﻿of the common Surface of two Liquids. 457 



1 and 2 is equal to or less than the difference of the capillary 

 constants of the free surface of liquids 1 and 2, or than the value 

 of the capillary constant of the common surface of two liquids de- 

 duced from Poisson's theory. 



Moreover this proposition follows, when the question is not 

 to determine the angle co 3 from it, simply from the observation 

 that the difference of any two sides of a triangle must always be 

 less than the third side. 



For liquid 1 the liquid with the greater capillary constant must 

 always be chosen, as the particles will adhere whose reciprocal 

 attraction is the greater, or the particles of that liquid which 

 possesses the greater (dependent on the reciprocal attraction) ca- 

 pillary constant. 



The sign of equation (3) is always to be so chosen that the 

 left side will be a positive magnitude, as a capillary constant or 

 surface-tension of a liquid is an essentially positive magnitude. 



It may here be mentioned that the whole theory of capillarity 

 may be deduced from the principle that the surface of a liquid is 

 a minimum. It appears that by bringing several liquids together 

 they so arrange themselves that the sum of their surface-tensions 

 becomes the least possible. 



If a liquid n be displaced from the common surface of liquids 

 1 and n by a liquid 2, then the liquid 2 can be displaced by a 

 liquid 3 from the common surface of liquids 2 and n, and so on. 

 The conditions, according to equation (3), are 



am > a i2 + a 2n> 

 a 2«>«23 + *3n, 



or (by adding these inequalities) 



a iw > a 12 + a 2 3+ ...«»-i«. ... (5) 



For a gas or for rarefied air as liquid n, the suffix n would be 

 omitted in the above equation, and u x and a n _! would denote 

 the capillary constant of the open surface of liquids I and n— 1. 



The different common surfaces then succeed one another as if 

 they were arranged according to the magnitude of their capillary 

 constant or tension of surface. The thickness of the single 

 layers of liquids can never be 0, and must, in case the magni- 

 tudes a have the usual signification, be >2/, or greater than 

 twice the radius of the sphere of action. 



If the thickness of liquids 2, 3, . . . n — 1 is very small, as, for 

 example, in the experiments of Section II., then the sum of the 

 single tensions of surfaces is equal to the collective tension of the 

 superposed surfaces, and always less than the tension of the 

 original (open or bounded by liquid n) iurface of liquid 1. 



26. The best method of observing the spreading of a liquid 2 



