impulsure pressure be applied for an instant uniformly over the whole
membrane, and then instantly let the membrane be dissolved into liquid.
This action originates a motion of the liquid relatively to the solid, of a
kind to which I have given the name of "irrotational circulation," which
remains absolutely constant however the solid be moved through the liquid.
Thus, at any time the actual motion of the liquid at any point in the
neighborhood of the solid will be the resultant of the motion it would have
in virtue of the circulation alone, were the solid at rest, and the motion
it would have in virtue of the motion of the solid itself, had there been
no circulation established through the aperture. It is interesting and
important to remark in passing that the whole kinetic energy of the liquid
is the sum of the kinetic energies which it would have in the two cases
separately. Now, imagine the whole liquid to be inclosed in an infinitely
large, rigid, containing vessel, and in the liquid, at an infinite distance
from any part of the containing vessel, let two perforated solids, with
irrotational circulation through each, be placed at rest near one another.
The resultant fluid motion due to the two circulations, will give rise to
fluid pressure on the two bodies, which, if unbalanced, will cause them to
move. The force systems--force-and-torques, or pairs of forces--required to
prevent them from moving will be mutual and opposite, and will be the same
as, but opposite in direction to, the mutual force systems required to hold
at rest two electromagnets fulfilling the following specification: The two
electro magnets are to be of the same shape and size as the two bodies, and
to be placed in the same relative positions, and to consist of infinitely
thin layers of electric currents in the surfaces of solids possessing
extreme diamagnetic quality--in other words, infinitely small permeability.
The distribution of electric current on each body may be any whatever which
fulfills the condition that the total current across any closed line drawn
on the surface once through the aperture is equal to ¼ [pi] of the
circulation[1] through the aperture in the hydro-kinetic analogue.