236 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 



the liquid mass is not too great, the curvatures again terminate abruptly al5ng 

 the rim of the plate. By gradually augmenting the volume of the primitive 

 sphere of oil, without, however, rendering it sufficiently large to allow of the 

 mass completely enveloping the plate so as to retain the spherical form, a limit 

 is attained at which the edge of the plate ceases to reach the superficial layer 

 of the new figure of equilibrium except at the two summits of the ellipse. The 

 discontinuity in the curvatures then only occurs at these two places. Figs. 4 

 and 5 exhibit the result of the experiment in this case. In Fig. 4 the long axis 

 of the ellipse is presented to view, in Fig. 5 its short axis. 



IG. All the facts which we have hitherto detailed show that so long as the 

 interior of the mass is modified its external shape undergoes no alteration ; but 

 that directly the superficial layer is acted upon, the mass acqua-es a different 

 form. To complete the proof, by experiment alone, that the configuring actions' 

 exerted by the liquid upon itself emanate solely from the superficial layer, the 

 only point would then be the possibility of reducing a liquid mass to its super- 

 ficial layer, or at least to a thin pellicle, and to see if in this state it would 

 assume the same figure of equilibrium as a complete mass. Now this is com- 

 pletely realized in soap-bubbles ; for these bubbles, when detached from the 

 tube iu which they have been made, assume, as is well known, a Spherical form, 

 i. c, the same figure as that which we find a complete mass acquires in our 

 apparatus when withdrawn from the action of gravity and perfectly free. 

 When the mass adheres to a solid system, which modifies its figure, it is clear 

 that the entire contigurative action is composed of two parts, one of which 

 belougs to the solid system ; and we find that this system only exerts it when 

 acting upon the superficial layer ; the other belongs to the liquid, and emanates 

 directly from the free portion of this same superficial layer. The facts which 

 we have related show clearly what is the seat of this second part of the whole 

 configurative action, but they do not make us acquainted with the nature of 

 the forces of which it consists. On referring to theory, Ave find that these forces 

 consist in pressures exerted upon the mass by all the elements of the superficia 1 

 layer, pressures the intensity of which depend upon the curvatures of the surface 

 at the points to Avhich they correspond. Hence it follows that the mass is 

 pressed upon by every part of its superficial layer, with an intensity depending 

 in the same manner upon the curvatures of the surface. For instance, a mass 

 the free surface of which presents a convex spherical curvature, will be pressed 

 upon by the whole of the superficial layer belonging to this free surfsice, with a 

 greater intensity than if this surface had been plane ; and this intensity will be 

 more consid(.'rable in proportion as the curvature is greater, or as the radius of 

 the sphere to which the surface belongs is less. Let us see whether experiment 

 will lead us to the same conclusions. 



17. The solid system which we shall employ is a circular perforated plate, 

 (Fig. 6.) It is placed vertically, and attached by a point of its circumference 

 to the iron wire which supports it. Let the diameter of the sphere of oil be less 

 than that of the plate, aiul let the latter be made to penetrate the mass by its 

 edge in a direction which does not pass through the centre of the sphere. At 

 first, as in the experiment at paragraph 14, the oil will form two unequal 

 spherical segments : but matters do not remain in this state. The most convex 

 segment is seen to diminish gradually in volume, consequently in curvature, 

 whilst the other increases, until they have both become exactly equal. One 

 part of the oil then passes through the aperture in the plate, so as to be trans- 

 ferred from one of the segments towards the other, until the above equality is 

 attained. 



Let us now examine into the consequences deducible from this experiment, 

 judging from the preceding ones, and independently of all theoretical considera- 

 tions. When the oil has once become extended over both surfaces of the plate, 

 in such a manner that the superficial layer is applied to every part of the 



