V] 



OF FIGURES OF EQUILIBRIUM 



223 



modified, and the cylindrical drop will assume the form of an 



miduloid (Fig. 64 a, b), with its dilated portion below or above, 



as the case may be ; and our cyUnder 



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, hke 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 fiat 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oil be cautiously withdrawn from the mass by help of a small 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. 65 b. This figure is a catenoid, which, as 



B 



Fig. 65. 



we have already seen, is, hke 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. 65 a). 



