﻿Measurements of Pendent Drops. 



429 



It is worth noting that the assumption of a parabolic 

 section permits o£ the equations of equilibrium of the part of 

 the drop in the neighbourhood of the vertex being put into a 

 very simple form. 



Fig. 4. 



Let the coordinates of B be (,r, y). Draw the tangent at 

 B v and consider the equilibrium of the portion of the drop 

 below the horizontal section ACBD. 



Resolving vertically, we have, if P be the atmospheric 

 pressure, h the distance from to the "free/' horizontal 

 surface of the liquid, and V the volume of the drop below 

 the horizontal plane AOBD, 



or 



'Itta-T sin <j> + P . Tr.r = Vpg + [P -rgp(Ji — y)~] . ir.r. 



2xT^m4>=, ff -^+ 9P {h-^ 9 



(i.) 



since 



2b 



Considering the equilibrium of the portion BCDO, and 

 resolving horizontally, we have, if s be the length of the 

 parabolic arc DOC, 



Ts + Px 7,.<y/ = 2./'.Teos(£-f -(P+gpli) t v(/ — - <jp.fi/\ 



or 



2,r T cos $ — Ts = - gpxy* — - gphtry 



(u.1 



And, eliminating gph between (i.) and (ii.), we obtain on 



