2G2 Mr. W. Sutherland on Molecular 



all the molecules of 2 is ^jS^^/i^ 3 multiplied b} T n 2 p/2 

 times 2,R 2 3 , s ° for the n 1 molecules the factor n x is introduced 

 and a factor 2 introduced because of the contrast pointed out 

 above between n x 2 l2 and n x n 2 . Thus we arrive at the same 

 result as before. For the total potential energy of the n 1 + /j 2 

 molecules in unit mass of mixture we have 



where p x and p 2 = l— p l are the masses of liquids 1 and 2 in 

 unit mass of the mixture. 



The attractional virial for such a mixture is 3/2 times the 

 potential energy. As to the surface energy we shall consider 

 only the case where the effect of the vapour is negligible. 

 Then by similar reasoning to that just used in calculating 

 the potential energy of unit mass we find that liquid 1 in the 

 mixture contributes the fraction («]p//?oi/°i) 2 of its surface 

 energy per unit area as a pure liquid to the surface energy 

 of the mixture, and so 



a = (nip/?i iPi) 2 *i + 2(n 1 ?i 2 p' 2 ln 0l n 02 p l p.2)a 1 2u 2 2 -f (n 2 pjn 02 p 2 yoi 2 



/. ^p 2 = {p l u^p l +p 2 u 2 i\p i )\ . . . (18) 



This equation was verified (Phil. Mag. [5] xxxviii. 1894, 

 p. 188 ; xl. 1895, p. 1) by the same experiments as proved 

 the formula corresponding with 4^5] e 2 s 2 \ x R 2 4 for the force of 

 attraction between two unlike molecules. If this formula 

 were to hold in a purely statical theory of surface energy it 

 would imply that the distribution of the mixed sets of mole- 

 cules was a purely random one. Any regular distribution 

 favouring the existence of a minimum potential energy would 

 be excluded. Such a result is highly improbable, and there- 

 fore the formula just established maybe regarded as evidence 

 in favour of the active motion of the molecules in a liquid. 

 This kinetic method of investigating mixed liquids has been 

 neglected in the past, but it has many useful applications. 



By means of the results of this section we can explain the 

 remarkable fact that so many ordinary liquids mix with so 

 little contraction or expansion and so small an evolution of 

 heat. Such cases as the rise of temperature on mixing water 

 with sulphuric acid or with ethyl alcohol are marked excep- 

 tions. For the change of potential energy on mixing a mass 

 p x of liquid 1 with jt? 2 = l— p^ of liquid 2 we have 



4:p(p 1 e 1 s 1 jm 1 ^ p 2 e 2 s 2 Jm 2 ) 2 — ^p^s^jmi 2 — Ap 2 p 2 e 2 2 s 2 9 lm 2 2 . 



In u Further Studies on Molecular Force " (Phil. Mag. [5] 

 xxxix. 1895, p. 1) it was shown that for most elements in 



