52 Mr, A. M. Worthington on Calculating Surface-Tensions 



the liquid, but the surface-tension multiplied by the cosine of 

 the edge-angle. Thus a special significance has been attached 

 to the high values obtained by the method of flat drops or 

 bubbles, and these values have been widely copied and made 

 the basis of numerical calculations. 



The calculation of the results involves the integration of 

 the equation to the liquid surface 



*(W)- 



Dz. 



Prof. Quincke starts by writing — ; =0, i. e. by assuming 



XV 



that the drop or bubble may be treated not only as flat at the 

 vertex, but also as having an infinite diameter. It is true that 

 in § 5 of the paper referred to he himself comments on the 

 fact that these assumptions are only approximately correct ; 

 but he does not attempt to show that the error entailed by 

 these tw r o assumptions is insignificant. It is the object of 

 this paper to show that the error is very considerable, amount- 

 ing in most cases to as much as 10 per cent, of the whole 

 value, and that when duly corrected the values obtained by 

 this method do not appreciably exceed those obtained with 

 capillary tubes. 



Prof. Quincke's process consists in measuring by means of 

 a cathetometer-microscope the dimensions of a large drop or 

 bubble, such as is represented in section in figs. 1 and 2, that 

 has been placed on, or below, a horizontal glass plate. 



Fig.l. 



Fig. 2. 



The dimensions measured are 



(1) The distance K of the vertex from the plate. 



(2) The distance k of the section of maximum radius from 



the plate. 



(3) The maximum diameter AB. 



The first two measures afford the value K— k of the dis- 

 tance between the vertex and the section of maximum radius, 

 and the last affords the value L of the maximum radius. 



The physical meaning of the assumptions made in the 

 calculation may be explained in the following manner. 



Imagine a central slab to be cut out of the drop between 

 two parallel vertical planes at small unit distance apart, and 

 that the slab is again cut in half at right angles to its length, 



