346 Mr. A. M. Worthington on the 



to 



sion of a solid or liquid substance by an external force involves 

 in general a fall of temperature ; the release from the state of 

 tension and consequent contraction involves a rise of tempe- 

 rature. Consequently the heat-energy necessary to endue the 

 less dense surface liquid with its given temperature is more 

 than sufficient to maintain this liquid at the same temperature 

 when its density is assimilated with that of the mass of the 

 liquid. The contraction of the surface is therefore accom- 

 panied by an evolution of heat-energy and a rise of tem- 

 perature; and the surface-layers may be regarded as a portion 

 of the liquid on which extra heat-energy has been spent in sepa- 

 rating the molecules against the action of cohesive forces. 



8. We have ; for the sake of clearness, first supposed the 

 liquid to be non-volatile, so that the surface should have above 

 it a vacuum entirely without action on the liquid below. We 

 will now proceed to the more general case of a liquid (a.) 

 in contact with some second substance (/3). 



Let the surface of separation be a horizontal plane, and 

 let us think of (a) as the lower substance, and let us imagine 

 the second substance (/3) to have its molecules uniformly dis- 

 tributed and rigidly connected so that a pressure or tension 

 is transmitted through it without producing any appreciable 

 change of density, while we examine what must be the condi- 

 tion of equilibrium of the liquid (a) in the neighbourhood 

 of the surface. We shall also suppose that the liquid (a) has 

 its molecules uniformly distributed at first, and they are en- 

 dowed with the cohesive attraction which they would possess 

 in nature. We will, as before, use Fj to signify the resultant 

 vertical attraction between any molecule of (a) and the 



adjacent layer; F 2 , F 3 , ¥ n for the corresponding action 



between each molecule and more distant layers, and, as 

 before, we will write Fj + F 2 + F 3 + + F n = tF. 



The action between (ft) and (a) may be regarded as made 

 up of the action of each molecule of (a) on each layer of mole- 

 cules of (/5), if we write </> Ai for the action between any molecule 

 A of the surface-layer of (a) and the first layer of (/3), <£a 2 for 

 the action between the same molecule and the next layer of 

 (/3), and so on. 



We may write 20a = <£a, +</>a 2 + <£a 3 + + <f>A m for the 



whole action of (/3) on the molecule A. 



Similarly, the action of any molecule B of the second layer 

 of (a) on the substance (/3) will consist of a number of similar 

 terms of which an appropriate symbol for the first will be 

 </>b 2 , since it expresses the attraction between the molecule B 

 and the lowest layer of molecules in (ft), which is the second 

 adjacent layer above it. 



