (2) 



V 



1 — 2 - 



V 



h 

 1—2- 



V 



It is clear that the fraction -— — occurring in these formulae 



11 (' 

 1 



8 V 

 is only the first approximation of the more general 



available volume 

 surface of distance spheres 



total 



If Ave wish to determine this fraction more accurately we must 



add to the denominator of this fraction the surface which is found 



\vithin two distance spheres at the same time, as this quantity has 



11 /. 

 been twice instead of once subtracted in the term — — ; avIicji deter- 



b '/ 



mining this fraction we luwe namely assumed tliat all distance spheres 

 fall outside each other. But this is not the whole term of the order 



-, as Boltzmaxn') has shown, for in the determination of the 



1) These Proc. I p. 348. 



