Using an electrical counter, the number of α- and β-particles from a source of Radium D, Radium E and Radium F in equilibrium has been measured: it has been found that after correction for reflection at the source, their numbers were about equal. According to previous work on their absorption, the β-particles from Radium D would not be recorded under the conditions of these experiments. On this assumption the observed β-radiation was due to disintegration of Radium E, and since this was in equilibrium with Radium F, it follows that about one β-particle is emitted per disintegrating atom of Radium E.

The problem of the temperature distribution in transformer or other laminated cores in which heat is generated at a uniform rate, does not appear to have been treated by exact mathematical methods. A good deal of work of a semi-empirical nature has been done by Vidmar, Kuchler and others, the object of which has been to enable designers of transformers to obtain an estimate of the maximum temperature likely to prevail in the core.

In all methods of measuring excitation and ionisation potentials which are in common use the current-voltage characteristic curves of the apparatus are plotted. In the absence of gas these curves are smooth, but on the admission of gas at a suitable pressure sharp upward bends occur at definite voltages, which are interpreted as the critical potentials of the gas. In a variation by Franck and Hertz, the so-called inelastic impact method, these bends are downward, the critical points being represented by maxima.

The purpose of this note is to calculate, on the basis of the assumptions which underlie the theory of the stopping of α-particles by matter, the influence of space quantization on this phenomenon. The results arrived at may be capable of an experimental test and will serve to illuminate these assumptions and to indicate their limitations.

It is possible to obtain approximate theoretical relations between the spectra of different atoms ionised to such an extent that they possess the same electron structure. In this paper these relations are used to extrapolate values of the terms of the spectra of various lithium-like and sodium-like atoms.

From the terms so estimated lines can be calculated, and in many cases correlated with lines observed by Millikan and Bowen in the hot spark spectrum of the corresponding element. Revised term values can then be calculated from the lines so identified.

The spectra of lithium-like atoms treated in this way include those from Be II up to O VI, and those of sodium-like atoms, the spectra P V and S VI.

1. The extended Riesz-Fischer theorem, in the special case of the trigonometrical orthogonal system, states that, if a and β are real numbers such that

then

implies, whenever α ≤ 2, the existence of a solution of the system of integral equations,

such that

and further

When a = 2, this reduces to the original Riesz-Fischer theorem.

The actual form of the set of linear substitutions on 3 symbols, which gives a representation of the simple group of order 168, has been known for many years.

In these Proceedings (vol. 20, pp. 247–9) I have determined the form of the set of linear substitutions on 5 symbols which gives a representation of the simple group of order 660.

During the last six months we have succeeded in achieving two of the improvements which were foreshadowed in a former paper on this subject.

If G is a group of finite order which contains an operation P of prime order p, permutable only with its own powers, the order of G must, by Sylow's theorem, be of the form (1 + kp) pś, where s is a factor of p – 1. The greatest subgroup of G, which contains self-conjugately {P};, the subgroup generated by P, must be a metacyclical subgroup {S, P}, where

while g is a primitive root of the congruence gs = 1 (mod. p).

When an atomic system emits or absorbs radiation, the frequency of the radiation is connected with the change of energy of the system by Bohr's frequency condition δE = hv. This equation is usually applied to the transition of an atom from one stationary state to another, the frequency of the radiation being measured in a frame of reference in which the atom as a whole is at rest, both before and after the transition. It has been pointed out by Bohr that difficulties arise when no natural frame of reference presents itself in which to measure the frequency, which is the case for non-isolated systems, or even for isolated systems when the process of radiation is connected with a change of momentum.

Experiments carried out with the aim of elucidating the action of the α-particle counter are described. A normal counting circuit including an ionization chamber with point and plane electrodes was used. The “wave-form” and intensity of the transient impulses resulting from discharges stimulated by single electrified particles have been determined using a cathode-ray oscillograph. It is found that the nature of the impulse is determined largely by the capacity and resistance of the system, and not by the nature of the electrical stimulus. The potential impulse normally detected by string electrometer methods is shown to be proportional to the current responsible for the recharging of the electrostatic capacity of the counter after the rapid discharge of the capacity initiated by the electrified particle.

§ 1. Bohr's original (1913) theory of the stopping power of light atoms for α-particles seems to invite further study. It is well-known that in this theory, which exhibits a general agreement with experiment, the loss of energy by the α-particle is calculated on purely classical principles, as the energy transferred to electrons initially at rest; and elastically bound to atoms. A large part of the loss so calculated (about one-half) comes from transfers to electrons in distant atoms of amounts less than the energy required to transfer those atoms to their next higher stationary state. This has created a serious difficulty according to more recent views of the quantum theory in which it has been presumed that any effective interaction must always leave the atom in a stationary state, and has given rise to the investigations of Henderson, which however do-not agree with experiment. In some recent speculations Bohr has suggested a possible way of escape from this difficulty, of great theoretical interest, to which he has been led by somewhat similar difficulties in the theory of radiation. He suggests that there may be reason to expect that energy may be only statistically conserved in just such a type of interaction by the atomic switches, while the classical calculation for the α-particle ought to retain its validity.

Experiments with a helical method of focussing β-rays are described. Although the method does not appear to be so generally useful for obtaining ordinary β-ray spectra, it possesses certain advantages, of which may be mentioned:

(1) Large dispersion;

(2) Greater intensity;

(3) Good screening.

The method produces some evidence on the question of the continuous background, and experiments with it in this connection are described.

On certain assumptions as to the quantum numbers of the normal orbits of the successive electrons captured by an atom, the successive ionisation potentials can be estimated by making use of the relations between terms of the same quantum number for different atoms of the same electronic structure. Formulae for several of the successive ionisation potentials are given, the form of the formulae being suggested by theoretical reasoning and numerical values of the constants determined from known spectra; the successive ionisation potentials of O, Fe and Ag, calculated from these formulae, are tabulated. It is pointed out how far different these ionisation potentials are from the X-ray excitation potential of the same orbit of a neutral atom.