An excellent dissertation, entitled Dissertatio Physica de Tubis CapillaHbua Vitrei•, was published by M. Mus chenbroek, which contains a great variety of interesting experiments upon this subject. He has committed a mis take, however, in maintaining that the height of ascent in creases with the length of the tube. The constant quantity for water, as deduced by Dr Young, from his best experi ments, is 0.592.
In the year 1736, Josiah \Veitbrecht published a valuable paper in the Commentarii Acad. Petropolitante, entitled Tentamen Theories qua ascensua ague in tubia capillaribus ex/ilicatur. He chews that water is more strongly at tracted by glass than it is by its own particles ; that the sphere of activity of the attraction of the glass is extreme ly small, that is, the action of the glass does not extend to the axis of the tube ; that the water must be partly sup ported by the mutual attraction of its own particles ; that the water in the capillary tube is drawn downwards, not only by its own gravity, but by the attraction of the water in the vessel ; that the water in the tube is elevated by the attractive force of the whole internal surface of the tube successively applied ; but that it is suspended solely by the action of the ring of glass immediately above the fluid co lumn. M. \Veitbrecht considers the force which suspends the water as represented by Q—Q', Q representing the force with which the water is attracted to the glass, and Q'the force with which it is attracted downwards by the water in the vessel ; and as Q is greater than Q' in water and most fluids, the quantity Q—Q' is affirmative, and the water rises above its level. \Vhen the tube is taken out of the water, the force Q' he considers as vanishing, and there fore the remaining force is allowed to act without opposi tion, and consequently the water rises to a greater height in the tube. In mercury Q' is greater than Q, and there fore the expression is negative, and the fluid consequently sinks below its level. M. \Veitbrecht made the following • experiments on the ascent of water.
In a subsequent memoir, entitled Explicatio experimentorum tired ascensum aqua in tubis Capillaribus, published in the Comentarii Acad. PetropoNand', for 1737, M. Weitbrecht resumes the subject. He slims that Mus chenbroek was mistaken, in considering the height of ascent as affected by the length of the tube. He points out the effects produced by interposing bubbles of air be tween the different parts of the elevated column ; he ex amines the phenomena exhibited by conical tubes, and tubes where the diameter of the bore changes rapidly ; and he terminates his memoir with several interesting ex periments on the effects of capillary syphons and bent ca pillary tubes.
Hitherto mercury was the only metallic fluid which had been employed in capillary experiments. M. Gellert, however, communicated a memoir to the Academy of Sci ences at St. Petcrsburgh, entitled De Phenomenis plumbi fusi in Tubis Capillaribus. In making these experiments, be employed the thinnest glass tubes he could procure, and heated them gradually before he immersed them into the melted lead. In this way he found, that melted lead always stood below its level in a tube of glass, and that the altitudes in different tubes were nearly in the reciprocal ratio of their diameters. When the diameter of the tube was 10.21 of an English inch, the lead sunk 0.27 of an inch, whereas in a tube 0.07 it sunk 0.73 of an inch. These re sults give 567 and 510 for the constant quantity, the mean of which is 5385. In another paper, entitled, De Tubis Capillaribus Prismaticis, M. Gellert treats of the ascent of water in prismatic tubes of a triangular and quadrangular form, made of iron. He found, that they gave results per fectly analogous to those which were made of glass.
Before the time of Clairaut, no attempt had been made to analyse with accuracy the different forces which concur in the elevation of water in capillary tubes, and to subject the phenomena to a rigorous calculation. The merit of doing this belongs wholly to this eminent mathematician, who has published his investigations in the tenth chapter of his Theorie de la Figure de la Terre tiree des Princi/zes de i'llydrostatique, which was published at Paris in 1743, and of which a second edition appeared in 1808. In this chap ter, which is entitled De l'Elevation ou de l'?baissement des Liqueurs dans les tuyau.r Capillaires, he begins by pointing out the mistake in the reasoning employed by Dr Ellin in the establishment of his hypothesis, and he then proceeds to the analysis of the forces by which the water is elevated and suspended. An account of this analysis has already been given in our article on CAPILLARY ATTRAC TION. The resulting formula which he obtains for the al titude 1 1, (Plate CX. Fig. 9.) is I i = fdx[b,x]+ fdx [6,x. (4, (n, whereQ = the Intensity of the attraction of the glass.