In many radio investigations of the ionosphere it is desirable to use senders working on different wave-lengths and situated in different positions with respect to the receiver. For this purpose it is very convenient to make use of commercial senders which work more or less continuously at high power. It so happens, however, that these senders usually emit Morse signals consisting of dots and dashes of variable lengths and with variable intervals between them, so that an instrument which records the mean signal will give an indication which depends on the speed of sending and on the spacing and length of the signs. In order to obtain a reading which depends only on the signal amplitude, it is possible to employ a quick moving recorder such as a string galvanometer or a cathode ray oscillograph, which will follow the individual Morse signs. With both these types of recorder the record must be made photographically so that changes in the signal strength are not noticed until the record is developed. This is a serious disadvantage in investigations of short-lived disturbances of the “catastrophic” type.

The methods used to measure separately the electronic and lattice heat conductivities κe and κg in a metal are reviewed, and it is pointed out that care is necessary in interpreting the results in view of the underlying assumptions. The equations given by Wilson for κe and for the electrical conductivity σ are used to plot the theoretical values of the electronic Lorentz ratio Le = κe/σT as a function of T, both for the monovalent metals and for a model metal with 1·8 × 10−2 conduction electrons per atom, which is taken to represent bismuth sufficiently accurately for this purpose. Curves for κe and κg as functions of T are given in both cases, and these, together with a comparison of the observed Lorentz ratio and Le, show that in the monovalent metals κg is unimportant at any temperature, but in bismuth it plays a major part at low temperatures, in agreement with experimental conclusions. Quantitatively the agreement is good for copper and, as far as the calculations go, reasonable for bismuth.

Scattering of lattice waves at the boundaries of single crystals (including insulators) at temperatures of a few degrees absolute is shown to be consistent with the experiments of de Haas and Biermasz on KCl and to be responsible for the rise in thermal resistance in this region as suggested by Peierls.

The assumption in the theory of electronic heat conduction that the lattice energy distribution function has its thermal equilibrium value is examined in an appendix. The conclusion is that it should be satisfactory, though the proof of this given by Bethe is seen to be inadequate.

The recent experiments of Mohr and Pringle on the anomalous scattering of α-particles in hydrogen, deuterium and helium have revealed the existence of appreciable deviations from Coulomb's law at quite large distances (of the order 10−12 cm.). One explanation of this result which immediately suggests itself is that these deviations arise from ordinary electrostatic polarization of the colliding nuclei due to their electric charges, an effect considered originally by Debye and Hardmeier by classical methods to explain anomalous scattering. It is fortunately easy to examine whether this is the correct explanation. If we assume polarization to be the main cause of long-range anomalies in nuclear interaction, it is clear that these anomalies must fall off inversely as the fifth power of the distance. From the observed scattering of α-particles in helium which have √20 units of angular momentum relative to the struck nuclei and so pass at distances where the long-range anomalies are alone important, it is possible to determine the constant in the inverse fifth power law. From this constant the polarizability of the α-particle necessary to give rise to the observed effects can be determined. Now although it is not possible to calculate the polarizability of an α-particle with any degree of accuracy, our knowledge of its structure not being sufficiently definite, we can perform the calculation for the deuteron with some accuracy. Since the a-particle is certainly a more compact structure than the deuteron there is no doubt that it has a much smaller polarizability. Comparison of polarizabilities derived from the scattering and calculated from the known structure of the deuteron can therefore decide for or against this explanation of the anomalies.

Note on a Theorem of Myrberg*

On p. 421, line 30, of that note I remark “δ(x) is a lower semi-continuous function of x”. That statement is, in general, untrue. The proof should rather run as follows:

The subset of E1 where δ(x) ≥ a > 0 is clearly closed and, as α tends to 0, tends to h−mE1. Hence, by taking α sufficiently small, we find a closed subset of E1, of positive h-measure, every point x of which has the property that

whenever 0 < d ≤ α. We may call this subset again E1 and the proof, from the top of p. 422, goes as before.