24G THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 



face of the modified cube presents in intaglio. Then, in fact, in passing from 

 the hollow surface to that in relief, the radii of curvature corresponding to each 

 point will only change their signs without changing in absolute value ; conse- 

 quently, (§ 8,) since the condition of equilibrium is satisfied as regards the first 

 of these' surfaces, it will be equally so with regard to the second. 



Now, let us imagine a plane passing through one side of the plate, and tan- 

 gentially to the surface of the liquid which adheres to it at that point. As 

 long as this liquid is in small quantity, we should imagine — and experiment 

 bears us out — that the plane in question will be strongly inclined towards the 

 plate; but if we gradually increase the quantity of liquid, the angle comprised 

 between the plane and the plate will also continue to increase, and instead of 

 bein"- acute, as before, will become obtuse. Now, so long as this angle is less 

 than''45°, the convex surface of the liquid adhering to the plate will remain 

 identical with the concave surfaces of the mass attached to the metallic frame, 

 and suitably diminished ; but beyond this limit, the coexistence in the frame 

 of the six hollow identical surfaces with the surface in relief becomes evidently 

 impossible, for these surfaces must mutually intersect each other. Thus, when 

 the withdrawal of the liquid from the mass forming the cube is continued, a 

 point is attained at which the figure of equilibrium ceases to be realizable in 

 accordance with the ordinary law of pressures. We then meet with a new 

 verification of the principle enunciated in § 28, i. e., that the formation of 

 layers commences. These layers are plane ; they commence at each of the 

 wires of the frame, and connect the remainder of the mass to the latter, which 

 continues to present six concave surfaces. In fact, we can. imagine that, by 

 this modification of the liquid figure, the existence of the whole of this in the 

 metallic frame a"-ain becomes possible, as also the equilibrium of the system ; 

 for there is then no further impediment to the concave surfaces assuming that 

 form which accords with the ordinary law of pressures ; 

 I and, oil the other hand, in supposing the layers to be suffi- 



ciently thin, the pressure belonging to them might be 

 equal to that which corresponds to these same concave sur- 

 faces, (§ 25.) 



On removing still further portions of the liquid, the layer 

 will continue to enlarge, whilst the full mass which oc- 

 cupies the middle of the figure will diminish in volume, 

 and this mass can thus be reduced to very minute dimen- 

 sions : Fig. 12 represents the entire system in this latter 

 state. It is even possible to make the little central mass 

 disappear entirely, and thus to obtain a complete laminar 

 system; but for this purpose certain precautions must be taken, which I 

 shall now point out. When the central mass has become sufficiently small, 

 the point of the syringe must first be thoroughly wiped ; otherwise the oil 

 adheres to its exterior to a certain height, and this attraction keeps a cer- 

 tain quantity of oil around it, which the instrument cannot absorb into its 

 interior. In the second place, the point of the syringe must be depressed to 

 such an extent that it nearly touches the inferior surface of the little mass. 

 During the suction this surface is then seen to become raised, so as to touch 

 the orilice of the instrument, and the latter then absorbs as much of the alco- 

 holic mixture as of the oil ; but this is of no consequence, and the minute mass 

 is seen to diminish by degrees, so as at last completely to disappear. The 

 system, then, consists of twelve triangular layers, each of which commences at 

 one of the wires of the frame, and all the summits of which unite at the centre 

 of the figure; it is represented in Fig. 13. But this system is only formed 

 during the action of the syringe. If, Avhen this is complete, the point of the 

 instrument is slowly withdrawn, an additional lamina of a square form is seen 



D^.J2. 



