The paper deals with new solutions of the differential equations of the two-centre problem which are expressed in terms of the confluent hypergeometric function. By means of this function a solution of the λ-equation (1) is obtained which enables the separation constant A to be found for small values of the parameter p in a rapidly convergent series, which for the special case of m = 0 is still more rapidly convergent. The solution for the μ-equation (2) in the general case is of the same character as regards rapidity of convergence as solutions previously obtained, but when m = 0 it again possesses a higher rate of convergence as compared with solutions given by other investigators.

A general discussion is given of the momentum wave functions of simple molecules in which only single bonds occur; the momentum functions are obtained by transformation of the space wave functions, for which two distinct approximations are possible. In each case it appears that the presence of the bond decreases the mean component of the velocity in the direction of the bond, increases the mean component of velocity perpendicular to the bond, and increases the mean momentum averaged over all directions. The analysis is illustrated by consideration and H2; in the latter case the strong dependence upon the mutual orientation of the two electronic momenta is emphasized.

It has been shown by M. Born (1) that the equation of state and other thermo-dynamical properties of crystals, for example the melting temperature and its dependence on pressure, can be derived by a logical development of the lattice theory of crystals. I was able to show in a recent paper (6) that the results of a very large number of experiments of various kinds on the mechanical and thermal behaviour of solids are in satisfactory agreement with this theory. In the present paper I wish to show that new experiments of Bridgman (7) on the compression of solids under very high pressure can also be used for a comparison with the same theory, and that the results of this investigation are in favour of the theory. Some considerations on the range of stability of a lattice under a high uniform negative pressure are added, which support the idea that there is a close relation between the theory of stability of crystal lattices and the theory of melting.

It is assumed that the viscosity of a liquid is due to the transfer of momentum by the irregular movement of the holes (see part I of this paper). A formula for the absolute value of the viscosity and its dependence on the temperature can be derived by the theory and is in agreement with its experiments.

The momentum distribution for the electron in the hydrogen molecular ion has been calculated for various wave functions, including the one used by James with which he obtained such a good value for the binding energy. The method adopted for this particular wave function is outlined and the results show appreciable change with improvement in the wave function. In conclusion there are discussed the implications of the present calculations on similar work on the H2 molecule.

1. In the classical theory there is no difficulty in treating the effect of radiation damping on the scattering of light by a free electron in so far as it is a result of the conservation of energy. In the non-relativistic approximation the equation of motion of a free electron under the influence of a light wave is

with the periodic solution

The total energy radiated per second is then

and the total cross-section(1) is

Formula (1) differs from the Thomson formula by the factor 1/(1 +κ2). This factor becomes appreciable for energies ħν ≥ 137mc2.

The momentum distribution has been calculated for an electron in one of the hybridized orbitals of a carbon atom, and is shown as a function of the degree of hybridization. The mean momentum shows a steady increase from pure s to pure p binding. Similar calculations have been made for the momentum distribution in the C—H bond, and it is shown that this also depends upon the degree of s-p mixing. The mean momentum for the bond is less than for an isolated hybridized carbon orbital, but behaves similarly to such an orbital when the degree of hybridization is varied. The differences are about within the limit of experimental determination.

The paper describes the results obtained from a study of the bombardment of gold with deuterons of energy up to 9·1 M.e.V. The reactions found to take place in gold are the formation of 2·7 day Au198 by a (d-p) process and of 32 hr. Hg198* in a metastable state by a (d-n) process. The β-ray and γ-ray energies associated with each radioactivity have been measured by absorption methods. Excitation functions for the two reactions have been determined and the results have been compared with those to be expected on theoretical grounds.

The author takes this opportunity of expressing his gratitude to the past and present members of the Cavendish Cyclotron Laboratory for assistance in running the cyclotron. He wishes to thank the Royal Commission for the Exhibition of 1851 for the award of a Science Scholarship.

The discussion of momentum distribution is extended to cover electrons in double bonds and conjugated bonds of fractional order. The mean radial distribution function is obtained, and it shows that the mean momentum of the electrons is less than if they were rigidly attached to their own particular nuclei. Polar diagrams show that, if electronic mobility is high in any direction in a molecule, the momentum is generally small in that direction.

A general method is given of calculating the effect of damping on the collision cross-sections for problems involving free electrons and mesons. The result is expressed in the form of an integral equation which can only be solved if certain simplifying assumptions are made. It is shown that radiation damping has a negligible effect on the scattering of light by free electrons, so that the Klein-Nishina formula is unchanged by the inclusion of damping effects. The effect of damping for mesons, on the other hand, is extremely large and reduces the cross-sections considerably. The main problems considered are the nuclear scattering of mesons and the energy radiated by mesons during collisions. The revised cross-sections are much more reasonable than those calculated previously, but on account of the inadequacy of the data no detailed comparison with the experimental results is possible.

Theoretical calculations on the mean radial momentum distribution of the electrons are made for the molecules CH4, C2H6, C2H4 and C2H2; from these distributions the profiles of the Compton line are deduced. It is assumed that each electron acts as a single scattering centre so that the mean radial distribution for the molecule is just the sum of the various “partial distributions” for each electron separately. The electrons are supposed to be paired together in the formation of localized bonds, and the contributions from each type of bond have to be separately determined. When superposed, these give the momentum distribution for the whole molecule. Such distributions are similar in shape, but the peak value of the momentum curves moves to higher values of p as the C—C bond becomes more saturated.

A comparison of the various partial distributions for C2H4 shows that the C—H bond is an important factor in the momentum distribution of such molecules. In other hydrocarbon molecules, we may presume that the proportion of C—H bonds will be very significant in determining the breadth of the momentum distribution curve, and hence of the width of the Compton line; in fact the half-width of the Compton line decreases both with an increase in the number of the C—H bonds, and with increased saturation of the C—C bonds.

In the only case where experimental results are available, CH4, the discrepancy between theory and experiment amounts to about 30%. Reasons for this discrepancy are discussed; in part the discrepancy may be attributed to the approximations used in the wave functions; but reasons are given for supposing that in part also it arises from an incorrect interpretation of the experimental results.

The formation of 62Cu, 106Ag and 120Sb by deuteron bombardment of copper, silver and antimony respectively is reported. The energy-yield curves for these reactions were determined and it is concluded that in each case the process involved is taking place, in all probability, through the formation of a ‘compound nucleus’ of the Bohr type.

Experiments on the bombardment of platinum with 9 M.e.V. deuterons are reported. Radioactive isotopes of platinum of periods 32 min., 18 hr. and 2·8 days, and isotopes of gold of periods 2·6 and 5·6 days are reported. The 2·6 day gold isotope is formed directly by deuteron bombardment as well as by decay of the 32 min. platinum isotope. The absorption of the β-rays in aluminium and of the γ-rays in lead has been measured, and assignments have been made for most of the isotopes reported. Excitation function measurements have been made for the 32 min. and 18 hr. platinum isotopes, and the form of the energy-yield curve is the same for both these elements. The form of the curve seems to favour the Oppenheimer-Phillips process for the formation of these radioelements by the reaction.

In developing the theory of adsorption taking into account the interaction between adsorbed particles it has been usual to use a physical model in which it is assumed that there is a fixed interaction energy between particles adsorbed on neighbouring sites on the surface. In this paper the differences between the behaviour of this model and that of actual surfaces are discussed by considering a one-dimensional film in which the potential energy of a single adsorbed particle varies continuously and periodically with its position on the surface and in which there is a repulsive force between adsorbed particles which varies with the distance between them according to an inverse power law. For such a physical model the variation of the heat of adsorption with the fraction of the sites occupied is considered in detail and it is shown in particular that there is much less difference between the behaviour of mobile and immobile films than is indicated by the earlier model in which a fixed interaction energy is assumed. These results are considered in connexion with the interpretation of experiments on the adsorption of hydrogen on tungsten.

The geometrical constraints on the forms of quaternary alloy equilibrium diagrams have been derived.