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.'. .    399.
ON THE THEORY OF THE CAPILLARY TUBE. [Proceedings of the Royal Society, A, Vol. xcn. pp. 184—195, Oct. 191
A RECENT paper by Richards and Coombs* discusses in some detail t determination of surface-tension by the rise of the liquid in capillary tub and reflects mildly upon the inadequate assistance afforded by mathemati It is true that no complete analytical solution of the problem can be obtain-even when the tube is accurately cylindrical. We may have recourse graphical constructions, or to numerical calculations by the method of Rung* who took an example from this very problem. But for experimental pi poses all that is really needed is a sufficiently approximate treatment of t two extreme cases of a narrow and of a wide tube. The former question v successfully attacked by Poisson, whose final formula [(18) below] woi meet all ordinary requirements. Unfortunately doubts' have been thro' upon the correctness of Poisson's results, especially by Mathieuj, who reje them altogether in the only case of much importance, i.e. when the liqi wets the walls of the tube—a matter which will be further considered la on. Mathieu also reproaches Poisson's investigation as implying two differ*; values of h, of which the second is really only an improvement upon t first, arising from a further approximation. It must be admitted, howev that the problem is a delicate one, and that Poisson's explanation at a criti point leaves something to be desired. In the investigation which follow: hope to have succeeded in carrying the approximation a stage beyond tl reached by Poisson.
In the theory of narrow tubes the lower level from which the height the meniscus is reckoned is the free plane level. In experiment, the lo^ level is usually that of the liquid in a wide tube connected below with t narrow one, and the question arises how wide this tube needs to be in ore that the inner part of the meniscus may be nearly enough plane. Care:
* Journ. Amer. Cliem. Soc. No. 7, July, 1915.
t Math. Ann. Vol. XLVI. p. 175 (1895).
J Theorie de la Capillarite, Paris, 1883, pp. 46—49.sive, of the integrand,                                                        *.. In neither case can R vanish for a finite (real) value of ?;, and the same is true of S± and 8Z. being blown from a loaded bag, charged beforehand with a foot blower. In this respect they are not fully comparable with those of Prof. Titchener, whose whistle was actuated by squeezing a rubber bulb. However, I have also tried a glass tube, 104 in. long, supported at the middle and rubbed with a resined leather. This should be of the right pitch, but the squeak heard did not suggest an s. I ought perhaps to add that the thing did not work particularly well.