Abstract
LONDON. Royal Society, February 9.—Sir Charles Sherrington, president, in the chair.—Sir J. Alfred Ewing: The atomic process in ferromagnetic induction. In the old model representing the process of ferromagnetic induction, the Weber elements or ultimate magnetic particles were represented by pivoted magnets the alignment of which, in the absence of an impressed field, was determined by the forces which they exerted on one another. The model is unsatisfactory; when the range of stable deflection is sufficiently narrow the stability becomes too great. In the new model the idea of magnetic control is retained, with a Weber element in each atom, but the controlling force is supposed to be exerted between the electrons of the atom itself, namely, between the shell, which is held more or less fixed by its relation to neighbouring atoms, and an inner electron system which constitutes the Weber magnet. The control depends on the difference between two nearly equal opposing forces; this characteristic permits the model to combine a sufficiently weak control with a narrow range of stable deflection. In one model considered the structure is based on the grouping of electrons suggested by Hull in connection with his X-ray analysis of iron crystals; in another the electron orbits are assumed to have the nucleus of the atom at their common focus.—J. W. Nicholson: Problems relating to a thin plane annulus. Only first approximations of solutions of problems relating to a thin plane annulus appear to have been used hitherto. Higher approximations have now been obtained, and the actual difference of radii of the circles bounding the annulus is of comparatively small significance in such magnitudes as the electrical capacity of the annulus. The whole investigation is carried to the second order of significance by treating the annulus as a special case of the elliptic anchor ring, but it can be extended. The convergence of such approximate solutions appears to be analogous to the degree of convergence found by Lord Rayleigh in certain solutions of problems of vibration of discs in which eccentricity is taken into account.—T. H. Havelock: The effect of shallow water on wave resistance. An analysis of the wave resistance of a surface pressure symmetrical round a point and moving over the surface of deep water is extended so as to include the effect of finite depth of water. The wave resistance is given By a definite integral which is evaluated by numerical and graphical methods. The cases intermediate between deep water and shallow water show the effect of limited depth in lowering the principal wave-making velocity and in increasing the effects near the velocity of the wave of translation.—R. H. Fowler and C. N. H. Lock: The aerodynamics of a spinning shell. Pt. 2. Of the shells fired from two guns giving different degrees of axial spin, those fired from the gun giving the more rapid spin were all stable, most of the others being unstable, as shown by the larger yaw developed. For yaws up to 35° a solution of the equations of motion can still be obtained in elliptic functions which proves adequately general.—F. B. Pidduck: The kinetic theory of a special type of rigid molecule. The methods of Chapman and Enskog in the kinetic theory of gases are applied, with modifications, to a type of rigid molecule to discover how viscosity is affected by energy of rotation, and the relative transport of translational and rotational energy in thermal conduction. The molecule model is considered as a sphere which grips at each collision and rebounds without dissipation of energy. The results support Eucken's views on Chapman's conslant f for polyatomic gases.—J. E. Jones: The velocity distribution function and the stresses in a non-uniform rarefied monatomic gas. From Boltzmann's equation a symbolic solution of the velocity distribution-function is obtained; from the new equation, by an analogous treatment, the exact nature of the function is deduced. The rate of change of molecular properties by collision follows more directly from this equation than from that used by Maxwell. To illustrate the present method, the results obtained by Chapman and Enskog for a normal gas are calculated anew. The treatment is extended to a rarefied gas and expressions are obtained for stresses due to non-uniformity of temperature. The special Maxwellian model is considered and Maxwell's result confirmed. The molecular model of a gas consisting of rigid elastic spheres is then considered in detail. The numerical coefficient in this case differs by about 20 per cent, from that of the Maxwellian gas.—H. Bateman: The numerical solution of integral equations. An approximate solution of an integral equation of Fredholm's type is obtained by using an approximate representation of the kernel by means of a double series of known functions. One such series is written down immediately in the form of a determinant, and the solution of the integral equation with the approximate kernel is also written in the form of a determinant. The kernel of the integral equation can also be represented approximately by a polynomial.—W. B. Hardy and Ida Doubleday: Boundary lubrication: The paraffin series. The lubricating properties of normal paraffins and their related acids and alcohols have been studied under the conditions of boundary friction. Amonton's law, that friction varies as the loads and is independent of the areas, is rigorously true for the sarne bearing surfaces and lubricants. The friction is independent of the quantity of lubricant present. It is a linear function of molecular weight, so that μ = friction ÷ load = α-bM, where M is molecular weight and b a pure function of chemical constitution; the slope of the curve is greatest for acids, and sensibly the same for paraffins and alcohols. Changing from one acid to another shifts the curves parallel to themselves, so for the same chemical series a is a pure function of the nature of the solid faces. Each solid face contributes one-half of a, and each molecule of lubricant furnishes a constant quantity to the total effect independently of the total number of molecules present.
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Societies and Academies. Nature 109, 224–226 (1922). https://doi.org/10.1038/109224a0
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DOI: https://doi.org/10.1038/109224a0