﻿of the common Surface of two Liquids, 255 



bubbles in Table III. be compared with the values of the same 

 constant of Table II. derived from the capillary heights, the 

 former will be found greater than the latter. For the sake of easy- 

 inspection these values are placed side by side in the following 

 Table, IV. 



This difference partly results from the assumption that the 

 air-bubble has a plane top and an infinitely large radius B/ at 

 all points of its surface. Now B/ = r for the vertical meridian- 

 elements, and is less than at the top of the air-bubble, where 

 the principal radii of the curves are equal and very large. Thus 



the magnitude ^ for the vertical meridian-element may be 



greater than the magnitude ^— for the surface-element of the 



top of the air-bubble, or the capillary pressure in the vertical 

 meridian-element of the air-bubble greater than was assumed in 

 the approximative calculation in § 2. In this case K — k must 

 be found greater than the actual value of the constant a. 



After the production of the capillary surface the constant a 

 gradually diminishes with the time, and a must be found just 

 so much the greater the quicker it can be observed. Generally 

 a drop gains its equilibrium much quicker than a column of 

 liquid which rises in a capillary tube ; and for this reason the 

 value of the capillary constant must also be found greater in a 

 drop or an air-bubble than from the heights in tubes. For this 

 reason also the diameters of the capillary tube should not be 

 chosen too small. 



If the angle w were really 180°, then would 



But this only happens in the fewest cases, as Table III. shows. 



If from the separate Tables the mean of K s/\ be taken and 

 the following expression formed, 



a= 2"'2' (12) 



then a. will always be < «, as Table IV. shows. 

 But according to equations (4) and (8), § 2, 



_ a 1 — cos co . c .co 



= 18O o -a> = 18O o -2arcfsm=^fV . (13) 



The last column but one of Table IV. gives the values of the 

 acute angle calculated from equation (13), the last column the 

 values of cos 6 reckoned from columns 4 and 6. 



