and the Surface-Tension of Solutions. 491 



which has been done for normal liquids on p. 241 of " The 

 Laws of Molecular Force," the result being that I is approxi- 

 mately proportional to aT/yLt/o 2 , where a is the coefficient of 

 expansion, and T is the absolute temperature ; and in " A 

 Kinetic Theory of Solids " (Phil. Mag. 5 ser. xxxii. pp. 530, 

 531) it is shown that 1///,, there denoted by k, is approxi- 

 mately proportional to an expression which is equal to lp 2 

 divided by «T. Thus both for normal liquids and solids I is 

 proportional to aT/pp 2 ; so that in spite of the abnormality of 

 water and solutions we are entitled for comparative purposes 

 to assume a similar form of relation with the additional 

 assumption that as aT represents the ratio of the space free of 

 matter to the space occupied by the molecules, it may be 

 taken to be the same for solutions (especially dilute ones) as 

 for water, so that for water and solutions at a given tempe- 

 rature I is approximately proportional to l//x/> 2 . Now lp 2 

 represents the attraction exerted by the matter on one side of 

 a plane on a cylinder on the other side which stands normally 

 on unit area in the plane. If the matter consists of p x parts 

 of 1, and p 2 parts of 2, forming a gramme of mixture of 

 density p, then the density of the p Y gramme distributed 

 through a space 1/p isp^, and the attraction due to molecules 

 of 1 on opposite sides of the plane is l\p 2 p 2 , so for the 

 molecules of 2 it is l^p^p 2 ) an( i f° r the mutual attractions of 1 

 and 2 it is 



2 1 A 2 (WW 2 />7(iA 12 A 2 )*, 

 so that 



l= P^ + ( a 1A a ^ ViPSihf+pA, ■ • (19) 

 and if l = e/fjip 2 , li = c/fi ] pi 2 , then 



1 _ p* ... 2A PlPi (y e f 



w* wrti^ w f +iW ' • (0) 



which is the law connecting the compressibility of a solution 

 with its concentration and with the properties of its com- 

 ponents ; remembering that p x — 1 — p 2 , this becomes 



_!_ J_ =2 p ( i A 2 / V° V H 



W 2 Wi ^ I d Ax 2 A 2 ) * WiV /^i 2 / 



4- a term in p 2 2 ; . (21) 



for dilute solutions the term in p 2 2 can be neglected. We 

 can illustrate the truth of this form of relation by applying it 



