Abstract
LONDON. Royal Society, November 18.-Sir William Crookes, president, in the chair.-Lord Rayleigh: The theory of the capillary tube. In a recent paper Richards and Coombs comment on deficiencies in the mathematical treatment of the capillary tube, some of which it is here attempted to remedy. In the best experimental arrangement a wide and a narrow tube are connected below, and the difference between the levels of the lower parts of the two meniscuses is measured. In the interpretation of the results for deducing the surface-tension of the liquid, two problems arise (i) how to allow for the weight of the meniscus in the narrow tube, and (ii) to find what diameter is necessary for the wide tube in order that the elevation due to curvature of the liquid surface may be neglected. The first problem was considered by Poisson, but his results in the only really important case, viz., when the liquid Wets the walls of the tube, have been disputed. Poisson's formula is here confirmed and extended. If r denotes the radius of the tube, h the measured height of the meniscus above the truly plane level, T the surface-tension, g gravity, and p the density of the fluid, 2T/£/o.r = fe + r/3-o-i288r!/k+o-i3i2r3/fc2. an approximation which should suffice for experimental purposes. It may be remarked that the first two terms on the right correspond to the assumption of a spherical surface, which is legitimate when r is small enough. A completely adequate solution of the second problem is more difficult. But it is easy to show theoretically that such diameters as are sometimes used for the wide tube (2-5 cm. or 3-0 cm.) are quite insufficient, at any rate in the case of water, a conclusion reached also by Richards and Coombs in direct experiment. It appears further that the widest tube used by these observers (3-8 cm.) would be insufficient to take advantage of the actually achieved delicacy of reading. An approximate calculation of the diameter necessary for this purpose gives 4-7 cm. -Prof. C. H. Lees: The effect of the form of the transverse section on the resistance to the motion of an elongated body parallel to its length through a fluid the viscosity of which is not negligible. When a very elongated body moves parallel to its length through a fluid, the resistance due to the viscosity of the fluid varies considerably with the form as well as with the magnitude of the cross-section of the body. Values of the total resistance and of the resistance per unit area of contact with the fluid are given in various cases. In all cases so long as the fluid is in streamline motion, the law of resistance can' be expressed in a simple form, and it is desirable that measurements of the resistance when the motion is turbulent should: be made in order to determine the extent to which these laws may be utilised in practical engineering.- Prof. J. Joly: A method of estimating distance at sea in fog or thick weather. The method proposed is based upon the different velocities of disturbances in differing media. If aerial and submarine signals are simultaneously emitted at a lighthouse station or lightship the lag of the aerial compared with the submarine sound is about 4-3 seconds to the nautical mile. An approaching ship picking up the signals and measuring the lag to an error even of one second becomes aware of her distance to less than one-quarter of a mile. Similarly, wireless signals and submarine signals, or wireless and aerial signals, may be used. If the faster-moving signals be sent out in groups, the individual signals being spaced to regular intervals- say, of one second-and the slower moving signal be always emitted simultaneously with the first signal of a group, the navigator has only to count the faster signals until the slower signal reaches him, in order to estimate his distance from the signal station. In this case the signals themselves tell him his distance, and no actual time-measurements are required on board ship. It is shown that this system enables the mariner to determine his position completely in all circumstances which may arise.-Prof. J. Joly: A method of avoiding collision at sea. This paper deals with an extension of the method described in the preceding paper for estimating distance at sea to the problem of avoiding collision in fog. It is shown that if vessels possess the means of emitting a loud and crisp sound signal which can be sent out simultaneously with a wireless or a submarine signal, the determination of distance rendered possible thereby, along with wireless information as to course and speed, will enable the navigator on each ship to determine with certainty (i) whether there is risk of collision or whether there is no risk, and (2) the point upon his own course and the moment at which collision is, threatened. The solution of the problem is based upon the fact that at each instant the rate of mutual approach is the maximum if the ships are advancing so as to collide. A simple geometrical construction, which by its character is unlikely to involve error, enables the mariner to solve the problem immediately the signals are received.-S. W. Richardson: The flow of electricity through dielectrics.-S. Chapman: The kinetic theory of gaseous viscosity and thermal conduction, and the law of distribution of molecular velocities in the disturbed state. The first object of the paper is to determine the velocitv-distribution function /.(it, v, w) in a gas in which there are small variations of temperature and velocity from point to point. Both simple and mixed gases are considered; the mixtures are supposed uniform, the study of diffusing mixtures being deferred to a later paper.
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Societies and Academies . Nature 96, 360–362 (1915). https://doi.org/10.1038/096360a0
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DOI: https://doi.org/10.1038/096360a0
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