﻿456 M. G. Quincke on the Capillary Phenomena 



common surfaces of three liquids meeting in a point, then the exte- 

 rior angles of this triangle give the angles at the edge of the said 

 three liquids for this point*. 



It follows directly from this, that, along the curved line which 

 cuts the three liquids, the marginal angle within each liquid must 

 be constant, since the magnitudes a only depend on the nature 

 of the liquids in contact, and are constant within the same liquid 

 surface. 



The sectional curve of the three surfaces must be a circle. In 

 fact experiment at once shows the correctness of these last two 

 conclusions when water is placed on the ordinary horizontal 

 surface of mercury, where the water forms upon the mercury a 

 lens-shaped drop or a thin layer with a circular opening (com- 

 pare § 27) . 



If of the capillary constants a ]2 , x 3l , a 23 , and the angles S 3 , 2 , 

 L , three magnitudes are known, from these the remaining three 

 can be found, and by the same methods which serve to determine 

 the sides and angles of a triangle from three given elements. 



For the case in which two liquids only are brought into contact 

 (for example, water placed on mercury in air), c* 3X = a { , « 23 =a 2 , 

 or a 31 and a^ denote the capillary constants of the free surface 

 of liquids 1 and 2. 



25. With the magnitudes of the capillary constants deter- 

 mined by means of experiment in the first section of this me- 

 moir, the angle of the edge can be calculated from the equation 



«?2 = < + *23 ~ 2a 31<*23 COS ft) 3 - COS 6 3 



a? A- oft — a? 

 = COSft) 3 = 31+ 23 I 2 (2) 



2 31 a 23 



Equations analogous to the above can be established for <o 2 

 and <o v 



The angle 6 3 is impossible (that is, a spreading of liquid 2 

 over the common surface of liquids 1 and 3 takes place) when 

 cosg>3^ 1, 



<*31 + a 23 ~" a i2 > 2 *31 a 23> 



(a 31 — a 23 ) >« 12 , 



±( a 3i~ a 2s) > a i2 ( 3 ) 



A liquid 2 placed on the surface of a liquid 1 which is bounded 

 by air, spreads itself out, provided 



*i2<( a i- a 2 ); W 



that is, when the capillary constant of the common surface of liquids 

 * This proposition was, I believe, first enunciated by Neumann. 



