342 Mr. A. M. Worthington on the 



quantity comparable with that of the metals themselves, while 

 the extension corresponding to it would still be a very small 

 fraction of the total volume of the liquid. 



As regards the distance to which the attractive action of a 

 molecule extends, it is customary to say that at all sensible 

 distances the action is zero ; and to regard the molecule as 

 situated at the centre of an imaginary sphere whose radius is 

 called the radius of molecular action, and whose surface marks 

 the limit beyond which the cohesive attraction of the molecule 

 is insensible, within which it is sensible. 



It is to be observed, however, that inasmuch as a distance 

 or an action which is insensible in one experiment may be 

 sensible in another, the value of the radius of molecular action 

 as defined in this way would probably vary with each expe- 

 riment in which it is concerned. But we shall not require a 

 more precise statement in the present investigation. Nor is 

 it at present necessary to examine whether the number of mole- 

 cules contained within the sphere of molecular action be great 

 or small. The reasons which will afterwards appear for re- 

 garding this number as great rather than small are derived 

 chiefly from capillary phenomena themselves. 



. Again, as regards the repulsive force, which is of the nature 

 of an elastic reaction varying with the temperature, it is not at 

 once apparent whether it is to be considered as exerted only 

 between adjacent layers of molecules, or whether it extends to 

 molecules separated from each other by intervening layers. 



In the argument which follows we shall proceed upon the 

 former supposition, the justification of which will be better 

 understood after it is seen in what manner either hypothesis 

 enters into the discussion. 



6. In order to prove that the molecules of a liquid near the 

 surface are in the condition which corresponds physically to a 

 state of tension, let us select some non-volatile liquid, and 

 imagine the molecules deprived of their attractive or cohesive 

 action and of their repulsive action, and to be distributed at 

 equal distances from each other, those at the surface lying in 

 the same horizontal plane. Now let us endow each molecule 

 with the attractive force which we ascribe to it in nature. 

 Each molecule now exerts an attraction over those of its 

 neighbours which fall within the radius of molecular action. 

 We will suppose that the uniform distance which we have 

 arbitrarily selected as that which shall separate adjacent mole- 

 cules is small in comparison with the radius of molecular 

 action, a condition which (for reasons that will afterwards be 

 detailed) we believe to obtain in the mass of the liquid in 

 nature. Let us select a molecule A at the surface, and 



