448 Mr. J. H. Shaxby on Vapour Pressures 



is to substitute a constant K for the quantity 



2RTlog^ loo^ Tr/7 7X 



d?-df ' inas rf 1 -rf 2 - 2RT 



T^T - — 

 and P=-^ e b '^\ (1«) 



where C is a new constant (independent of density and 

 temperature), and b has its modified value, nearly but no 



longer exactly equal to -. j . 



In the same way the Equation of State becomes 



*>= r <? y61 (2 a) 



. v — b v y 



In applying the equation (la) to actual substances, we may 

 make our adjustments most readily as follows : 



C 

 logp ■= log RT- log b- ^ 2 . 



The term log b is small and not very different from 



log , , , , so we may replace it by the latter without 



U]_ -j- a 2 f% 



serious error and so evaluate ^, using experimentally 

 determined values of p. 



Again substituting (d 1 ^-cl 2 ) 2 lor r , we obtain the general 



magnitude of C, and finally select from the array of slightly 

 varying C's a value which is seen to give good agreement 

 (for its own particular temperature) with experimental fact, 

 i. e. the for a temperature at which the original unmodified 

 formula (1) gave a satisfactory value of p. 



From the adopted value of the quantity b is recalculated 

 for each temperature, and the new value of p then obtained 

 from the equation (1 a). The results of this semi-empirical 

 method are given in column 10 of Table I., column 9 giving 

 the recalculated values of b, upon which they are bused. 



It can be seen that a much closer approximation to experi- 

 mental fact is thus attained. The lack of agreement now 

 seldom amounts to much more than 1 per cent., and in the 

 best " fitting " part of each table is very slight indeed, 'but a 

 systematic deviation is still apparent. The closeness of fit 

 for any particular substance depends on the selected value 

 of C, and no very great care was taken in most cases to 



