





and the Isotliermals of Vapours. 





447 



regai 



rded 



as d 



ue to the 



fact that the relation 



Ai 



A2 • 



d 2 



only 



appi 



oximately true 



for any assigned temperature. 





If 



we write 



Aj A 2 



-j- or T 

 «i "2 



for A, we have 











A 



A, 



A 2 A x - 



A 2 





d^ + d.2 d l (d 1 ^-d 2 ) d 2 (d 1 + d 2 ) d{ 2 — d<?' 



and these expressions should also be independent of tem- 

 perature. For an actual substance, let us suppose that 

 A, = rd u and that A 2 = r(l -ru)d 2 , where r and a are of course 

 not independent of temperature. 

 Then 



A A, -A, 



d 1 -{-d 2 d^ — d 



\ — d 2 ~ct.d 2 _ / 1 ad 2 \ 



d{*-d 2 2 ~ r \a\ + T 2 ~a\ 2 -d 2 2 ) 



With rise of temperature the first term inside the bracket 

 increases slowly ; the second, apart from a, also becomes 

 greater, and very rapidly so as the critical temperature is 

 approached. Hence, if we may regard r and a. as not 

 varying very rapidly with temperature, it is easy to see that 

 for small positive values of a the quantity Kb will at first 

 increase slowly to a maximum and then decrease, as the 

 temperature rises. 



§ 4. For an " ideal " substance, then, we may suppose that 



RTlogJ 



A is proportional to (d l + d 2 ), i. e. that -^ — -7-/ is inde- 



d\ — a 2 



pendent of temperature. For actual substances this is not 

 exactly true, but we may none the less suppose that there is 

 for them also a relation, A6 = constant, expressing the con- 

 stant relation of the cohesive forces to the cohesive density. 

 In this, however, either A or b or both differ slightly from 



/ 2RTlo 4 1 \ 



the values I — 7 - 7 — - and -, r respectively ) which we 



v d x - d 2 d v + d 2 r J J 



have hitherto assigned to them. To test this point we must 



modify our original equation for the saturation pressure 



d, +t(n 



and the most simple way of doing this in the required way 



