( 401 ) 



proportion, while also a part of the volume, represented above by 72, 

 will fall in the ilistance-sphere of other molecules. 



Xext we may state the following' rule. According to proba- 

 bility the relation between the number represented above by dn and 

 the total number w of the molecules will be the same as between 

 that part Ei of the space li which is left for the centre of a new- 

 added molecule and the whole space which is left inside the vessel 

 for the centre of a new-added molecule, i) 



According to formula (1) the last mentioned space is V — 2 Gb. 

 The last term of the proportion (2) should therefore be represented 

 by V — 2 Gb instead of by V. 11^ is still to be found. For this 

 purpose we construe inside each of the above considered n spherical 

 shells with a radius .r and a thickness dx^ which we have called 

 the spherical shells S^ a concentrical spherical shell with an inner 

 radius y and a thickness dy,. The latter spherical shells wc shall 

 call the spherical shells T. 'J'he sum of the number of the centra 

 of molecules, which lie in any of the sjihericnl shells T is^ analo- 

 gous to the equation (3) 



4 71 n- ifl du 

 <^y = y^~ (8) 



The part 



O" — (X — Iff 



n X 



y 



of the surface lies within the distance spheres of every separate one 

 of the molecules ; thence the part 



(0 — n X d.r ^^ ~ v-^ ~ yy ((,^ 



!J 



of the inner space of the spherical shells in question with a radius 



X and a thickness d.v, as an easy calculation shows. That part of 



the volumes of all the spherical shells S which is covered by the 



distance spheres of all the dy molecules together is therefore « di-. 



If no molecules were to be found inside the spherical shells aS, 



wc might integrate this expression with respect to y from v — g to 



X -\- f7 and 



16 n- n^ x"- o'-^ 2b G ^ 



CO dy = da- = — T- • 4 .T ?i x- dx . . . (10) 



3 T" \ 



ƒ 



would follow. 



■) For ii I'liller cxpnsilion of this riilo coini). 1. i'. § 51, 



