404 Mr. R. A. Lehfeldt on the 



and the value of 



p= _J^ = (^1^ + 7TB ^T- .(22) 



This is a maximum if r < 1, a minimum if r > 1. 



Now cases exist in which p has a maximum (propyl alcohol 

 and water) or minimum (formic acid and water) ; but in others 

 neither has been observed (methyl or ethyl alcohol and water). 

 If, however, r has any value not very different from unity 



— —will be large ; and the stationary value of p will be for 



a liquid containing only a very little either of the substance 

 A or B — so little that it would not have been observed in 

 Wullner's or Konowalow's experiments. The function ex- 

 pressing p cannot have both a maximum and a minimum, and 

 no liquid mixture has been observed to possess both. 

 4th, at the maximum or minimum point, 



i. e. the liquid and vapour have the same percentage com- 

 position. That this is necessarily the case when p has a 

 stationary value was first pointed out by Konowalow. 



(iv.) Comparison of the Integral Equation with Experiment. 



The experiments of Wiillner, Konowalow, and F. D. 

 Brown, mentioned above, do not afford much material for 

 testing the accuracy of equation (18). The equation contains 

 one unknown constant, r, so that one observation of the 

 vapour-pressure of a mixture, or of the composition of the 

 vapour rising from it, will enable us to determine r, and if 

 there is more than one mixture so investigated, we have 

 a test of the applicability of the equation. Wiillner observed 

 the pressures of four mixtures of water and alcohol, three of 

 alcohol and ether, and quotes from Regnault three of carbon 

 disulphide and ether. The observations were extended over 

 a range of temperature ; but as nothing in our investigation 

 indicates that the quantity r is independent of temperature 

 we get no direct help from this multiplication of data. It 

 will be seen in the sequel, however, that so far as the equation 

 is applicable at one temperature, it is usually applicable with 

 the same value of r at others. 



Konowalow gives his observations on the vapour-pressures 

 of the eight liquids he employed, mixed with water, for 



