This paper illustrates the problems of general linear propagation mainly by analysis of the conditions necessary for effective resonance, which are now of great technical importance. Another theory is also broached, that of the relation of the arterial pulse to the blood-flow, first explored with adequate hydraulic instincts by Young in 1808.

The most outstanding discrepancy between experiment and Dirac's theory of the electron is at present that shown by Dymond's experiments on the polarisation of beams of electrons by double scattering. It has been shown by Mott, using Dirac's relativistic wave equation, that one would expect a 15% asymmetry of beams of 140 k.v. electrons scattered twice at 90° by gold. The experiments of Dymond referred to above show that there cannot be more than 1% asymmetry. Several attempts have been made to explain this discrepancy, but without success. (For an account of these see Dymond's paper II.) One possibility which has not yet been investigated is that of exchange between the incident electron and the electrons of the struck atom. It is evident that only elastic exchange need be considered, since the probability of excitation of any form is known to be small. Only exchange with the K and L shells may be expected to give any appreciable effect.

Three main stages may be marked in the development of the theory of the optical properties of metals. First, there is Drude's original theory, based on Maxwell's equations; in this theory the current density j at any point in a metal is supposed to be equal to the product of the electric vector of the light and of the conductivity of the metal. The theory yields the well-known Hagen-Rubens formula for the reflecting power, which appears to be in agreement with experiment for very long wave-lengths (λ > 10μ), but leads to completely incorrect results in the optical region. Various investigators ‡ have therefore modified the theory to take account of the finite mass of the electron; the formulae obtained pass over into the Drude formulae for sufficiently long wave-lengths. Finally a quantum theory of the phenomenon has been given by Kronig§, the electrons being treated as moving in a periodic field due to the crystal lattice in the manner originated by Bloch; this theory, in its turn, becomes identical with the modified classical theory if the periodic lattice is neglected.

The cross-sections for the emission of radiation by very fast electrons (energy great compared with mc2) and for the production of pairs of positive and negative electrons by very hard γ-rays is calculated, considering the screening of the atomic field in which the processes happen. The main part of the paper deals with the integration of the differential cross-section over the angles. It is found that the integral cross-section increases steadily with increasing energy of the primary particle, reaching an asymptotic value for extremely high energies.

An account is given of experiments to determine the polarisation of downcoming waves of long wavelength, using the method devised by Ratcliffe and White. The results show that on the whole the polarisation is left-handed, although there is a tendency for right-handed polarisation in the region of 1500 metres.

An improved circuit is described for a two thyratron counting unit such as is used in the “scale of two” thyratron counter. The advantages which result are that the minimum time of resolution is reduced and a source of occasional failure (“jamming”) of the counter is removed. Any type of impulse may be counted and, with selected thyratrons, impulses separated by only 0.00015 sec. may be reliably counted as separate. This makes possible a counting speed of 8000 random impulses per minute with a probable loss of only 2%.

The modification introduced into the circuit used in the original “scale of two” counter is that small condensers (0·0015 μF max) are cross connected between the grids and anodes of the pair of thyratrons, and the extinguishing condenser connected between the anodes is made small (0·02 μF max). The anode resistances are 10,000 ohms and grid leaks 100,000 ohms for the values of capacity mentioned. A valve amplifying stage is introduced, to pass the impulses from the modified circuit of the first pair to the second pair of thyratrons. For greater convenience the mechanical counting meter operated by the third pair is modified to count in multiples of eight so that no multiplication of its reading is necessary.

The protons emitted from boron, when it is bombarded by α-particles from radium C′ and polonium, have been examined. All have been ascribed to the disintegration of the B10 isotope following the capture of an α-particle. Four energy changes with values 3·1 m.v., 0·4 m.v., − 0·1 m.v., and − 1·0 m.v. are necessary to explain the range distribution observed. Experiments with α-particles from polonium also show that penetration through the top of the potential barrier stops at an energy of 3·6 m.v. and that below this there is a resonance level at about 2·9 m.v.

1. The theorem of quantum mechanics that “the spin part of the angular momentum is approximately a constant of motion provided that the forces depending on the direction of the spins are small compared with the total interaction forces” is introduced into the discussion of artificial nuclear transformations. A definition is given for the terms “probable” and “not probable” nuclear reaction.

2. Attention is drawn to the experimental result that the reaction Li6 + H1 → He4 + He3 is more probable than the reaction Li7 + H1 → 2He4, and an explanation is suggested.

3. The nuclear spin of Lie is derived from nuclear transformations and found to be 1.

4. Similar derivations for the spins of H3, He3 and B11 are summarised in a table.

The flow due to a rotating disc. By W. G. Cochran.

In the footnote on p. 368 the third reference should be National Research Council, Bulletin No. 84, Hydrodynamics (1932), 280–2.