CAPILLARY CONSTANTS 435 



but its usefulness is seriously limited by the fact that with 

 many liquids it is difficult, indeed impossible, to form true films 

 which shall be sufficiently permanent to enable the weighings to 

 be carried out. In this method, as in the one last described, a 

 distinct maximum pull is observable just before the true film 

 is formed, and in this case also the surface-tension may be 

 calculated in terms of this maximum pull. Indeed, this method 

 is, analytically, simply a particular case of the former one, and 

 the equation which gives the surface-tension may be deduced 

 from the equation of the anchor-ring method by supposing the 

 radius of the anchor-ring to become infinite. But the ring- 

 method is, on the whole, preferable, since it avoids troublesome 

 end-corrections. 



The first of the methods classified under the heading 

 " Bubbles and Drops," is fairly simple both in theory and in 

 practice. If one limb of an inverted U-tube be plunged into a 

 beaker full of liquid, by suitably raising or lowering the beaker 

 a pendent drop may be formed at the end of the other limb. The 

 pressure-excess at the vertex of this drop may be determined 

 by measuring the distance from the drop-vertex to the horizontal 

 level of the liquid in the beaker. But this pressure-excess is 



2T 

 equal to -r-, where R is the principal radius of curvature of 



the vertex of the drop. R may be determined by photographing 

 the drop on a large scale, and measuring the co-ordinates of a 

 few points in the neighbourhood of the vertex taken as origin. 

 If one assumes, what is very nearly the case, that the outline of 

 the drop in the neighbourhood of the vertex is parabolic, R may 

 be calculated from the values of the co-ordinates. The method 

 is very suitable for certain special cases, but considered as a 

 general method it is not of a sufficiently high order of accuracy, 

 as it is somewhat difficult to determine R with great exactness. 



Methods (7) and (8) depend for their accuracy primarily 

 on the closeness with which one can obtain integrals of the 

 differential equation to the capillary surface. As is well known, 

 this equation, in its most general form, is not susceptible to 

 exact integration ; and even if we restrict ourselves to those 

 cases where the capillary surface is one of revolution about a 

 vertical axis, the difficulties in the way of an exact integration 

 are insurmountable. Approximate integrals can, however, be 

 obtained in certain special cases — broadly speaking, those cases 



