The vertical force produced by the attraction of the solid matter begins to act the instant the fluid comes into contact with the solid ; it first causes the ring to rise, and then keeps it suspended.
If denote the area of a section of the ring made by a vertical plane perpendicular to the sur face of the plate, then or x 1, will be the vo lume of a portion of the fluid equal in weight to If two parallel plates, AB and CD (fig. 5.), very near one another, have their lower ends immersed in a fluid, it is observed that the fluid will rise between them above the natural level. Conceive a superficial canal extending between the plates in a direction at right angles to their surfaces, having its depth equal to the greatest range of the corpuscular force, and its horizontal width equal to unit; then all the fluid below the canal will be in equilibrium with respect to the attractive forces that act upon it, and there fore the suspended weight must be supported by the action of the two plates upon the canal. Of the forces which act upon the canal, we may neglect the attrac tion of the fluid below it, which causes the particles in the inside to press perpendicularly on the bottom. At each end it is attracted by the plates with a force equal to K', or IK and, at the vertical sides between the plates, by the fluid on the outside with a force equal K. Wherefore, when the canal is reduced to equilibrium by equalizing the pressure up on its sides, there will remain at each end an excess of force equal which compresses the fluid upon the plates ; and the compressive force is ne cessarily accompanied with a lateral pressure equal to which tends upwards and supports the weight of the fluid suspended below the canal.
Hence the weight elevated between the plates, in the horizontal length X is equal to x; and, since x 1 is the volume corresponding to the weight (H'-3H) x 1, the volume corresponding to the weight 2(H'-114) x X, will be equal to 2flie X X. Let D denote the distance of the plates, and Q the least height of the curve surface between them above the natural level, then, if we conceive a horizontal plane touching the curve surface at its lowest point, the whole fluid between the plates, in the length X, wiH be composed of a small curved portion in the shape of a meniscus, and a parallelopiped equal in volume to XxDx Q. Now, when the plates are
very near one another, and the elevation is consi derable in comparison of their distance, the menis cus will be so small, that the parallelopiped alone may be reckoned equal to the whole volume of the fluid. Hence, if we equate the two expressions of the same bulk, we shall get Q=2,0 ; which proves, that the elevations of a fluid, between plates of the same matter, are reciprocally propor tional to the distances of the plates ; and this agrees with observation.
When a capillary tube, or one with a bore less than one-tenth of an inch, is partly plunged in a fluid, the fluid will rise within the tube above the level on the outside. Let AB and CD (fig. 5.) represent the sides of such a tube, MHN the curve surface of the elevated column, having below it an imaginary surface at a depth equal to the range of the corpus cular force, and conceive two planes intersecting one another in the axis of the tube at any angle, then all the fluid below the superficial stratum will be in equilibrium with regard to the attractions to which it is subjected ; and the triangular portion of that stratum, bounded by the inside of the tube, and the two planes intersecting in the axis, would likewise be in equilibrium, if the pressures upon all its verti cal sides were equal. But the side in contact with the tube is attracted with a force equal to K', or iK A-(K'--al(); and each of the other two sides is attracted with a force equal to aK ; therefore, when the equilibrium of the attracting forces is provided for, there will remain an unbalanced pressure, pro portional to K'—iK, upon the inside of the tube ; and this directs compressive force is accompanied with a lateral tendency, proportional to H'—aH, which is directed upward, and sustains the elevated fluid between the two intersecting planes.