in the Theory of Pendent Drops. AT 
avoided, while that level may be so chosen that the tangent 
is there vertical or changes its inclination very slowly. 
Let ADCE (fig. 4) represent a horizontal circular section 
of the pendent drop taken at any level ; ABC the generating 
curve in the plane of the paper; DBE the same curve ina 
plane at right angles to the paper. Consider first the equi- 
librium as regards vertical forces of the mass of liquid below 
the plane section. We may equate the vertical component 
of the surface-tension (T) round the circumference ADCH, 
to the weight (W) of the liquid below the section + the 
pressure on the area ADCH; so that, signifying by 2 the 
unknown distance of this section from the level of the free 
surface of the liquid, and by A the weight of unit volume of 
the liquid, we have 
TcosO0x7AC=W+7AO*'#A. . . . (i) 
Again, if we consider the equilibrium, as regards horizontal 
forces parallel to the plane of the paper, of the mass 
ABDOH, we see that the surface-tension acting horizontally 
round the periphery DBE is equal to the hydrostatic pressure 
on the area DBE + the sum of the tensions across each 
element of the semicircumference DAKE, each resolved first 
horizontally and then normally to DH. Now the hydrostatic 
pressure is equal to the area DBE x density of liquid x 
depth of the centre of gravity G of the area below the level 
of the free surface, and this depth =OG-+z2; and I have found 
that OG can be determined with great accuracy by cutting 
the figure out of carefully selected writing-paper, and balan- 
cing ; again the sum of the horizontal tensions across the 
semicircumference resolved normally to DE=T sin ODE; so 
that 
T x length DBH=T sin @DE +area DBE (OG+z2) A, 
or 
T(length ABC — AC sin 0)=area ABC (OG+2)A; (ii.) 
and from these two equations 2 can be eliminated and T 
found. 
Now the section can be chosen at a place of contrary 
flexure, where the value of cos @ can be obtained with very 
great accuracy ; or, again, if the circular base from which 
the drop depends be small enough the drop will assume the 
form shown in fig. 5, in which at a certain level MN the curve 
is vertical, and sin@=0. When this is the case equation (i.) 
becomes 
Poem == We aA ga es 25, (lly) 
