Table of contents

It is shown that if the geodesic ray congruence associated with an empty space-time of type N is not hypersurface orthogonal (that is the geodesic rays are twisting) then the space-time has at most one symmetry.

The Yang-Mills gauge theory is applied to the space-time invariance groups responsible for the conservation of Zilch, with the result that non-local interactions are forced upon the authors. In this case, if there is also an internal symmetry group present, the Yang-Mills trick yields gauge fields which transform according to not only the regular representation of the group, but also all the representations whose coupling to the original fields is allowed by non-zero Clebsch-Gordon coefficients.

Random chains on three lattices (i) plane square, (ii) plane triangular and (iii) simple cubic are considered. The mean square end-to-end distance is calculated for those chains all of whose sub-chains of order p are non-selfintersecting, and for small values of p.

The angular distribution and vertical intensity of cosmic-ray muons have been measured at depths of 71.6, 734, 1068 and 2235 hg cm^-2 of standard rock. The angular distribution was fitted by a law of the form I_theta =I_v cosⁿ theta and values of the exponent n were found to be 1.8+or-0.1, 2.1+or-0.1. 2.3+or-0.1 and 3.6+or-0.2 respectively. The corresponding vertical intensities were found to be (5.00+or-0.17)*10^-4, (3.12+or-0.15)*10^-6, (1.03+or-0.04)*10^-6 and (9.7+or-0.5)*10^-8 cm^-2 s^-1 sr^-1 respectively. From a survey of all previous measurements best estimates of the n-depth and intensity-depth curves are derived. The results are explicable entirely in terms of pion and kaon decay for the origin of the muons and do not agree with the direct muon production hypothesis advanced by Bergeson et al. (abstr. A15886 of 1968).

The usual method of determining the rate of energy loss of muons by comparison of the sea-level spectrum with the intensity underground is shown to be inadequate to determine the energy-dependent term because of the impression of the spectrograph results. An alternative method has now been developed in which the rate of energy loss is deduced from the observed mean pulse height of a scintillation counter operated underground. This method requires a knowledge of the intensity depth curve but not of the muon momentum spectrum. The various corrections necessary to apply the method to the results of the Tilmanstone Colliery experiment, described in the preceding paper are considered and shown to be small. The energy loss by direct pair production is found to be 1.05+or-0.20 times the value predicted by Kobayakawa (abstr. A19217 of 1967).

By using atomic beam magnetic resonance techniques it has been shown that the nuclear spin of ²⁰⁶Tl (half-life 4.2 min) is either zero, or else the nuclear magnetic moment mu _I<10^-5 nuclear magnetons. Measurements on isotopes of copper and silver have yielded the values for their nuclear spins I and hyperfine interaction constants A, from which their nuclear magnetic moments have been deduced using the Fermi-Segre relation. No diamagnetic correction has been applied.

Two methods of deriving the integro-differential equations for light nuclei are given. The resonating-group method of J.A. Wheeler (abstr. A392 of 1938), is employed to construct the wave function and from the Schrodinger equation a set of simultaneous integro-differential equations is derived.

The masses within an isobaric multiplet are related by the general model-independent mass formula M(A,T,T_z)=a(A,T)+b(A,T)T_z+c(A,T)T_z². The values of the coefficients b(A,T) and c(A,T) are extracted from experimental data function of mass number for several triplets ranging from A=6 to A=32. Theoretical calculations are made for these coefficients on the basis of Coulomb interaction alone after accounting for the neutron-proton mass difference, and the residual shifts are attributed to charge dependent effects in the nuclear forces. A phenomenological effective charge-dependent potential is introduced and its parameters are determined by a least-square analysis.

The intensity and degree of coherence in a field due to a slit illuminated by a line source are studied. The propagation of the mutual coherence of a polychromatic light beam is used to obtain the intensity and the degree of coherence due to the slit at points distant from those at the slit. The variations of the intensity and of the degree of coherence with different variables are studied.

The flow rates of hydrogen, helium, air, carbon dioxide and water vapour between two parallel optically flat glass surfaces have been measured. The distance between the two surfaces was of the order of 10 mu m and the flow experiments were carried out with pressures in front of and behind the channels of the order of 10 torr and 0.1 torr respectively. A flow equation is presented which describes the flow of the gases and the vapour through the channels.

The thermal conductivity of binary polar gas mixtures CH₃Cl-H₂S has been measured over the temperature range 0-200 degrees C for various compositions by applying the thick-wire variant of the hot-wire method. From the analysis of the data it is concluded that the Hirschfelder-Eucken expression for the thermal conductivity of the mixture is in fair agreement with the experimental data, provided the pure-component thermal conductivities are replaced by their corresponding experimental values. The effect of inelastic collision and resonant exchange of energy is investigated in detail and found to be not negligible.

The generating function, the corresponding integrated intensity distribution, and the photon-counting distribution and its fractional moments are derived for the superposition of coherent and chaotic M-mode fields on the basis of a formalism of arbitrary ordering of field operators in quantum optics. An alternative description is also given based on a recent analysis of the superposition of coherent and chaotic fields in terms of the correlation functions which makes it possible to derive a number of results valid for arbitrary mean occupation numbers per mode from which the model considered follows as a special case. Many earlier results obtained for coherent and chaotic fields and their superposition are included as special cases. The present results generally describe a superposition experiment for an N-mode coherent field (e.g. generated by an N-mode laser operating far above threshold) and an M-mode chaotic field (M>or=N) as well as a field generated by an M-mode laser operating above threshold.

The author considers helicon propagation in a cylindrical resistive plasma with vacuum boundary conditions. The author shows that the wave fields (which he assumes to be continuous at the boundary) develop rapid variations as eta to 0, which can be represented physically by surface currents and a surface dipole layer. The contribution of the dipole layer to N (E) clears up a difficulty in a recent paper by Francey and Gates (abstr. A9907 of 1969).

An example of accidental degeneracy in quantum mechanics arising from virtual symmetry is exhibited and discussed.