Table of contents

Many problems in probability connected with n events occurring randomly in space can be substantially simplified by dealing first with an indefinite number of events distributed in a Poisson series. A combinatorial problem arising in cosmic-ray counting discussed recently by Schrödinger provides a good example, and several properties of the corresponding distribution are derived. A generalization of this problem is considered, and the method is also applied to the random division of a line.

A set of nuclear parameters (ranges and depths of potential wells) yielding the established values of the binding energy, quadrupole moment and magnetic moment of the deuteron, and consistent with the other experimental data relevant to the ground state of the neutron-proton system has been found.

An expression is given for the potential differences set up in colloidal suspensions of solid particles by the passage of sound waves which is correct to the first power of the zeta potential of the particles. The question was examined in detail by Enderby in 1951. For a certain range of values of relevant parameters it was found necessary to introduce the simplification that the mobilities of the various ionic species in the electrolyte surrounding the colloidal particles were identical. In the present paper it is shown how the potential may be calculated quite generally without this restriction by the use of vector methods

It is demonstrated that magnetic discontinuities accompany changes of temperature at constant field. The effect is investigated for hard-drawn iron and nickel and is accounted for in terms of two mechanisms, one associated with the decrease of coercivity with rise of temperature and the other associated with the disperse field due to the thermal oscillations of the carriers of magnetic moment

The first set-up of a very simple high resolution β-spectrograph is described. The instrument employs the focusing action of a magnetic prism with circular plane poles of 20 cm diameter. For this area of pole surface the dispersion is large, giving advantage to the width of source that may be used, and the instrument can focus electrons with energies up to 4 MeV It has been used with resolving powers Hρ/Δ(Hρ) up to 1 300 as measured from microphotometer traces on the plates. It appears to be the only instrument that has been operated at these resolutions as a spectrograph

As a β-spectrometer, the resolving power should be 15% higher, but this has not yet been tested. As far as can be seen it has a luminosity roughly comparable with that of the ketron, but unlike that instrument it has considerable flexibility of experimental arrangement promising improved performance.

It has been used to look for the fine structure of the K-conversion line corresponding to the 1414 keV γ-transition in the disintegration RaC.C' reported by Latyshev and others. In agreement with the work of Bashilov and others who employed the ketron, and of Serebriskaya, Shpinel and Forafontov who used a spectrometer of completely novel design, this line was found to be highly monokinetic

The β-ray spectrum of thorium (B+C) has been re-investigated using the β-ray spectrograph described by Siday and Silverston. The range 200 keV-300 keV was studied in detail using photographic recording and a previously unobserved γ-ray of energy 294.6 keV has been attributed to the transition thorium C.C". The conversion lines of the γF ray of thorium B C in the L_I, L_II electronic shells have been resolved and their relative intensities have been found using a Geiger counter The conversion of the same γ-ray in the M_I, M_II electron shells has been measured and the lines have been partially resolved. The M photoelectron line associated with the transition thorium C".D has been examined, and its suspected doublet structure confirmed.

The connection between the elastic behaviour of an aggregate and a single crystal is considered, with special reference to the theories of Voigt, Reuss, and Huber and Schmid. The elastic limit under various stress systems is also considered, in particular, it is shown that the tensile elastic limit of a face-centred aggregate cannot exceed two-thirds of the stress at which pronounced plastic distortion occurs.

The eigenvalues and wave functions for the conduction electrons in metallic sodium are calculated for various points of high symmetry in the Brillouin zone. The method adopted is an extension of that used by von der Lage and Bethe in which boundary conditions are applied at a large number of points on the surface of the atomic polyhedron. Eigenvalues are obtained for states whose wave vectors lie at the ends of the 2-fold, 3-fold and 4-fold axes. The energy gap at the centre of a face of the zone is found to be 0.65 eV. A method of testing the results, of a more general nature than the empty lattice test of Shockley, is outlined and applied to certain cases.