526 Lord Rayleigh on the 



During the expansion fresh vapour is formed ; and if the 

 composition of the vapour were poorer than that of the liquid, 

 the latter would inevitably be enriched by the operation. 

 We conclude that at the point in question the vapour cannot 

 be poorer than the liquid. In like manner if the vapour- 

 pressure falls with increasing richness of liquid, compression 

 of a given mass cannot enrich the liquid, and this requires 

 that the vapour be not richer than the corresponding liquid. 

 If we suppose the vapour-pressure to be plotted as a function 

 of richness of corresponding liquid, we may express these 

 results by saying that rising parts of the pressure-curve can 

 have no representation in the lower triangle of our former 

 diagrams (where vapour is poorer than liquid), and that 

 falling parts cannot be represented in the upper triangle. 



It is now evident that the passage from a rising to a 

 fulling part of the pressure-curve can only occur when the 

 vapour is neither richer nor poorer than the liquid, and we 

 arrive at Konowalow's important theorem that any mixture, 

 which corresponds to a maximum or minimum of vapour-pres- 

 sure, has (at the temperature in question) the same composition 

 as its vapour. 



The particular case in which one ingredient is wholly in- 

 volatile is worth a moment's notice. The vapour over a 

 solution of salt in water can never have the same composition 

 as the liquid ; and from this we may conclude that the 

 vapour-pressure has no maximum or minimum, or rather that 

 there is no transition anywhere between rising and falling. 



The converse of Konowalow's theorem is also not without 

 importance. Consider two mixtures of slightly differing 

 composition, one of which is richer than its vapour and the 

 other poorer. Expansion of the first entails an enrichment 

 of the liquid, and during the operation the pressure cannot 

 rise. Expansion of the second impoverishes the liquid, and 

 again the pressure cannot rise. The curve exhibiting pres- 

 sure as a function of composition (of liquid), if it slopes at all 

 at the two points, must slope in opposite directions. Hence 

 by approaching nearer and nearer to the point where the 

 compositions of vapour and liquid are the same, we see that 

 the vapour-pressure must there be stationary in value. 



An example of the use of the converse theorem is afforded 

 by the consideration of mixtures of water and common 

 alcohol. The question of the existence of a mixture having 

 the same composition as its vapour is not easily settled 

 directly, but the recent observations of Noyes and Warfel * 

 show conclusively that the mixture containing 96 per cent. 

 * Am. Chem. Soc. xxiii. p. 463 (1.901). 



