﻿of the common Surface of two Liquids, 381 



If the length of the upper column of liquid in the capillary 

 tube be h, and if h denote the elevation of the common meniscus 

 above the horizontal plane level or the surface of the lower liquid 

 u outside the capillary tube, r the radius of the capillary tube at 

 the place of the meniscus of the open surface (bounded by air) 

 of the upper liquid, r ou the radius for the meniscus of the com- 

 mon surface of the two liquids within the capillary tube, and the 

 notation already adopted be retained, the weight of liquid raised 

 above the horizontal level of liquid u is borne by the two menis- 

 cuses, and, according to equation (1), § 1, we have : — 



2« cos o* 2a ou cos co ou 



+ h <r + h u <r u = O t 



1 r 



a ou cosco ou = ~ — [r (h (T -f h u <r u ) —2a cos o) ] . . (16) 

 4 r 



For the special case in which r = r ou this equation becomes 

 ToK^o + h u <r u ) — 2*0 cos oj ■ 



cos aw= 



2 



'Zrha— 2a cos o) 



(17) 



2 



It follows from this that the capillary constant of the common 

 surface is determined when %rhcr, as well as « (the capillary 

 constant of the surface of the upper liquid 6) and the two angles 

 co and (o ou are known. The first is in many cases =0°, or at least 

 may be assumed to be known, since the magnitude cc cos <o is 

 determined from the elevation of liquid o in capillary tubes 

 (compare § 4) ; but co ou is not known, and can only be supposed 

 = 0° or 180° in a few cases, as we shall afterwards see. 



Hence this method is not to be generally recommended for the 

 determination of the capillary constant of the common surface 

 of liquids. However, it has the advantage of being easily carried 

 out, requires only small quantities of liquid, and admits of liquid 1 

 being above and liquid 2 below, or conversely, and <r 1 may be 

 greater or less than cr 2 . 



By means of this method it is immediately seen that the ca- 

 pillary constant ot u of the lower liquid (upon which alone, accord- 

 ing to the theory of Poisson*, the weight of liquid borne by the 

 capillarity depends) has no influence whatever, and that a ou 

 cos o) ou and oc cos co alone determine it. 



It may also be observed that h may be very small, provided it 

 is > 21 (than twice the radius of the sphere of action) . Equation 

 (17) then holds good completely, as the free surface of liquid o 



* Nouvelle Theorie de V Action Capillaire, p. 142 (1831). 



