﻿of the common Surface of two Liquids. 



249 



that is to say, the vertical distance of the horizontal from the ver- 

 tical element of the meridional curve (of the point K from the 

 point k in the accompanying figure, which in future will always 



be denoted by K— k), measured in millimetres, gives, when squared, 

 the specific cohesion of the common surface of the two liquids — and 

 if multiplied by half the difference of the specific gravity, the capil- 

 lary constant a 1<2 or the tension of the surface of the common limit 

 of the two liquids. 



Equation (7) also holds good, and strictly so, when a liquid 

 rests at an angle of 180° against vertical plane sides — for ex- 

 ample, mercury against a vertical glass plane wetted with alcohol 

 or water. 



If the drop rests on a horizontal base, and if the vertical dis- 

 tance of the summit of the drop K and of the vertical meridional 

 element k from the horizontal base be denoted by K and k re- 

 spectively, then 



K-*=fl 18 , . . . (8) 



K=^ 0l2=wl2 =« 12 \/l-cos&) 12> .... (9) 



in which (o 12 is the angle at which the last element of the 

 surface of the drop cuts the horizontal base. By combining 

 equations (8) and (9) the values of a n and cos a) n may be ob- 

 tained. 



If the horizontal base is wetted by liquid 2, which frequently 

 happens, then 



© l8 =180°, 

 K =« 12X /2. 



} 



(10) 



Accordingly as <r x > or < <r 2 will z, K, and k be positive or ne- 

 gative. A drop of oil in water under a horizontal glass plate 

 wetted with water has the same form as a drop of water in oil on 

 a horizontal base wetted with oil, and so forth. 



It is obvious that equations (2) to (9) are transformed into 

 those for free liquid surfaces when cr 2 or a x is put equal to zero. 

 In the first case the drops are exposed to the air or a vacuum ; 

 in the second case they are air-bubbles which rest against either 

 a horizontal or a slightly curved side. Of course, in the second 

 case, the magnitudes K, k, and are always negative. 



