76 Mr Zeleny, On the Conditions | 
less than what would correspond to a drop having the 
potential of the discharge point, and so an estimate was made) 
based on later considerations and it was found that the radius! 
of the drops is probably between 10-*> cms. and 10~-‘cms. Accord- 
ingly many millions of these drops must be formed every second) 
under the conditions existing in the conical form of discharge from) 
an alcohol surface. | 
The ejection of these comparatively small pieces from the! 
surface is evidently quite a different matter from the outflow of 
large drops from the tube, and is doubtless the result of a state) 
of instability of the surface. 
Conditions for Instability. 
11. The conditions that are necessary for a charged surfalen 
to become unstable are exemplified by considering the equilibrium) 
equation for a spherical drop 
where 7’ is the surface tension, r the radius of curvature, o the 
electric surface density, and p the excess pressure inside the drop!) 
over that outside. 
The equilibrium becomes unstable when, p remaining un-/ 
changed, a small outward displacement of a portion of the surface) 
increases the outward force due to o, because of the increased curva- 
ture produced, more than it does the restoring pressure arising from | 
surface tension. a | 
To obtain a solution by this simple method, it is necessary, 
to know not only the shape of the surface but also the distribution’ 
of the charge on it, both before and after the displacement in 
question. 
The surface of a small drop at the end of a vertical tube is one 
of revolution and is nearly spherical. Let us consider the surface’ 
to be an ellipsoid of revolution about the axis of the tube, and! 
consider a displacement arising from an elongation of the rotation) 
axis. This elongation might result from liquid flowing into the) 
drop from the tube above, the minor axis remaining unchanged, or) 
it might result from a contraction of a portion of the drop near its 
place of attachment, the change of shape at the apex approximating 
more or less closely that of an ellipsoid of constant volume. The} 
calculation of the distribution of the charge on any shaped drop) 
suspended at the end of a cylinder is rather difficult. However, it 
is of interest to consider some ideal cases of isolated, charged,| 
ellipsoidal drops, undergoing changes of shape as a whole in one of) 
the two ways mentioned above, namely by keeping the minor axis 
