of Instability of Electrified Drops, ete. 77 
of the generating ellipse constant and hence having a variable 
volume, or by keeping the volume constant. 
Let “c” be the semi-axis of rotation and “a” the transverse 
/semi-axis, and consider in each case the ened tt of a portion 
of the surface at the end of the axis of rotation, inasmuch as 
experiment showed the instability to begin at this place on the 
drops examined. 
_ 12. First, consider the volume of the ellipsoid constant and 
‘that it has a constant charge Q. Equation (1) becomes 
2c as 
Putting the first derivative equal to zero, to get the relation for 
the limit of stability, and remembering that a’c=a constant, 
G2 NG azo nae ea eee tent en titi ce (3). 
Equation (2) shows that for this value of Q, the excess pressure, 
p, inside the drop vanishes. 
For a sphere, equation (3) becomes 
Ora erat wen uit Tela da: (4), 
a result obtained long ago by Lord Rayleigh*. 
If Q and “a” are taken as constant, there is no instability, but 
for every value of Q there is a value of “c” which gives stable 
equilibrium. 
Since in the drops experimented upon the potential V, and not 
Q, was maintained constant, cases will next be considered with that 
supposition. 
13. Consider V and “a” constant. Equation (1) becomes 
2Tc Gee 
ee eS Ou iatastsys ate. (5), 
2ara4 log? 5 = 
he ellipsoid being considered prolate, and “e” being the eccen- 
tricity of the generating ellipse. The neces at the limit of 
stability is 
ge 
VI = é log? 5 
ee a cel ea 
V2 = ral te (6), 
which becomes for a sphere, at the limit e = 0, 
VANEAU OM Utne SAGhOk Hane ee Sennen (7). 
* Lord Rayleigh, Phil. Mag., Series 5, Vol. 14, p. 184, 1882. 
