124 Physical Properties [OH. vi 



satisfied at once. This again must be corrected on account of the possibility 

 of more than two of these conditions being satisfied at once, and so on, 

 indefinitely. 



In this way we obtain an expansion in descending powers of H', of which 

 the first two terms have been shewn to be 



/(a, b, c, d. ..) = &*-- -N(N-I)a*-i + ......... (291). 



o 



The integral 7(6, c, d ...) can be evaluated in a similar way except that 

 in this case the molecule A is supposed already to be in collision with the 

 boundary, and therefore in position in. in fig. 5. Hence the available space 



O 3 



for the centres of the molecules B, C ... is H' -- - instead of the former O', 



o 



and the number of molecules is N 1 instead of N. Making the necessary 

 alterations in equation (291) we obtain an expansion in the form 



...... (292). 



Equation (289) accordingly leads to the value 



27TO- 3 N - 1 



~3~^r 



on expanding as far as the first two terms; and since, in the limit, we 

 may put 



N-l N _N _ 



a' ~ n' ~ n ~ "' 



we obtain v b in the form 



v b =v+^v t + ........................... (293). 



Using this value for v b in equation (287) we obtain the equation 



(294), 



which agrees with equation (279) as far as the first two terms. 



143. We shall now examine what correction is to be applied for the 

 forces of cohesion. The principle underlying this correction has already been 

 explained ( 134) in deducing Van der Waals' equation, so that we may start 

 at once with the conception of a permanent field of force at and near the 



