method is to fill the vessel with water till the level of the water
stands a little higher than the rim of the vessel. The float will then
be repelled from the edge of the vessel. Such floats, however, should
always be made so that the section taken at the level of the water is as
small as possible.
[_The Size of Drops._--The relation between the diameter of a tube and
the weight of the drop which it delivers appears to have been first
investigated by Thomas Tate (_Phil. Mag._ vol. xxvii. p. 176, 1864),
whose experiments led him to the conclusion that "other things being the
same, the weight of a drop of liquid is proportional to the diameter of
the tube in which it is formed." Sufficient time must of course be
allowed for the formation of the drops; otherwise no simple results can
be expected. In Tate's experiments the period was never less than 40
seconds.
The magnitude of a drop delivered from a tube, even when the formation
up to the phase of instability is infinitely slow, cannot be calculated
a priori. The weight is sometimes equated to the product of the
capillary tension (T) and the circumference of the tube (2[pi]a), but
with little justification. Even if the tension at the circumference of
the tube acted vertically, and the whole of the liquid below this level
passed into the drop, the calculation would still be vitiated by the
assumption that the internal pressure at the level in question is
atmospheric. It would be necessary to consider the curvatures of the
fluid surface at the edge of attachment. If the surface could be treated
as a cylindrical prolongation of the tube (radius a), the pressure would
be T/a, and the resulting force acting downwards upon the drop would
amount to one-half ([pi]aT) of the direct upward pull of the tension
along the circumference. At this rate the drop would be but one-half of
that above reckoned. But the truth is that a complete solution of the
statical problem for all forms up to that at which instability sets in,
would not suffice for the present purpose. The detachment of the drop is
a _dynamical_ effect, and it is influenced by collateral circumstances.
For example, the bore of the tube is no longer a matter of indifference,
even though the attachment of the drop occurs entirely at the outer
edge. It appears that when the external diameter exceeds a certain
value, the weight of a drop of water is sensibly different in the two
extreme cases of a very small and of a ver
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