Nunn May (1) has developed the theory of the mode of action of the Geiger-Müller counter in terms of the photoemission produced in the electron avalanches constituting the discharge of the tube. An avalanche of electrons in the counter produces excitation and ionization of atoms and molecules in the neighbourhood of the positive central wire: the photons liberated by these in their turn release from the walls of the counter the photoelectrons which initate the following avalanche. Direct experimental evidence that such a sequence of events may occur is to be found in the work of Greiner (2).

In consequence of the magnetic and exchange interactions between the ions of a paramagnetic salt, a new mechanism of interaction between ion and lattice is possible, involving the simultaneous transition of two or more ions with the emission or absorption of only one elastic quantum. This new mechanism seems to be capable of removing the discrepancy between theory and experiment for iron alum, and considerably reduces the discrepancy for caesium titanium alum.

It is shown in this paper and the preceding one that two separate forms of theory can be developed in which a “finite size” is attributed to a charged particle by means of its interaction with the radiation field. The region attributed in this way to the particle is four dimensional and is determined in such a manner that the usual difficulties with relativistic invariance do not arise.

The advantage of such a theory becomes clear when the theory is applied to those problems in which the usual calculations give infinite results. The problem of the method of successive approximations is considered and satisfactory results are obtained provided that the space dimensions of the finite region are of the order of the classical radius of the electron, when the electron is at rest.

It may be noted explicitly that the difficulty that has been associated with the emission of low energy quanta by “Bremsstrahlung” will not arise in the present formulation of the electromagnetic interaction between field and particles. This case is interesting since an infinity arises here which is not analogous to the self energy infinities, but occurs in the direct calculation of a physical process and not in a virtual transition.

The theory seems satisfactory so far as low energy processes (< 137 mc2) are concerned and the real test of its applicability may be expected to arise in discussing processes of high energy. It is hoped to treat these in a later paper.

The cross-sections for the elastic scattering of mesons by protons and electrons are calculated by analogy with Møller's theory of collisions between electrons, and the results are compared with those of Bhabha for the collisions with protons and electrons of Fermi-Dirac particles with the same mass as the meson. For collisions with electrons, the difference is inappreciable for energies of the meson less than 100 times its rest energy, but for collisions with protons the difference is important at much lower energies. The ratio of the corresponding cross-sections for scattering by a Coulomb field is found to tend to infinity as the square of the energy of the incident particle, giving a finite cross-section for the scattering of a meson of infinite energy by such a field. It is pointed out that, if an exact solution of this problem is possible for the meson case, the question of the validity of meson theory for high energies would be considerably clarified.

We consider an ideal problem of adsorption of single and double particles upon a solid surface which has its sites of accommodation regularly arranged, and by comparing the equilibrium properties obtained by Bethe's method with the ordinary statistical formulae, we obtain approximate expressions for:

(1) g(N, n, X), the number of ways of arranging n particles upon N sites of a lattice so that the number of neighbouring sites occupied by the particles is X.

(2) g2(N, n, X), the number of ways of arranging n double particles upon N sites so that each of the double particles takes up two adjacent sites and the number of neighbouring sites occupied by two different particles is X.

Both these expressions are found to agree with the exact values when the N sites lie on a straight line. When we use the first expression to construct the configurational partition functions of certain physical assemblies and expand them in powers of 1/kT, they are found to agree with the corresponding rigorous expressions as far as (1/kT)3, which is the highest power which we can find rigorously at present. With the help of the first expression, formal equations for superlattice formation in an alloy with the composition 1: 1 and equations for the separation into phases of regular liquids are given. Lastly we show that atoms and molecules in a regular liquid may dissociate or recombine suddenly accompanied by a latent heat. This is a new cooperative phenomenon, which may bear some resemblance to the melting process between the solid and liquid states.

In the present paper application of the work of paper I is made to a specific problem, namely the excitation of an adsorbed atom by the surface electrons of the underlying metal. It is shown that the corresponding mean life-time in a typical excited level is 3·7 × 10−11 sec., which is comparable with the value 1·7 × 10−12 sec. for deactivation by the conduction electrons when the Brillouin zone is only partly filled. Thus, though this is an essentially surface phenomenon, the effect of the surface electrons is begligible. This suggests that their effect can, in general, only become appreciable in semi-conductors or insulators.

Bethe's method is applied to determine statistically the rate of condensation of diatomic molecules which are adsorbed with dissociation to form an immobile film, the two atoms of one adsorbed molecule occupying two neighbouring sites. A lower limit to the number of gaps, or isolated unoccupied sites, in the final film is also obtained. The results calculated statistically agree with those obtained earlier by using models.

Many problems in physics, chemistry and other subjects give rise to differential equations which are difficult or impossible to treat mathematically. It has long been possible to obtain numerical solutions by arithmetic methods, and the development of adding and multiplying machines to their present state of perfection has made these much simpler to carry out. The amount of work involved is, however, still very great.

The disintegration of the separated isotopes of boron, under proton and deuteron bombardment, has been investigated, and it is shown that the groups of disintegration particles previously discovered had been attributed to the transmutation of the correct isotopes. In addition, experimental evidence has been obtained for a previously unknown excitation level of 8Be at about 7·5 × 106 e.V. above the ground state.

When the differential analyser (1) is being used it is often necessary to supply to the machine information in the form of a functional relation between variables occurring in the equation. This is usually done by keeping a pointer on a graph on an input table. The x-coordinate lead screw of the input table is driven by the machine, and the y-coordinate lead screw is rotated by hand so as to keep the pointer on the given curve. The disadvantages of this method, namely the necessity for the continuous attention of an operator and the possibility of personal errors, would be obviated by the use of an automatic follower instead of a hand control.

The decay period of the α-activity produced when boron is bombarded with neutrons from a (Li + D) source has been measured, and found to agree with the known decay period of 8Li. It has been shown that no activity is produced when (Be + D) neutrons (maximum energy 4·5 × 106 e.V.) are used. The results are explained by postulating the formation of radioactive 8Li according to the process

A short investigation of the number-range distribution for the α-particles emitted by 8Li indicated that a maximum occurred in the distribution at a range of about 6 mm.