Since the pioneer work of Prof. R. H. Fowler(1) on the statistical foundations of the Debye-Hückel theory of strong electrolytes (2), several attempts have been made to obtain as much information as possible on the question of the equation of state of electrolytes from merely thermodynamical and dimensional considerations.

If a simple calculation is made of the amount of heat liberated when one body is slid over another, and of the possible rate of escape of the heat by conduction and emission, it shows that the temperature of the surface may reach a high value.

Taylor and Fisk have discussed the internal conversion of magnetic multipole radiation by K electrons and have found internal conversion coefficients which are much larger than those for electric multipoles, and which increase with the order of the multipole. The object of the present note is to determine whether this state of affairs holds also for pair production by internal conversion of magnetic multipole radiation.

Experiments are described for measuring the lateral deviation of wireless waves after reflection from the E and F regions of the ionosphere. It was found that the greatest lateral deviation observed, 20° or more, was that due to the e region, and the least, about 0·5°, was due to the normal E region in the case of a distant transmitter.

The time variation of amplitude of a reflected wave was found to be consistent with a random scattering at the ionosphere.

In the theoretical discussion it is shown that changing horizontal irregularities, ion clouds, are a very important cause of fading. Values are calculated for the average fading periods which would result from the horizontal winds in the neighbourhood of the E region known to exist from other evidence. These calculated periods agree with the observed and it is inferred that horizontal winds are a very important cause of fading.

From experimental results on the shape of the upper portion of the continuous β ray spectra of thorium C and thorium C″ the distribution of energy is deduced. This distribution is compared with Fermi's theory wherein the shape of the curve depends on the mass of the neutrino. The comparison supports Fermi's conclusion that the mass of the neutrino is zero or certainly not more than a very small fraction of the electronic mass.

All the light elements up to aluminium and some heavier ones have been examined for disintegration by slow neutrons. Large effects have been found in lithium and boron and a small effect in nitrogen, the reactions being

and probably

The charged particles emitted in the disintegration of lithium and boron afford a convenient and sensitive indicator for slow neutrons.

One of us (M. G.) desires to acknowledge the financial assistance received from the International Student Service, London, and from Magdalene College, Cambridge.

The discovery of Fermi and his collaborators, that neutrons are much more readily captured by various atoms, e.g. silver, when their kinetic energies, originally of the order of 106 e.v., have been reduced by collisions with hydrogen nuclei, has been confirmed.

The process of slowing down of the neutrons has been studied in some detail, and the nuclear cross-section for collisions with hydrogen nuclei has been determined for the primary neutrons and for the slow neutrons which are readily captured by silver atoms.

The nature of the “gas” of slow neutrons was also discussed, but it was not found possible to reach a definite conclusion as to the energy of the neutrons concerned.

Experiments are described comparing the effects of neutrons slowed down in paraffin wax at the temperatures of liquid nitrogen and liquid hydrogen with those obtained at ordinary temperatures. It is found that the absorption produced by certain substances increases as the temperature is lowered. The transformations produced in these substances also increase, but generally to a smaller extent, probably owing to more neutrons being absorbed in the paraffin: the exact figure depends on the thickness of the layer of cooled paraffin.

A few experiments were also made substituting liquid hydrogen for paraffin wax (without change of temperature). The effect of this also appears to depend on the thickness of the layer, but it is not yet possible to draw definite conclusions.

It is well known that the motion of a dynamical system can be pictured in two distinct ways, which Dirac names the Heisenberg picture and the Schrödinger picture. The equations of motion take different forms in the two pictures, but of course have identical physical consequences, since the motion of the system does not depend in any way on which picture we choose. It should therefore be possible to express the equations in an invariant form (independent, that is, of the picture used). It will be shown in this note that not only can this be done (equation (3)), but it can be done in such a way that it is not even necessary to introduce a picture at all (equation (3′)).

1. The purpose of this note is to prove the uniqueness of the solutions of two closely related differential equations, under suitable boundary conditions. The first is the equation satisfied by the potential in the electrostatics of the new field theory proposed by Born, namely,

where øx stands for etc.

Attention has recently been directed to the measurement of the relative amplitudes of wireless echoes from the ionosphere, and some interesting methods of automatic registration have been devised (1, 2). For vertical incidence, and for wave-lengths shorter than 200 metres, visual observation shows that a single echo, even when separated from its accompanying oppositely polarized magneto-ionic component, shows considerable rapid fading (3). This fading is evident on the records published by White (1), and it is clear from these that it is not easy to determine the relative amplitudes of two echoes. This paper is an account of an apparatus which automatically integrates the amplitude of an echo over a time long compared with the period of the fading, and at the end of the period registers the integrated value on a recording galvanometer. The process is then repeated so that the final galvanometer trace represents the average value of the intensity throughout successive equal periods of time. It is further described how by using a double thread recording galvanometer, it is possible to record the averaged amplitudes of two different echoes (e.g. ordinary and extraordinary, or E and F) during alternate integrating periods.

The statistical method described in 21·4 of Fowler's Statistical Mechanics was devised to deal with assemblies in which the total numbers of elementary physical systems remained constant. The same method is applicable, with no formal changes, to assemblies in which elementary physical systems of two different sorts can be created and annihilated in pairs, like the negative and positive electrons in the theory of Dirac.