Table of contents

The transverse 'Fresnel ether drag' experienced when light passes through a refracting medium moving at right angles to the original direction of the light, and confirmed indirectly by Airy's water- filled telescope experiment, has been observed directly. A change in rotation speed from 600 to 1800 rpm of a glass disc, of 19.1 mm thickness and refractive index 1.51, produced a transverse displacement of about 1.5*10^-6 mm in a light beam passing twice through the disc at a radius of 110 mm from the axis of rotation. This agrees with the Fresnel formula to within the 10% accuracy of the experiment.

A numerical method for calculating the S-state energy eigenvalues for a local potential is given. The method makes use of a first-order differential equation which is easily derived from the Schrodinger equation.

A recent statement of L.M. Stephenson (ibid., vol. 3, 368, 1970) in connection with complete clocks is disputed and the traditional time dilatation of the special theory of relativity is upheld.

A recent paper on time measurement by L. M. Stephenson (ibid., vol. 3, 368, 1970) is examined in detail. It is argued that the paper sheds no new light on the subject and that it is altogether misleading. In particular, while the notion of a primary time scale in special relativity bears some relation to certain elements that are familiar and valid. Stephenson's own treatment of the notion appears to be wholly erroneous.

Impact ionization of micrometer-size particles has been observed at velocities down to 60 m s^-1, where the empirical law q varies as m^alpha v^beta is shown to remain valid, the indices having the values alpha =1 and beta =3.4.

The difference between the aperture of a counter telescope for single particles and for pairs is explained. Expressions are given for both apertures and the significance of the difference for the interpretation of underground data is indicated.

A flexible cylinder in a viscous fluid is used to model a dilute polymer solution, with a non-slip boundary condition between the polymer chain surface and fluid. The problem is solved using Green functions and a perturbation expansion. The model generalizes that of Kirkwood and Riseman (1948) by having thickness, and avoids the friction coefficient they use.

An extension is developed for an inhomogeneous system of a result originally derived for a homogeneous system concerning the sign of successive time derivatives of the entropy in the passage to equilibrium. A new microscopic derivation is given of two macroscopic thermodynamic equations used in the treatment.

A generalization of Levi-Civita's static solution for the exterior gravitational field of a cylinder of infinite length and finite cross section, corresponding to the field equations T_ab=qk_ak_b, k_ak^a=0, is discussed. The expression for q is of the form f'(u)/ rho , which shows the typical cylindrical fall-off over the null hypersurface u=constant. It is pointed out that the passage of an outgoing wave affects permanently the static Levi-Civita space-time and the energy for this class of solutions is a particular case of the C-energy defined by Thorne. The geodesic equations for a test particle moving in the radial direction display a gravitational 'induction field' which is associated with a changing mass in the Newtonian field and is directed towards the axis of the cylinder. In contrast with the spherically symmetric case the induction field always acts to decrease the energy of a test particle on which it acts. It is shown that the mass per unit length of the static cylinder strongly affects the shear and divergence of the null congruence. The asymptotic behaviour of the Weyl tensor is analysed and a peeling theorem proved for this case.

Exact relativistic differential cross sections for the incoherent scattering of gamma rays by the inner shell electrons of heavy atoms are developed from the second order S matrix element for the electron-photon interaction in the Furry (1951) picture. Electron binding is accounted for completely by using the bound electron propagator and Dirac eigenfunctions for the initial and final electron states. A pure Coulomb potential is used to calculate the energy spectrum and the differential cross section for 662 keV gamma rays scattered by the K electrons of lead. In contrast with the results of Di Lazzaro and Missoni (1966) the energy spectrum maximum is displaced by 10% from the Compton energy towards higher photon energies, and there is no increase in the spectrum at the low-energy end. The relativistic results for the ratio of the bound electron to feed electron cross sections are larger than the incoherent scattering function calculations and exceed unity for scattering angles above 52 degrees .

Using covariant Regge couplings and invariant amplitudes for the process gamma N to O^-N the author examines the constraints imposed upon the t-channel helicity amplitudes by the hypothesis of s-channel helicity conservation. Class III pion conspiracy is consistent with the hypothesis as are contributions from conspiring pi , B and rho , A₂ Pomeron cuts. Regge cut contributions arising from omega Pomeron exchange are forbidden to conspire.

The authors make a variational calculation of the binding energy of the alpha particle with the velocity-dependent potential of Nestor et al (abstr. A33865 of 1968) which contains a tensor component. The trial wave function used is a mixture of the ¹S₀ and the principle ⁵D₀ states, the radial dependence of both these states being Gaussian. The Coulomb energy of interaction is calculated by the usual perturbation method with the potential of Schneider and Thaler (abstr. A11023 of 1965) which takes into consideration the finite size of the nucleons. The calculation gives the values of the binding energy and the root-mean-square radius of the alpha particle in reasonably good agreement with experiments.

The authors calculate the integrated and the bremsstrahlung-weighted cross sections in the photodisintegration of ⁴He by applying the sum rules of Levinger and Bethe (1950) and using the velocity- dependent potential of Nestor et al (abstr. A33865 of 1968). The wave function used is a mixture of the ¹S₀ and the principal ⁵D₀ states, the radial dependence of both these states being Gaussian. They obtain the parameters of the wave function from a variational calculation of the binding energy. The results show good agreement with experiments and with similar calculations using hard-core potentials.

A procedure is given which in principle permits the exact evaluation of any term in the asymptotic expansion in a/c of the velocity U_o and energy E of a circular vortex line of radius c in a Bose condensate (where a is the healing length). The procedure is used to obtain the two leading terms (previously only inaccurately determined by a variational calculation), namely U₀= kappa /4 pi c(In(8c/a)-0.615); E=¹/₂ rho kappa ²c(1n(8c/a)-1.615); where kappa denotes the quantum of circulation, and rho denotes the fluid density at infinity.

It is pointed out that the perturbation expansion procedure about a certain flow state requires a priori knowledge of the statistical distribution of the flow field. In Wyld's laminar perturbation procedure it was indeed natural by invoking Kraichnan's maximal randomness principle to assume the laminar flow to have a Gaussian distribution. On the other hand, one attempts to develop perturbation about a turbulent flow as in Phythian's procedure, the difficulty is that the distribution of the velocity field is just as unknown as the turbulence problem itself. It is shown that Phythian's assumption of Gaussian random force for the zeroth-order equation has the effect of deriving the direct- interaction equations under the quasi-normal hypothesis.

The two-particle distribution function for a system of liquid and vapour in equilibrium is approximated by the product n(z₁)n(z₂)g( mod r₂-r₁ mod ), where the radial distribution function g is taken to be that of the liquid. The Born-Green-Yvon equation for the density n(z) is solved, giving the form of the interface between liquid and vapour as well as a relation between their densities n_L and n_V. The relation between the densities is shown to be consistent with experimental results. Further, when this relation is combined with the demand that the pressures in the two phases be equal, it is shown that the empirical scaling law n_L-n_V varies as (T_c-T)^1/3 is a consequence of a simple assumption about the approach of the liquid and vapour correlation functions towards equality near the critical temperature.

The authors consider the behaviour of elastico-viscous liquids as they deform under the action of an unsteady shear field consisting of a small-amplitude oscillatory shear superimposed on a steady simple shear. The theory for such a situation is developed in detail and certain predictions, some quantitative, and some qualitative, are made. These predictions are shown to be in good agreement with experimental results obtained from a Weissenberg rheogoniometer for certain aqueous polymer solutions.

It is shown that by proper choice of a reference temperature in the theoretical expression for the separation factor for a thermal diffusion column, the separation factor may be made to depend on the potential model and the interaction parameters solely through the thermal diffusion factor, the other terms in the expression becoming independent of the model and parameters.

An investigation of the temperature variation of the work function of an electron gas is made by collective electron theory methods.

A theoretical description of the current limit phenomenon based on the limited ionizing ability of the electrons has been obtained. The current limit is found to be a double-valued function of pressure. This limited ionizing ability implies that positive column existence is only possible when the product of the gas density and column radius is greater than a critical value. High currents reduce the gas density to the critical value causing current limitation. Assumptions of the form of the electron velocity distribution at current limit are avoided by working with the mean free path of the neutral for ionization, lambda , as a parameter. Both the ion wall current and the neutral depletion are calculated in terms of lambda and, by relating ion wall current and arc current, gas density is related to arc current. Low currents reduce the plasma radius until the critical value is reached causing current limitation.

This paper presents the experimental details and the results obtained when a feedback system is used to suppress or enhance drift instabilities present in a magnetoplasma. A nonlinear phenomenological theory is developed which predicts how the amplitude and frequency of the instability should change as a function of gain and phase shift in the feedback loop. Comparison of the results with this theory show good agreement. Further, the effect on the density and temperature profiles when the instability is suppressed has been investigated, and from these results a quantitative change in the cross-field diffusion constant has been inferred. Also, experiments are reported which show the effects of feeding back distinct azimuthal mode numbers m=0, +or-1, and +or-2, as well as the results obtained using more than one separate system.

Ion flow is important in many laboratory discharges, vacuum switches, gas-filled valves, thyratrons and space satellites. A model is presented for subsonic ion flow past a negative spherical probe immersed in a collisionless ionization-free plasma; a stagnation point develops downstream. Although the floating potential given by previous analyses (which all assume spherical symmetry) is substantially correct, there is some dependence on the ion flow velocity (a few % at M=0.5). Thus the change in floating potential can be used to measure ion flow. In general, only slight modification needs to be made to low pressure probe theories in order to include flow effects.