﻿Liquid Drop suspended in another Liquid. 151 



For at such a point 



d / 

 dy' 



and therefore i£ T is constant 



(r + fqH 



d_ 



\*y-\ pdyf=0, 



I. <?., 



Without analysis this is evident from the following con- 

 sideration. A difference of pressure exists between points 

 at the same level, inside and outside the drop, and this 

 difference is proportional to the curvature of the drop at 

 this level. Such difference of pressure increases from the 

 top of the drop until the level of equal densities is reached, 

 since in this region the density of the drop exceeds that of 

 the surrounding liquid. Thereafter, the pressure-difference 

 decreases ; for below the level of equal densities the density 

 of the drop is the lesser. 



Let us assume as a further restriction that 



=*K) 



where li is a linear constant. 

 We readily obtain 



1 + JL= 2 + ^( Q "-pQ . JJ - 1 ^i..y 2 



R PQ Ki T y 2 T h y 



or putting 





b = 



pi 



l -.n 





and 





c 2 = 



T 



' 9Pi 









i + 

 R 



1 



PQ 



2 



2/(26- 

 2he> 



y) 



It is easily seen that y = b is the level of equal densities and 

 maximum curvature. In other words, 2b is the vertical 

 height of: the drop. 



Transfer the axis of x to CAX' at this level, and the above 

 equation becomes 



U -*--*- + £=** fl ) 



