﻿of the common Surface of two Liquids. 



455 



pendicular plane of the element P of the curve. These forces 

 are equal to the capillary constants or tensions of the surfaces of 

 the three capillary surfaces, and in equilibrium when the equation 



sin 6 3 sin 6 2 sin 1 

 is satisfied. 



In this equation 6 3 , 2 , 6 l denote the angles which the elements 

 of the meridian of the curved capillary surface intersecting at 

 the point P, whose directions coincide with those of the forces 

 a ]2 , a 23 , and a 34 , make with one another. a 12 is the capillary 

 constant of the common surface of liquids 1 and 2, &c. 



A lens-shaped drop of water on a surface of mercury, over 

 which is air or oil, would correspond to the given hypotheses. 

 The mercury may represent liquid 1, the water liquid 2, and 

 the air or oil liquid 3. 3 , 6%, { are the angles at the common 

 edge of the wedge-shaped pieces of the three liquids, as may be 

 seen from fig. 1 . 



Fig. 1. 



The angles 6 3 , 2 , 0, may be replaced by their supplements &> 3 , 

 ft) 2 , ft)j in equation (1) ; these are then the angles of a triangle 

 whose three sides are a 12 , # 31 , and a 23 respectively, or whose 

 sides are parallel to the three meridian -elements of fig. 1, as 

 fig. 2 shows. 



Fig. 2. 



If therefore a triangle he constructed whose three sides are pro- 

 portional to the capillary constants (tensions of the surfaces) of the 



2H2 



