348 Mr. A. M. Worthington on the 



and for the repulsive reaction between the (r+ l)th layer and 

 a molecule R of the rth layer, we have 



Now if 2F > %<p A , i. e. if the action of the liquid (a) itself 

 on a surface-molecule is greater than that of the substance 

 beyond the surface, we may assume F x > <f> A , F 2 > <j> A , and so 

 on. For this will be the case if the condition SF > 20 A is 

 due, on the one hand, to a less density of the molecular struc- 

 ture of the substance (ft), or, on the other hand, to a smaller 

 intrinsic energy in the molecules of (/3) ; or, thirdly, to both 

 of these causes combined; and it is difficult to conceive of any 

 other cause than one of these. 



In this case the value of each of the expressions 



[(2)(3)]-[(l)(2)], [(3)(4)]-[(2)(3)], &o. 



i3 positive ; and equilibrium at a given temperature can only 

 be obtained by an increase of repulsive reaction (i. e. of den- 

 sity) as we descend into the substance. 



If, again, XF = 2(/> A in such a manner that 



Fi = Ai , F 2 = A2 =(/> B2 , &c, 



then it is evident that we have at the opposite sides of the 

 surface two substances in which the physical properties with 

 which we are concerned are identical, and the value of each 

 of the expressions [(2) (3)] — [(1) (2)] &c. becomes zero, and 

 the density at each side of the surface is everywhere the same, 

 and there is no surface-tension. 



If, on the other hand, SF < 2<£ A , the substance (/3) must 

 have, owing either to greater density or to greater intrinsic 

 energy of its molecules, a greater action on a surface-molecule 

 of A than the liquid itself, and we may assume that any term 

 ¥ n is greater than the corresponding term c/> A , or </> B , or cf> c , 



&c. Therefore the value of each of the terms 



[(2) (3)]-[(l) (2)], [(3) (4)]- [(2) (3)], &c. 



* The meaning of this result may with advantage be illustrated by the 

 geometrical diagram (fig. 2), which will not require explanation. The 

 downward attraction on the elementary volume A may be written %Z n ~F; 



the upward attraction 2<p n </>. If there is to be equilibrium, the differ- 

 ence of these two" must be balanced by the difference in the repulsive 

 pressure on the upper and lower surfaces of the elementary volume. 



If (/3) is exchanged for a vacuum, i^ w (/) = 0, which gives the result 

 of the first case. 



