( P>09 ) 



small, rigid spheres (molecules), all of them having the same pro- 

 perties and of the mass »i and the diameter g. 



We represent hy ^i the first approximated value of the space D 

 left for the centre of a molecule new added into the gas. This 

 molecule has the same properties as the others. Then D^ = V. As 

 a second approximation we must subtract from this the volume of 

 the distance-spheres of all the ti molecules. The term distance-sphere 

 stands here for a sphere concentric to the molecule and with the 



4 2 ,T g' 



radius rx, so having a volume of — n o^. If we put — ^ — - = b and 



3 3 m 



the total mass of the gas m n r= (?, tlien the sum of all the volumes 



of all the n distance-spheres is 2öZ) and the second a])proximatcd 



value of D is therefore 



D,=zV — 2Gh (1) 



For the third approximation we must take into account (hat not 

 the sum of the volumes of all the distance-spheres is to be subtracted 

 from T", as here and there two distance spheres cover each other 

 partially, and that then the space which is common to them, is to 

 be subtracted but once. So we must add to -D^ the sum Z of all 

 spaces which two distance-spheres have anywhere in common. 



"We find the volume Z iu the following way: We construe round 

 the centre of every one of the n molecules a spherical shell con- 

 centrical with the molecule, with an innar radius a^ and the very 

 small thickness dr ^ which spherical shell we shall call .S'. The 

 volume 7i', which is the sum of all the spherical shells S construed 

 in such a way, is 4 ,t n x- dr. The number dn of the centres of the 

 molecules which are found in any of these spherical shells is to 

 the total number of the molecules in the first approximation as R 

 is to the volume of the vessel T', so that we get 



dn : n — 4 Tin x'- du- : V (2) 



or 



4 ;t n^ 3!^ dx 

 dn= ~. {^) 



The last expression gives the number of molecules whose centres 

 lie at a distance between .v and .r + dx from the centre of any 

 other molecule. The number of the pairs of molecules, whose centra 

 have a distance between these limits, is \ dn. As soon as .'• is 

 between a and 2 a, the distance-spheres of the two molecules of 



