If, in a sequel to the preceding experiment of Plateau’s, we use
solid discs instead of annuli, so as to enable us to exert direct
mechanical pressure upon our globule of oil, we again begin by
adjusting the pressure of these discs so that the oil assumes the form
of a cylinder: our discs, that is to say, are adjusted to exercise
a mechanical pressure equal to what in the former case was supplied
by the surface-tension of the spherical caps or ends of the bubble.
If we now increase the pressure slightly, the peripheral walls will
become convexly curved, exercising a precisely corresponding pressure.
Under these circumstances the form assumed by the sides of our figure
will be that of a portion of an unduloid. If we increase the pressure
between the discs, the peripheral surface of oil will bulge out more
and more, and will presently constitute a portion of a sphere. But we
may continue the process yet further, and within certain limits we
shall find that the system remains perfectly stable. What is this new
curved surface which has arisen out of the sphere, as the latter was
produced from the unduloid? It is no other than a portion of a nodoid,
that part which in Fig. 66 lies between such limits as M and N. But
this surface, which is concave in both directions towards the surface
of the oil within, is exerting a pressure upon the latter, just as did
the sphere out of which a moment ago it was transformed; and we had
just stated, in considering the previous experiment, that the pressure
inwards exerted by the nodoid was a negative one. The explanation of
this seeming discrepancy lies in the simple fact that, if we follow the
outline {225} of our nodoid curve in Fig. 66 from O, P, the surface
concerned in the former case, to M, N, that concerned in the present,
we shall see that in the two experiments the surface of the liquid is
not homologous, but lies on the positive side of the curve in the one
case and on the negative side in the other.
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Public-domain text, read in full here on John Shaqi.
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