Abstract
CAMBRIDGE. Philosophical Society, July 26.—P. A. M. Dirac: On quantum algebra. In this algebra the commutative law of multiplication no longer holds, but the other axioms of ordinary algebra are still valid. A general definition of a function is proposed, and the differential coefficient is defined without introducing the idea of a limit.—Miss B. Swirles: The polarisabilities of atomic cores. The polarisabilities of the cores of several atoms are calculated from the terms of their spectra by means of a formula due to Born and Heisenberg. The values so obtained agree with those given by a modification of the dispersion formula of Kramers and Heisenberg.—J. R. Oppenheimer: On the quantum theory of the problem of the two bodies. (Preliminary communication.) In addition to the Balmer terms derived by Pauli, Schrodinger and Dirac, the line intensities are computed; for example, the first Balmer emission line is 12.2 times as intense as the second Lyman line, and the first Balmer absorption line is 5.37 times as intense as the second. The probabilities of transition and capture are derived, and a method of obtaining the deflexion spectrum is sketched. The argument is based throughout on Schrodinger's theory.—G. P. Thomson: An optical illusion due to contrast. A blackened strip on a photographic negative sometimes has the appearance of being blacker at the edges than the centre, though the reverse is found to be the case when measurements are made by a photometer. The edges are narrower and clearer the more rapid the transition from light to darkness, but become too narrow to be seen when the transition is made as abrupt as possible. The eye appears to see rapid change of blackness as enhanced blackness. A converse effect appears for a light strip on a blackened ground.—M. H. A. Newman: Integral invariants of the affine field.—A. Young and H. W. Turnbull: The linear invariants of ten quaternary quadrics.—G. S. Mahajani: A contribution to the theory of ferromagnetism.-E. B. Moullin: On some resistance properties of a certain net-work containing inductances and capacities, and their analogies in a mechanical system. If the net work is in acceptor resonance at a certain frequency when excited from a particular member, then it will also be in resonance when excited from any other member, but then the resonance may be either acceptor or rejector.—J. C. Burkill: On Mellin's inversion formula.—Major P. A. MacMahon: The elliptic products of Jacobi and the theory of linear congruences.—R. Hargreaves: Geodetic and dyn amical principles, a comparison and connexion.—J. R. Oppenheimer: On the quantum theory of vibration-rotation bands. The dynamical problem of the diatomic molecule is solved on the new mechanics. The quantum numbers, chosen to give a normal state, are n = ½, 3/2 … ; m = – 3/2, – 5/2 …, ½ 3/2 5/2 …, r = –m + ½, … + m –½. The frequencies differ from the classical frequencies for half integral vibrational and rotational quantum numbers in having m2 – ¼ for m2 in the coupling term. The weights of the m states are 2m. The intensity of the central line of the band vanishes. The intensities of the lines are worked out to the second order in vrot./vlb..—P. A. Taylor: An approxi mation to the motion of two rotating electrical doublets in a plane.—D. R. Hartree: Some relations between the optical spectra of different atoms of the same electronic structure, (ii.) Aluminium-like and copper-like atoms. For penetrating orbits of the series electron, the quantum defect can be expressed as the sum of contributions from the groups of core orbits of different principal quantum number. Based on this, relations are obtained between the values of the quantum defect for corresponding terms of the spectra of an atom of a given element in different states of ionisation, and of different atoms in such states of ionisation that they have the same electronic structure.—J. P. Gabbatt: Note on the extension to higher space of a theorem of Wallace.—J. B. S. Haldane: A mathematical theory of natural and artificial selection (Pt. iii.).
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Societies and Academies. Nature 118, 323–324 (1926). https://doi.org/10.1038/118323a0
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DOI: https://doi.org/10.1038/118323a0