A Fourier integral is said to be of finite type if its generating function vanishes for all sufficiently large values of ¦x¦. Because the coefficient functions are defined by integrals over a finite range, the behaviour of such a Fourier integral usually resembles closely that of the corresponding series.

The motion of a light string loaded with equal masses at regular intervals has been discussed by operational methods. It is found that the system, though possessing only a. finite number of degrees of freedom, shows most of the characteristic features of dispersion. The operator e−σx/c that occurs in the discussion of uniform continuous strings is found to arise as the limit of an operator defined wholly in terms of definite integration, and its interpretation involves a theorem analogous to Taylor's theorem, but apparently more general. There is no phenomenon analogous to the conduction of heat. Any irregularity in the distribution of mass, however, produces strong internal reflexion of the shortest waves, and may provide a mechanism for conduction.

There are in the Fifth Book of Euclid's Elements twelve propositions, the object of which is to prove the equality of two ratios.

An account is given here of the measurements of the mass absorption coefficients of iron, nickel, copper and aluminium over a wave-length range 0·705 Å.U. to 1.932 Å.U.

Thomas's differential equation for the average field inside a heavy atom is analogous to Emden's equation for the polytropic equilibrium of a star. Emden's result that the total gravitational potential energy of a star is calculable once the differential equation has been solved is adapted to give the total electrostatic energy, and hence the total energy of binding, of an atom built on Thomas's model. This should be equal to the sum of the successive ionisation potentials. The total energy is found to be proportional to N, where N is the atomic number. The values found agree with Hartree's calculations of the successive ionisation potentials of certain atoms.

In this paper the results of some measurements of the Hall effect in single crystals of iron are described. This work was undertaken to determine whether the Hall coefficient varied with the direction in the crystal for which it was measured. Such a variation had been observed in other magneto-electric phenomena—the change of resistance in longitudinal* and transverse† magnetic fields—and had thrown some light on the nature of these effects. It was thought possible, therefore, that the study of the Hall effect in single crystals might yield some fresh light on this unexplained phenomenon.

Much attention has been focused on the excitation of atomic spectra by electrons whose velocities do not greatly exceed the critical value, and it is now possible to form a rough idea of the behaviour of the “excitation function,” or probability that an electron of given velocity shall excite on impact, when the energy of the electron is only slightly greater than that required for excitation. But the form of this excitation function for much higher velocities is still in considerable doubt.

A method of using a valve for amplifying ionisation currents 100,000 times is described, which avoids the instabilities usually associated with such apparatus. The necessary conditions to be satisfied, while extremely simple, are based on theoretical conditions which are discussed in full. Used in conjunction with a galvanometer of sensitivity 200 mm. per micro-ampere, the system behaves in a similar manner to a low capacity quadrant electrometer of sensitivity 6350 mm. per volt, shunted by a leak of 360 megohms, the value of the latter being slightly greater for negative currents than for positive. In addition, it has the advantages of portability, compactness, and ease and rapidity of erection and operation, being specially suitable for lecture demonstrations.

The method of compensation can also be applied to other valve circuits, resulting in a much steadier zero.

Rosseland proposed a theory of the production of characteristic X-rays. He calculated the number of atoms from which on the average an electron with definite energy will remove an electron from a particular core orbit, but neglected the velocity of the core electron in its orbit and the increased velocity of the impinging electron due to the atomic field. Taking these into account considerably alters his formula.

The Langmuir-Frenkel theory of surface action has been shown to involve a simple relation between the partial pressure of the catalyst poison, and the reduction in reaction velocity which results. Very interesting observations have been made by Beebe showing that the heat of adsorption of carbon monoxide on a reduced copper catalyst falls considerably and reaches a limiting value as the surface approaches saturation. Pease and Stewart have shown that the presence of less than one percent, of the total carbon monoxide that a given copper catalyst can adsorb will reduce the reaction velocity of the combination of hydrogen and ethylene at the surface of the copper by 88 per cent.

New factors arise in a species by the process of mutation. The frequency of mutation is generally small, but it seems probable that it can sometimes be increased by changes in the environment (1,2). On the whole mutants recessive to the normal type occur more commonly than dominants. The frequency of a given type of mutation varies, but for some factors in Drosophila it must be less than 10−6, and is much less in some human cases. We shall first consider initial conditions, when only a few of the new type exist as the result of a single mutation; and then the course of events in a population where the new factor is present in such numbers as to be in no danger of extinction by mere bad luck. In the first section the treatment of Fisher (3) is followed.