V} OF FIGURES OF EQUILIBRIUM 375 



In all these cases the ring or annulus is not merely a means of 

 mechanical restraint, controlling the form of the drop or bubble ; it 

 also marks the boundary, or "locus of discontinuity," between one 

 surface and another. 



If, in a sequel to the preceding experiment of Plateau's, we use 

 solid discs instead of annuli, we may exert pressure on our oil- 

 globule as we exerted traction before. We begin again 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 just 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 become convexly curved, exercising a precisely corresponding 

 pressure; the form assumed by the sides of our figure is now that 

 of a portion of an unduloid. If we increase the pressure, 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 find within certain limits the system 

 remaining 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. 109 lies between 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 of our nodoid curve in Fig. 109, from OP, the surface con- 

 cerned in the former case, to MN, that concerned in the present, 

 we shall see that in the two experiments the surface of the Uquid 

 is not the same, but lies on the positive side of the curve in the one 

 case, and on the negative side in the other. 



These capillary surfaces of Plateau's form a beautiful example 

 of the "materialisation" of mathematical law. Theory leads to 

 certain equations which determine the position of points in a 

 system, and these points we may then plot as curves on a coordinate 

 diagram; but a drop or a bubble may realise in an instant the 



