Explanation of the second law.—If the two floating bo dies A, B, Fig. t I, are not capable of being wetted by the liquid,the liquid will be depressed between them at be low its natural level, when they are placed at a capillary distance. The two bodies, therefore, are more pressed in wards by the fluid which surrounds them, than they are pressed outwards by the fluid between, and in virtue of the difference of these pressures they mutually approach each other.
Explanation of the third law.—If one of the floating bo dies A, Fig. 12. is capable of being wetted, while the other B is not, the fluid will rise round A, and be depressed round B : Hence the depression round B will not be sym metrical ; and therefore the body B, being placed as it were on an inclined plane, its equilibrium is destroyed, and it will move towards the right hand, where the pressure is the least.
The results of M. AIonge's experiments have been com pletely confirmed by the theory of capillary attraction given by La Place. From this theory it follow s, that whatever be the nature of the substances of which the floating planes are made, the tendency of each of them to one another is equal to the weight 01 a prism of fluid whose height is the elevation of the fluid between the planes, measured to the extreme points of contact of the interior fluid with the plane, minus the elevation of the fluid on the exterior sides of the tube, whose depth is half the sum of these eleva tions, and whose width is the horizontal distance between the planes. The elevation must be reckoned negative when it changes into a depression as in mercury. If the product of the three preceding dimensions is negative, the tendency of the planes becomes repulsive. La Place also concludes, that when the planes are very near each other, the elevation of the fluid between them is in the inverse ratio of their mutual distance, and is equal to half the sum of the elevation which would have taken place, if We sup Ilawksbee's table, subtracted from 20 inches ; and column 2d contains Ilawksbee's 2d column, diminished by 5' 22".
pose the first plane of the same matter as the second, and the second of the same matter as the first.
It follows from these theorems, that the repulsive force of floating planes is much more feeble than the attractive force which is developed when the planes arc very near each other, and which occasions them to appruach each other with an accelerated motion. In this case the elevation of the
fluid between the planes is very great, relative to its eleva tion on the outside of the same plane. In neglecting, therefore, the square of this last elevation in relation to the square of the first, the fluid prism, whose weight expresses the mutual tendency of the planes, in virtue of the first of the two preceding theorems, will be equal to the pro duct of the square of the ellition of the interior fluid, by half the horizontal distance IFthe planes. This elevation being, by the second theorem, reciprocally proportional to the mutual distance of the planes, the prism will be propor tional to their horizontal distance divided by the square of that distance. The tendency of the two planes to each other will consequently be in the inverse ratio of the square of their distance ; and therefore, like the forces of elec tricity and magnetism, it will follow the law of universal attraction.
When the two planes arc of such a nature that the one is capable of being wetted with the fluid, while the other is not capable of being wetted, then, in consequence of these two opposite actions, the surface of the intermediate fluid will have a point of inflection ; and it follows from the theory, that they will repel each other at every distance. But if they are brought near each other by force, the point of inflexion will approach more and more to °lie of the planes, and will at last coincide with it. If the planes are then brought still nearer each other, the fluid will begin either to ascend, or be depressed between them. From this arises another force, which pushes the planes towards each other, and which, when it conies to surpass the pressure of the exterior fluid, causes the planes to approach each other with an accelerated motion. This change of repulsion into attraction appeared to M. La Place so singular, that he requested M. Hat.+ to examine the subject experimentally. In order to do this, he employed planes of ivory and talc, the first of which is capable of be ing wetted with water, while the other possesses that kind of unctuosity which prevents the water from adhering; to it.