## Abstract

LONDON. Royal Society, February 10.—Sir Archibald Geikie, K.C.B., president, in the chair.—Dr. C. Chree: Some phenomena of magnetic disturbances at Kew. A recent paper (“Phil. Trans.,” A, vol. ccviii., p. 205) discussed the diurnal inequality of Kew magnetic declination derived from 209 of the most highly disturbed days of the eleven years 1890 to 1900. The present paper discusses the corresponding phenomena for the same days in the other magnetic elements. It is shown that the irregular changes which form the most obvious feature of magnetic storms are accompanied by large *regular* diurnal changes, which are specially striking in the vertical force. In this element the disturbed days referred to above gave a regular diurnal inequality, the range of which in the average month of the year was about four times that given by the Astronomer Royal's “quiet” days. The influence of the hour of the day on the character of the disturbance is visible even on casual inspection of the vertical force curves. When disturbances lasting only a few hours occur in the late afternoon, there is almost invariably a rise in the force, whereas when they occur in the early morning there is a fall. Besides dealing with the analysis of the diurnal inequalities derived from the disturbed day curves, the paper discusses some new phenomena observed in the a periodic changes of the magnetic elements. —R. B. Sangster: A novel phenomenon in the diurnal inequality of terrestrial magnetism at certain stations. The mean diurnal inequality at Greenwich for epoch 1900–6, at Falmouth, 1903–7, and at Pawlowsk (Russia), 1873–85, is dealt with so as to exhibit the inequality in the plane of the astronomical meridian. It is then shown that the component of the force parallel to the earth's axis has little, or no, variation during the hours from noon to about 5 p.m. There is, however, considerable simultaneous variation in the declination and in the horizontal and vertical forces. The winter months invariably showed a shorter duration of the feature, and, generally, a larger diurnal range produced a more exact and lengthened exhibition of the phenomenon. The phenomenon was found to exist whether “quiet” days or “all” days were dealt with, and, while long periods naturally furnished smoother curves, the feature was also prominent in cases where the mean of only five “quiet” days in a single month was employed.—Prof. P. V. Bevan: The absorption spectra of vapours of the alkali metals. The paper gives an account of the absorption spectra of vapours of the metals potassium, rubidium, and cæsium. Prof. R. W. Wood has shown that the absorption spectrum of sodium vapour has for its most striking feature the lines of the principal series. The same series lines for the metals of this communication appear in the absorption spectra. The author has measured the wave-lengths of these lines so that now 24 potassium lines, 23 rubidium lines, and 19 cæsium lines are known of the principal series. Of these, 15 are new in the case of potassium, 21 in the case of rubidium, and 12 in the case of cæsium. In the cases of rubidium and cæsium, the metals themselves were not available, but by heating the chlorides with sodium or potassium, enough vapour was obtained to show the absorption spectrum quite definitely. These lines, with the lines measured by Wood for sodium, give good data for testing various formulæ that have been suggested for representing the series lines. None of the suggested formulæ tested give values representing the series within the limits of experimental error. In particular, the quantity of Rydberg's formula N_{0}, or of the modified Rydberg formula of Rit_{2}, is shown not to be constant. One of the most interesting facts arising out of the investigation is that none of the lines of the associated series appear in these absorption spectra. Channeled space spectra appear which are analogous to the similar spectra for sodium vapour. Further interesting facts noted are in regard to the effect of mixtures of vapours. Some lines or bands appear in spectra of mixtures which are apparently unconnected with the spectra of either constituent. This was specially evident in the case of cæsium and sodium; a set of bands appeared at about W.L. 3000–3500 which do not appear in the sodium spectrum, nor in the mixture of potassium and cæsium spectrum. Other interesting phenomena appear as the density of the vapour is increased in the widening of the lines and the appearance of satellites connected with the lines of the series. The vapour of lithium has not yet been successfully investigated, as it attacks the material of all tubes hitherto tried.—Prof. C. H. Lees: The shapes of the isogeotherms under mountain ranges in radio-active districts. The author shows that for mountain ranges of many different forms of section, the shapes of the isogeotherms may be accurately determined in cases in which the heat conductivity and radio-activity of the materials of the range may be taken as constants. Curves showing the isogeotherms in three typical cases are given, and it is shown that some of the statements generally made with respect to them are not correct.— F. B. Pidduck: The propagation of a disturbance in a fluid under gravity. The paper relates to the determination of the motion set up in a heavy incompressible fluid of uniform depth by a limited initial disturbance; the generally accepted solution in terms of a definite integral represents the disturbance as being propagated instantaneously, although the velocities of the simple harmonic wave-trains of which the solution is built up are all finite. In the paper this solution is transformed into a series-solution analogous to that given by Cauchy and Poisson for infinite depth. In the more general problem of one-dimensional motions in dispersive media the integral solution may represent the disturbance as either being limited at any time by an advancing wave-front, or as being propagated instantaneously. A method, based on the examination of the convergence of the definite integral, is given for deciding between these conditions. An investigation is given of the propagation of waves over a slightly compressible heavy fluid. Solutions of the Cauchy-Poisson type give motions which such a fluid can execute; but these are not due to limited initial disturbances, as they imply a diffused initial condensation. The corresponding result for incompressible fluids is that solutions of the type in question imply a diffused unequilibrated distribution of pressure on release from the initial state.—Dr. A. H. Gibson: The flow of water through pipes and passages having converging or diverging boundaries. A series of twenty-five pipes, all having the same initial and final area, but having different angles of convergence or divergence, were examined. Some of these pipes were circular in section; others square; others rectangular. The following are the main conclusions:—(*a*) In a circular pipe with uniformly diverging boundaries, the total loss of head attains its minimum value with an angle of divergence *θ* of about 5° 30′. Owing to the comparatively large effect of friction in a pipe having a small value of *θ*, the value giving the minimum loss of head will be somewhat less in pipes larger than those examined, which had a larger diameter of 3 inches and a smaller diameter of 1.5 inches. (In large pipes of the type used in the Venturi meter, experiment shows that this value is about 5° 6′.) As *θ* is increased the loss of head, expressed as a percentage of (*v*_{1} − *v*_{2})^{2}/2*g*, increases very rapidly from its minimum value of about 13.5 per cent, to a maximum of about 121 per cent, when *θ* = 63°, afterwards diminishing to about 102 per cent, as *θ* is increased up to 180° (a sudden enlargement of section). (*b*) The effect of making the pipe trumpet-shaped so as to give a rate of change of velocity uniform per unit length of the pipe may in some cases be to increase, in other cases to reduce, the loss of head. In the only case tried in the circular pipes the loss in the trumpet-shaped pipe was 23.5 per cent., as against 17.3 per cent, in a straight taper pipe of the same length, and having *θ* equal to 10°. In the case of a rectangular pipe, however, boundaries curved to give respectively uniform retardation in time and length (*dv/dt* = const.) and (*dv/dx* = const.), showed that the loss, as compared with that in the corresponding straight-taper pipe (*θ* = 20°), was reduced respectively by 5.3, per cent, and 12.1 per cent. Further experiments are desirable to determine precisely the form of curve giving least loss of head, (*c*) The loss of head in a pipe of square section is greater—at the least 20 per cent, greater—than in a circular diverging pipe of the same length and same initial and final area, while the minimum loss is obtained when the angle between opposite facas of the pipe is approximately 4°. (*d*) A change in the shape, as opposed to the area, of the cross-section of a pipe leads to considerable loss of head. Thus, by changing the section of a pipe from that of a square, of 2.66 inches side to a rectangle 1.33 inches by 5.32 inches in a length of 9.94 inches, a loss of head equal to 0.484 *v*^{2}/2*g* was experienced. (*e*) Where a rectangular pipe has one pair of sides parallel and the second pair uniformly diverging, the loss of head is much greater than in a circular pipe having the same length and the same initial and final areas. The minimum loss is obtained with *θ* about 11°. (*f*) The critical velocity of flow in a circular pipe with uniformly converging boundaries is much greater than in a parallel pipe of the same mean diameter. The critical velocity increases rapidly with the angle of convergence, its lower value, at 57.5° F. in the experimental pipes (from 3 inches to 1.5 inches diameter), being as follows at the point where the diameter is 21/4 inches:—

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*Societies and Academies*
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*Nature* **82, **475–480 (1910). https://doi.org/10.1038/082475a0

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