514 Mr. A. Ferguson on the Theoretical 



be considered plane near the origin, formulse (x.) and (xi.) 



simplify considerably. Thus, let fig. 1 inverted represent, 



say, a large drop of mercury sessile upon a horizontal sheet 



of glass. Considering the equilibrium of the upper portion 



On 

 HOK, we have at once, where B = I x 2 dy, 



T=|f{..'i^i-B}, (xii.) 



.■a very simple equation to determine T. 



Further, if we consider the equilibrium, for horizontal 

 forces, of the portion of the drop to the right of the vertical 

 section OD, we obtain 



T (2a cos co + s) = 2gp C, .... (xiii.) 



where C has the meaning previously assigned, s is the length 

 of the arc AOB, and a is the radius of the small circle of 

 contact of the drop with the horizontal surface. Equa- 

 tions (xii.) and (xiii.), taken together, suffice to determine 

 both T and co. 



The equations developed above, with slight modifications, 

 will serve for the determination of interfacial surface-tensions. 

 Suppose, for example, we have a large drop of one liquid 

 formed within another. Equations (ii. b) or (iii.) are then 

 directly applicable, if it be understood that 



9T 



af = 



where pi and p 2 are the densities of the fluids under con- 

 sideration. If, on the other hand, we follow out the line of 

 argument which resulted in the formation of equation (xii,), 

 we find that 



T =■£■ OxD-p^-Bfa-*)]. 



where 



D = I xy da, 



Jo 



and may be evaluated by the methods previously discussed. 



Before turning to the experimental side of the question, it 

 should be noted that we can, in the case of large bubbles or 

 drops, obtain a close approximation to the outline of the 

 meridional curve bv again integrating the first integral 



