240 THE FIGURES OF EQUI1.IBRIUM OF A LIQUID MASS 



system, and let us suppose that .the liquid is in sufficient quantity then to project 

 outside the cylinder. In this case the mass will present on each side a convex 

 surface of spherical curvature, and the curvatures of these two surfaces will be 

 equal. This figure is a consequence of what we have previously seen; and we 

 must not stop here, for it will serve us as a starting point in obtaining other 

 lio-ures which we require. Apply the point of the syringe to one of the above 

 convex surfaces, and gradually withdraw some of the liquid; the curvatures of 

 the two surfaces will then gradually diminish, aud with care they may be ren- 

 dered perfectly plane. It follows from this first result that a plane surface is 

 also a surface of equilibrium, which is evidently in conformity with theory. Let 

 us now apply the end of the syringe to one of these plane surfaces, and again 

 remove a small quantity of liquid. The two surfaces will then become simul- 

 taneously hollow, aud A\ill form two concave surftices of spherical curvature, the 

 mar"-ins of which rest upon the metallic band, and the curvatures of which are 

 the same. Finally, by the further removal of the liquid, the curvatures of the 

 two surfaces become greater and greater, always remaining equal to each other. 



Hence it results, first, that concave surfaces of spherical curvature are still 

 surfaces of equilibrium, which is also in accordance with theory. Moreover, as 

 the plan(> surface left free sinks spontaneously as soon as that to which the in- 

 strument is applied becomes concave, it must be concluded that the superficial 

 layer belonging to the former exerts a pressure which is counterbalanced by an 

 equal force emanating from the opposite superficial plane layer, but Avhich ceases 

 to be so, and which drives away the liquid as soon as this opposite layer com- 

 mences to become concave. Again, as further abstraction of the liquid deter- 

 mines a new rupture of equilibrium, so that the concave surface opposite to that 

 upon which we directly act exhibits a new spontaneous depression when the 

 curvature of the other surface increases, it follows that the concave superficial 

 layer belonging to the former still exerted a pressure, Avhich at first was neutral- 

 ized by an equal pressure arising from the other concave layer, but Avhich be- 

 comes pre^jonderant, and again drives away the liquid, when the curvature of 

 this other layer is increased. 



Uttuce it f'ol]oA\'S, first, that a plane surface produces a pressure upon the 

 liquid ; second, that a concave surface of spherical curvature also produces a 

 pressure; third, that the latter is inferior to that corresponding to a plane surface; 

 fourth, that it is less in proportion as the concavity is greater, or that the radius 

 of the sphere to Avhich the surface belongs is smaller. These results were also 

 pointed out by theory, and had already been verified in the application of the 

 latter to liquids submitted to the, action of gravity, by the phenomenon of the 

 elevation of a liquid column in a capillary tube, the Avails of Avhich are moistened 

 by it. 



, Reasoning upon these facts, as Ave liave done at the end of paragraph 17 in 

 regard to coua'Cx surfaces of spherical curA'ature, Ave shall arrive at the conclu- 

 sion that the entii'e pressure exerted by a concave superficial layer of spherical 

 curvature is the result of minute individual pressures arising from all the elements 

 of this layer, and that thi; intensity of cacli of these minute pressures depends 

 upon the curvature of that clenKmt of the layer from Avhich it emanates. Our 

 last experiment, therefore, perfectly verifies that part of the theory Avhich relates 

 to plane and convex surfaces of spherical curvature. Lastly, in the state of 

 equilibrium of our liquid figure, the curvature being the same at all points of each 

 of the two concave surfaces, it is again evident that all the minute elementary 

 pressures are ec^iuil to each other, Avhich gives a new complete verification of 

 the general condition of equilibrium. 



22. The figure we have just obtained constitutes a biconcave lens of equal 

 curvatures, and possesses all the properties of diverging lenses, i. e., it dimin- 

 ishes objects seen through it, &c. More&ver, as the curvature of the tAvo sur- 

 faces may be increased or diminished by as small degrees as is Avisbed, it follows 



