iNX 



1211 



90° a 0^ a 



r r r r{-~ F' {r))dr X sin d dS C nr{-F '{r)) drx sin d dS' 



I ~—^sin'6-\-(f.F{r) o « Ix id. 



,(7) 



in which tlie first (double) integration refers to all the entering 

 molecules that do 7iot strike against the molecule in question, and 

 where, therefore, a ininimum value of r is passed through in B 

 (which minimum in the limiting case = 0^ will get exactly on 

 the circumference of the sphere r = s), whereas the second inte- 

 gration refers to all the colliding molecules. For the attractive force 



dP,. di-Pr) ,,^ 



= we have written — M r {r) according to the 



dr dr 



assumption — P,.-. M ^=^ F{r). In consequence of the negative sign 



of the root, the limits of integration are reversed with respect to r. 



Besides we still have multiplied by 2 in the above expression, 

 since evidently the second portion of the path from B to C, or 

 from the collision back to the circumference of the sphere of attraction, 

 will yield exactly the same integral value. Everything then takes 

 namely place in the reversed order, the limits of the integrals 

 remaining quite the same. Moreover the summation is extended over 

 all the molecules N, which with the virial factor \ yields therefore 

 in all still a pre-factor i X i ^^ X 2 = i N. (The total number of 

 molecules JSF has been divided by 2, because else all the pairs of 

 molecules would have been counted double). 



We now have to choose a suitable expression for F{r). The 

 accurate law referring to the attraction being unknown, it will not 

 make much difference for the determination of the dependence of 

 the temperature (lying in the quantity (p), which interpolation 

 function is used, provided F [r) become =0 for r =: «, and =1 

 for r = s. The more so when — as will probably be always the 

 case — a and s do not differ much. We can, therefore, choose a 

 function for which the above integrations become possible. This 

 cannot be completely reached, as we shall at once see, but through 

 the assumption 



1 1 



-Pr 7*^0* 

 F(r)=: -=: ^ (8) 



we can get a long way. In consequence of this we get: 



-F'(r) = ^ : T-i-AY . • . . . (8a) 



