as the case may be; and our cylinder may also, of course, be converted into an unduloid either by elongating it further, or by abstracting a portion of its oil, until at length rupture ensues and the cylinder breaks up into two new spherical drops. In all cases alike, the unduloid, like the original cylinder, will be capped by spherical ends, which are the sign, and the consequence, of the positive pressure produced by the curved walls of the unduloid. But if our initial cylinder, instead of being tall, be a flat or dumpy one (with certain definite relations of height to breadth), then new phenomena may be exhibited. For now, if a little oil be cautiously withdrawn from the mass by help of a small syringe, the cylinder may be made to flatten down so that its upper and lower surfaces become plane; which is of itself an indication that the pressure inwards is now _nil_. But at the very moment when the upper and lower surfaces become plane, it will be found that the sides curve inwards, in the fashion shewn in Fig. 65B. This figure is a catenoid, which, as [Illustration: Fig. 65.] we have already seen, is, like the plane itself, a surface exercising no pressure, and which therefore may coexist with the plane as part of one and the same system. We may continue to withdraw more oil from our bubble, drop by drop, and now the upper and lower surfaces dimple down into concave portions of spheres, as the result of the _negative_ internal pressure; and thereupon the peripheral catenoid surface alters its form (perhaps, on this small scale, imperceptibly), and becomes a portion of a nodoid (Fig. 65A). {224} It represents, in fact, that portion of the nodoid, which in Fig. 66 lies between such points as O, P. While it is easy to [Illustration: Fig. 66.] draw the outline, or meridional section, of the nodoid (as in Fig. 66), it is obvious that the solid of revolution to be derived from it, can never be realised in its entirety: for one part of the solid figure would cut, or entangle with, another. All that we can ever do, accordingly, is to realise isolated portions of the nodoid.