1210 



— *m»<y = l -\-- -^ . (5) 



Therefore we find for the limiting angle 8q, as ?■,„ becomes =z s in 

 Z), and — Pr^^ = M: 



a' M 



- sin^ 8, = \ ^ ~ , ....... (6) 



XVI. Calculation of the Virial of Attraction. 



Now the calculation of the virial of attraction can be carried out 

 in the following way. 



As the sum of the radii at the entrance of a molecule with 

 radius \ ,* inside the sphere of attraction a is exactly = a (the 

 centre of the entering niolecnle is then, namely, exactly on the 

 circumference of that sphere), the number of entrances per second 

 will be given by the well-known relation 



N ■=. nna* X "o ^^^ '^"o- 



The number of entrances for the direction 8 is therefore Nii=^ 

 = vjii^ X sinddO, so that the number of molecules that will be 

 found on the element ds of the portion of the path AB, is given by 



ds 

 oju^ sin 6 d8 ■ - = ü>^^J sin 8 d8 y^ dt^ 

 u 



ds . , ■ , 



when II =z is the velocity in the element of path in question. But 



dt ^ F i 



dt is given by (S-^), through which we get for the number in question : 



dr 



a>M, #m 8 d8 X 



-X^ 



sin' 8 ^ 



.MM ' 



As, namely, dr-.dt is negative on AB, the negative sign has 

 been taken in the extraction of the root. Let us write: 



2P/ — P, -Fr M 



-- V, , = -rr X 77 , = I" ir) X ^/, 



\XU 



in which (p is therefore in connection with the temperature through 

 ^', f^?<o^ {M again represents the maximum value of — Priov rz=s). 

 Hence we have for the total virial of attraction of the considered 

 molecule : 



