The differential equation of the surfaces of fluids inclos ed in capillary spaces of revolution, conducts La Place to the following general result ; that if into a cylindrical tube we introduce a cylinder which has the same axis as that of the tube, and which is such that the space comprehended between its surface and the interior surface of the tube has very little width, the fluid will rise in this space to the same height as in a tube whose radius is equal to this width. If we suppose the radii of the tube and of the cy linder infinite, we have the case of a tube included be tween two parallel and vertical planes, very near each other. This result has been confirmed, as we have already seen, by the experiments of Newton, Hauy, and Gay Lus sac. La Place then applies his theory to the phenomena presented by a drop of fluid, either in motion or suspend ed in equilibrium, either in a conical capillary tube, or be tween two plates, and inclined to each other, as discovered by Mr Hawksbce ;—to the mutual approximation of two parallel and vertical discs immersed in a fluid ;—to the phe nomena which take place when two plates of glass are inclined to each other at a small angle;—and to the determi nation of the figure of a large drop of mercury laid upon a horizontal plate of glass.
In the application of his theory to the experimental results obtained by Hawksbee respecting the angles required far suspending a drop of oil of oranges at different stations be tween two inclined planes of . glass, La Place obtained the results contained in the following table.
Column 1st contains the number of the first column of IT was long ago observed by philosophers, that when bodies floating on the surface of a fluid approached either one another or the sides of the vessel, they moved rapidly into contact, as if they had been two floating magnets. This phenomenon, which was in general ascribed to the mutual attraction of the floating bodies, was tolerably well ex plained by AI. Marriotte in his Traite the Mouvement des Xaux. It was reserved, however, for AL.Monge to de scribe and explain these phenomena with accuracy, which he has done in his illemoire stir quelques effets d'attraction on de repulsion apparente entre les Molecules de /llatiere.
The following are the principal experiments upon this subject : I. If two light bodies, capable of being wetted with wa ter, are placed one inch distant on the surface of water per fectly at rest, they will float at rest, and experience no mo tion but what is derived from the agitation of the air ; but if the distance at which they are placed is only a few lines, they will approach each other with an accelerated motion. If the vessel which contains the water is capable of being wetted by it, such as glass, and if the floating body is plac ed within a few lines of the edge of the vessel, it will move towards the edge.with an accelerated motion.
2. If the two floating bodies are not susceptible of be ing wetted with fluid, such as two balls of iron in a vessel of quicksilver, and if they are placed at the distance of a few lines, they will move towards each other with an acce lerated motion ; and if the vessel is made of glass, in which the surface of the mercury is always convex, the bodies will move towards the sides when they are placed within a few lines of it.
3. If one of the bodies is susceptible of being wetted with water, and the other not, such as two globules of cork, one of which has been carbonised by the flame of a taper, then if we attempt, by means of a wire or any other substance, to make the bodies approach, they will fly from each other as if they were mutually repelled. If the vessel is of glass, and if the cat bonised piece of cork is placed in it, it will be found impossible to bring the cork in contact with the sides of the vessel.
In these experiments it is obvious, that the approxima tion and the recession of the floating bodies are not pro duced by any attraction or repulsion between the two ; for if the bodies, instead of floating on the fluid, arc suspend ed by long and slender threads, it will be found that they have not the slightest tendency either to approach or re cede when they are brought extremely near each other. From these experiments the following laws are deducible: I. If two bodies, floating on the surface of a fluid, and capable of being wetted by the fluid, are placed near each other, they will approach as if they were mutually at tracted.
2. If the two bodies are not susceptible of being wetted by the fluid, they will still approach each other when brought nearly into contact, as if they were mutually attract ed.
S. If one of the two bodies is susceptible of being wet ted and the other not, they will recede from each other as if they were mutually•repelled.
Explanation of the first two plates of glass AB, CD, Fig. 8. are brought so near each other that the point 11, where the two curves of elevated fluid meet, is on a level with the rest of the water, they will remain in perfect equilibrium. If they are brought nearer each other, how ever, as in Fig. 9. the water will rise between them to the height G. The mass of water which is thus raised, at tracts the sides of the glass plates, and causes them to ap proximate in a horizontal direction, the mass of water hav ing always the same effect as a curved chain hung to the two plates. The same thing is true of two floating bodies, when they come within such a distance that the fluid is ele vated between them. This case is shewn in Fig. 10, where the bodies A, B, placed at a capillary distance, have the wa ter raised between theimand are therefore brought together by the attraction of the fluid upon the sides of the glo bules.