1. The wave function of an atom containing many electrons has not yet been solved completely, even that of helium being as yet unknown. In the absence of a direct solution of the Schrödinger equation for the electrons in an atom, various attempts have been made to devise approximate methods of solution in particular cases. The particular case of helium, being the easiest, has received considerable attention and a number of approximate wave functions appropriate to the normal state have been constructed. These functions usually contain empirical constants which are adjusted to make the energy of the system a minimum. Zener has attempted the more ambitious programme of finding the wave functions of all the atoms in the first period of the Periodic Table (Lithium to Neon), and has made interesting discoveries as to the way in which the wave functions differ from atom to atom. This work also is based on the variation of parameters.

The thyratron valve is essentially a triode which contains a small quantity of some inert gas, usually mercury vapour. If a suitable voltage be applied between anode and filament, with sufficient negative grid bias, the valve behaves like an ordinary vacuum tube; but, as the grid is made more positive, at a certain critical voltage an arc strikes between the anode and the filament, with enormous increase in the anode current. The grid then exercises no further control over the anode current, which must be limited by external resistance so as not to exceed the saturation emission current from the filament. If the voltage across the tube exceeds the “disintegration” potential, of some 20–25 volts, the cathode will be disintegrated by positive ion bombardment. Limitation of the anode current to the emission of the filament ensures that the voltage, while higher than the ionization potential of mercury, is considerably below the disintegration potential.

A portable apparatus is described which is capable of measuring directly, by means of a loop aerial, the magnetic field in an electromagnetic wave. Accurate measurements are possible of magnetic fields corresponding to field strengths of 0·2 millivolts per metre. Special means of providing small known calibrating E. M. F. S are described. The apparatus can be used to measure signals over the range 6 microvolts to 300 millivolts. Used in conjunction with a small portable vertical aerial, field strengths down to 2 microvolts per metre can be measured.

Davis and Barnes have recently reported new and unexpected phenomena concerning the capture of electrons by swift α-particles. A beam of α-particles from a polonium source was passed through a stream of electrons emitted from an oxide-coated filament and accelerated by a known voltage so as to move in directions roughly parallel to those of the α-particles. The α-particles were then deflected by a magnetic field, and finally fell on a zinc sulphide screen, where the scintillations were counted. If any of the α-particles captured electrons while passing through the electron stream, they would fall on a different part of the screen, since the magnetic deflection is proportional to the charge. Any capture could thus easily be detected, and its dependence on the accelerating voltage examined.

The assumption is often made that when competition is extremely intense at any stage in a life cycle, natural selection is bound to be intense also. This assumption will be examined quantitatively and it will be shown that the intensity of selection may diminish and become negative at high rates of elimination, while at its best its increase is extremely slow.

Almost every species is, to a first approximation, in genetic equilibrium; that is to say no very drastic changes are occurring rapidly in its composition. It is a necessary condition for equilibrium that all new genes which arise at all frequently by mutation should be disadvantageous, otherwise they will spread through the population. Now each of two or more genes may be disadvantageous, but all together may be advantageous. An example of such balance has been given by Gonsalez(1). He found that, in purple-eyed Drosophila melanogaster, arc wing or axillary speck (each due to a recessive gene) shortened life, but the two together lengthened it.

The equations of propagation of electromagnetic waves, simple harmonic in time, in an optically anisotropic stratified medium are obtained from the treatment of the refracted wave as the resultant of the incident wave and wavelets scattered by the elements of volume of the medium, and are reduced to a simple form.

The primitive property of the medium, from which the other optical properties are derived, is the scattering tensor, relating the induced dipole moment per unit volume to the applied electric field.

The relation between the dielectric tensor (corresponding to the dielectric constant of an isotropic medium) and the scattering tensor is obtained.

A medium consisting of classical oscillators in an external magnetic field is then considered, the scattering tensor and dielectric tensor are evaluated for such a medium, and finally a formula for the refractive index is obtained.

For an ionised medium the formula differs from that obtained by Goldstein; the difference is due to the inclusion in the present treatment of a term omitted by Goldstein; the significance of this term is discussed, and its inclusion justified.

Taking this term into account makes an important difference to the properties of the medium for long waves; an example is given.