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A formula is found for the axial sound-pressure due to a disc having a nodal circle and vibrating in an infinite rigid plane. Beyond a certain axial distance, when the nodal circle occurs at r = a/radical2, the pressure vanishes owing to interference caused by the inner and outer portions of the disc vibrating in opposite phase. The case of n nodal circles of arbitrary radii is treated by an approximate method. A rigid disc is imagined to be severed around each nodal circle, whilst contiguous annuli vibrate with equal amplitudes in opposite phases. Finally, the pressure on the axis of a conical shell having nodal circles is treated as in the previous case. When the semi-apical angle of the cone is ½π and there are no nodal circles, the formula reduces to that for a rigid disc.

In this paper formulae are obtained for the velocity-potential at the surface of a free-edge disc vibrating with nodal lines in a fluid. These formulae are used to ascertain the accession to inertia due to the fluid when the disc is set in an infinite rigid plane. The equivalent mass and the mass coefficient of the disc vibrating in vacuo are found also. By means of these results, the influence of the fluid on the frequency of vibration with (a) one nodal circle, (b) one nodal diameter, (c) stationary centre, is evaluated. In air the alteration in frequency is almost negligible, whereas in water the frequency is reduced to a small fraction of its value in vacuo.

In this paper attention is directed chiefly to the problem of measuring with precision the changes in the refractivity of a liquid for small alterations in temperature. An elaborated Jamin interferometer is described, as are also the several pieces of auxiliary apparatus necessary for setting up and maintaining differences in the temperature of the two interferometer tubes. Further, there is given a plan for measuring, by means of platinum resistance thermometers, differences in the temperature of the two tubes.

A method has been tried for obtaining accurate values of lattice spacings from X-ray powder photographs taken in the usual circular type of camera. There are two essential features of the method, (a) the calibration process, (b) the extrapolation process.

The calibration process: The exposed portion of the film is limited by sharp knife edges, and the length S_k is measured for each film at the same time as the distance S between corresponding pairs of lines. S_k corresponds to an angle θ_k in the same way that S corresponds to a glancing angle θ, so that θ_k = S_k / 4R, where R is the radius of curvature of the film. R is an uncertain quantity depending on the amount of film-shrinkage, and so in calculating θ from S we replace R by θ_k, which is a constant for a particular camera. θ_k having been determined in a preliminary experiment, it is possible to calculate θ for a given reflection, from the formula

θ = (S/S_k) θ_k

Errors due to film-shrinkage are hereby eliminated.

The extrapolation process: Other errors due to absorption by the specimen and eccentricity of the specimen may be eliminated by plotting the values of the lattice spacing calculated from a given pair of lines, against the corresponding values of cos² θ. For small values of cos² θ, the curve is almost linear, and is easily extrapolated to cos² θ = 0, where the correct value of the lattice spacing is to be found. Only a few accurate measurements at angles where cos² θ is small are necessary in order to carry out this process.

As examples of the method, results are given for the lattice spacing of iron taken in different cameras with specimens of different diameters. They are consistent to 1 part in 15,000, the mean value being 2.8605. A specimen of electrolytic nickel (3.5162 Å.) was found to give a different value from a specimen of Mond nickel which had been degassed (3.5170 Å.).

In this paper Prof. Chapman's theory of the ionization of the upper atmosphere by solar radiation has been applied to construct a set of charts giving contour lines of equal ionic density over the surface of the earth. A simple approximate method of solving the fundamental differential equation of the theory by a rapid arithmetical process is described. Charts are drawn for winter, equinox and summer conditions for the values 0.5 and 1 of the parameter σ₀ and the value 150 of the parameter R. A brief comparison of these charts with existing empirical charts is given with a short discussion of its practical and theoretical significance.

By photographing the spectrum of arsenic by the method of the hollowcathode discharge in helium and in neon about 100 new lines have been recorded. In the light of the experimental data, the analysis of As I published by previous investigators has been considerably altered and extended. Several new levels have been added and the higher members of the chief groups of the ms series of terms have been identified. A mean value of 85,000 cm.^-1 has been suggested for the deepest term 4p⁴S₂ which leads to a first ionization potential of approximately 10.5 V. for arsenic.