Forces of Attraction between Atoms and Molecules. 789 



previous papers. This method leads to the same equations 

 as those given at the beginning of this paper in perhaps a 

 more straightforward way, and besides brings out further 

 relations and points of importance. 



The surface-tension of a liquid is defined as the work 

 required to produce an increase of unit area of surface. 

 This increase in area may be produced in many ways. The 

 way which we will use in this investigation is to suppose a 

 mass of liquid cut into two portions by a plane, and these 

 then separated from one another by an infinite distance. If 

 W denote the work done in separating the portions, and A 

 the amount of new surface produced in each portion, X the 



W 



surface-tension is given by X = ^-r . 



Let AB in fig. 1 be a plane which cuts a thick slab of 



Fur. 1. 



■ A 



3? 







LZy c ?y, 



D 



liquid into two portions, and suppose the thickness of each 

 portion greater than the sphere of attraction of a molecule. 

 The work of separation per unit area will first be calculated 

 on the assumptions that, (1) the matter is evenly distributed 

 in space, (2) the attraction of one element of matter on 

 another is not affected by intervening matter. 



The coordinates of an element of volume in the portion 

 will be denoted by (a, y, z), AB lying in the yz plane ; and 

 the coordinates of an element of volume in D will be denoted 

 by (#!, y 1? ^i), the axes ?/i z x being common to the axes y z. 

 The attraction of a volume of matter whose mass is equal to 

 that of a molecule on another equal volume will be taken as 

 (2,c a ) 2 <f>(z), where (j>(z) is a function of the distance of separa- 

 tion of the volumes. According to condition (2), Xc a must 



