. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. 364 FIGURES OF EQUILIBRIUM OF A LIQUID MASS equally with tlie unduloid, susceptible of variations between certain limits, Fig. 38 should be regarded only as presenting one case of its meridian line. We Fi^. '.3d. will" urther recall the observation made in § 29, and which will now be better understood from the appearance of this curve, namely, that the complete figure can only be represented in the state of a simple surface, since, if
. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. 364 FIGURES OF EQUILIBRIUM OF A LIQUID MASS equally with tlie unduloid, susceptible of variations between certain limits, Fig. 38 should be regarded only as presenting one case of its meridian line. We Fi^. '.3d. will" urther recall the observation made in § 29, and which will now be better understood from the appearance of this curve, namely, that the complete figure can only be represented in the state of a simple surface, since, if it were supposed to be full, there would evidently be parts of it engaged in the mass. § 33. Before we proceed to the consideration of the nodoid in its variations, a question should be resolved which is suggested by the experiments of § 31. Since we know now the form of the meridian line, we see that those experiments realize the portion of the nodoid generated by a part, more or less considerable, of one of the arcs convex towards the exterior, such as wpv!, (Fig. 38.) But it maybe asked if this does not require that, with disks of a given diameter, the volume of oil should be comprised within certain limits, so that for larger or smaller volumes the figure realized would no longer pertain to the nodoid. To determine this, let us take one of the figures realized, follow the meridian arc beyond the point where it meets the edge of one of the disks—the upper one, for instance—and let us see whether it be possible to arrive at a curve other than the meridian line of a nodoid. We will suppose, first, that in that part of its course where it continues to approach the axis of revolution, and to withdraw from the axis of symmetry, the curve presents a point of inflexion, so that it shall afterwards turn its con- vexity towards those two axes. If, while still approaching tlie first, it changed a second time the direction of its curvature, the perpendicular corresponding to thi
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