Now let us consider more closely the coefficient of g in (8). 



Let a molecules be present in the unit of volume, then the mean 

 ]iumber of molecules in dv is equal to r/(//\ If we take c/r very small, 

 there may be no or one molecule in it. The chance for one molecule 



is, therefore, adv ; for none 1 — adv. In the first case r =i a, 



dv 



in the latler it is — a, thus 



— a 

 dv 

 or 



v^dv ■= a (9) 



Introducing this into (8), we find for the two elements x^yrjZ^ and 

 a\y^Zr 



Vr;V- ■=. ag[x^—XT;, yr;—y^., z^ — z.^) (10) 



This result can be used to indicate the values of (A^ — JSfy =z h N^ 

 for any volume. 

 We have 



hN — ivdv 

 AN^ = t iiy^^ dv^ dvr -\~ 11 iviv t/.?v dyr; dz, d.i'r dy-^ dz^ 



vv vv 



from which applying (9) and (10) 



AA^^ = rt K -)- a I \g (eiv — .t'r, y,j — y^, z^ — z-^) d.v^ dy^ dz, dx^ dyr dzr . 



VV 



This holds for every size and form of V. Elaborating it for a 

 cube with side / the dependence on V is seen more clearly. Putting 

 A'^ — ,v- = 5, i/^ — y- = 11, z^ — Cr — ?, and integratuig only for %^^ 

 positive, by which 7» ^f tlie integi*al in question is found then, we get 



/ / / / / / 



LN^ = N + 8a j77 ./ {1,1^) j ffdr, dy, dz. 



u (t 



/ / I 



iv+ 8a r0(P-/M5+^i+S) ^-i{^n+n^^m-%n^)9dldnd^' 



Hence 



