Q' = the intensity of the attraction of the water. b — the interior radius of the tube.
= the force of gravity.
The function of the distance which expresses the law of attraction both for glass and water is supposed given, and he employs x to denote the distance of a particle from the plane MN, [x] the force at which this particle is attract ed by a body, of which this plane is the exterior surface, supposing the intensity of the attraction of this body to be unity. The function [b x] expresses the force with which a particle Q, placed at the distance QO or x from the surface CH is attracted by the tube or bulb cylinder CDABG LIEF, and [b, x, Q, (2'] the force with which a corpuscle p placed at the distance x front VX is attracted by the small mass of water YVXZ.
" Without pushing the calculation farther," says M. Clairaut, " in order to find what will be the quantities [6, x] and [b, x, Q, Q'] according to the different func tions of the distances by which the law of attraction may be expressed, we may easily see that there will be an in finity of laws of attraction in which the preceding expres sion of I i will give a sensible altitude, when the diameter b of the tube is very small, and on the contrary, a height almost insensible when the tube is very wide." It follows from the value of I i, that if the attraction of the capillary tube is less than that of water, provided it is not twice as small, the water will still ascend; for it is obvious from the term (2 Q--Q') f d x [6, x], that while Q' is less than 2 Q, I i will be positive.
In the Transactions of the Royal Society of Gottingen for 1751, M. Segner has referred all the phenomena of capillary attraction to the attraction of the superficial par ticles of fluids. Considering the resemblance at the sur face of the drops of fluids and of fluids contained in capil lary tubes to the surfaces, which geometers have named lintearia or elastic, he was led to consider fluids as enve loped in such surfaces, which, by their tension and elasti city, gave to fluids the form indicated by experiment. It appears, however, that Segncr considered this only as a fiction which might represent the phenomena, but which ought only to be admitted in so far as it belonged to a law in which the attraction is insensible at sensible distances. Segner tried to establish this dependance; but in the opi nion of La Place, in following this reasoning it is easy to discover its inaccuracy, which is also proved by the incor rectness of the results to which he arrives. He finds, for
example, that we ought to consider only the curvature of the vertical section of a drop, and not its horizontal curva ture, which is not exact ; and besides this, he did not per ceive that the tension of the surface is the same, whatever be the magnitude of the drop."" The subject of the adhesion of fluids to plates of solid bodies, which was first investigated by our countryman Dr Brook Taylor,f was now resumed with great success by M. Guyton Morveau, in 1773. The same subject was pro secuted by M. Achard of Berlin, and M. Dutour, the last of whom made a great number of experiments both on the adhesion of discs, and on the ascent of fluids. An account of the general results which they obtained, will be found in our article ADHESION.
In the year 1787, M. Munge published in the Memoirs of the Academy of Sciences, a paper entitled Sur quelques effets d'attraction et de repulsion apparent( entre Us Mole cules de Matiere. These experiments relate principally to the apparent attraction and repulsion which are exhibited by floating bodies when they approach within a certain dis tance of each other ; to the phenomena of drops ; and to the ascent of water between two planes of glass. An ac count of his experiments will be found in the present chapter.
The subject of capillary attraction has been ably investi gated by Dr Thomas Young, in his paper On the Cohesion of Fluids, which appeared in the Philosophical Transac tions for 1805 ; and in which he has anticipated ninny of the views afterwards brought forward by La Place. This paper is divided into 8 sections. Sect. I. Contains the general principles ; Sect. II. Treats of the form di the surface of fluids ; Sect. III. Contains the analysis of the simplest form; Sect. IV. Contains the application of it to the elevation of particular fluids ; Sect. V. Treats of ap parent attractions and repulsions; Sect. VI. Treats of the physical foundation of the law of superficial cohesion ; Sect. VII. Of the cohesive attraction of solids and fluids ; and Sect. VIII. is entitled, additional extracts from Li Place, with remarks. A general account of Dr Young's views, and some of his experimental results, will be found under our article on CAPILLARY ATTRACTION.