CHEMICAL THEORY OF SOLUTIONS. PART I. 61 



in such cases the eluiracteristic magnitudes can be evaluated in 

 the following manner, provided the measurement of pressure and 

 composition at both ends of the curve is sufficiently accurate. 



The tangent to the total pressure curve may be expressed 

 as follows : 



dP dC^ dC\ ,, dC 



dx '* dx ^^ dx " dx 



At the end where a; = equations (37), (40), and (42) hold. 

 Hence 



V dx /o 



and we get 



'^»=(-;!i?-).+'' ; («) 



In other words the tangent to the total pressure curve at x = 

 intersects the pressure axis at x = 1 at the height of ~^. 

 At the other end of the curve we have 



(P)x = 7r.(Cy, + ;rp{l-(6y/; (47) 



These two equations, (46) and (47), do not suffice for the deter- 

 mination of the three quantities v, (Ca)i and tto. Another ex- 

 perimental datum is necessary for the purpose. The density of 

 the saturated vapour of the pure associated component at the 

 given temperature may be measured and employed to evaluate 

 (Ca)i. Or a point in the middle portion of the total pressure 

 curve may be taken into calculation ; then a few trials will 

 suffice to determine the value of y. 



It has been frequently observed that the vapours of as- 

 sociated liquids have normal densities, that is densities cor- 

 responding to the molecular weight of the simple chemical species 



