The quartz clock has made possible a notable improvement in the precision of timekeeping, with the additional advantage of providing a standard of frequency as well. This is perhaps putting the cart before the horse, for the quartz crystal oscillator was developed in the first instance as a precision standard of frequency; it was then adapted, by frequency subdivision and the use of a low frequency output for driving a phonic motor from which seconds impulses could be taken, to serve as a clock. It is primarily from its use as a standard of frequency that it is of navigational interest, for various radio aids to navigation, such as Gee, Loran, Consol and Decca depend upon accurately standardized frequencies. For the satisfactory checking of a frequency, comparison must be made with a standard whose accuracy is at least one degree higher than that of the frequency which has to be checked. Calibration laboratories, in turn, require to check their own standards. As the rotation of the Earth provides our fundamental unit of time, it follows that time, and therefore also frequency, must be determined from astronomical observations; hence it is necessarily the responsibility of the Royal Greenwich Observatory to provide both time and frequency with an accuracy sufficient for all practical requirements. The practical requirements have become more stringent in recent years, and that is why great efforts have been made to improve the precision of time determination and of timekeeping at the Observatory.

Investigations of reactions of the type

are of interest for their own sake, and also for the fact that, if is a radioactive nucleus, as it usually is, being a stable isobar, activation of a few different A nuclei in the same fast neutron flux will yield some information about the neutron spectrum. This follows from the fact that these (np) reactions (and the similar (nα) reactions) are nearly all endothermic, showing a threshold of neutron energy below which no activation takes place. Thus knowledge of the excitation functions of a few such reactions would enable the above-mentioned crude neutron spectroscopy to be realized. The detectors (A nuclei) would have a standard shape and size, and the induced β-activity would be measured with a standard counter in fixed geometrical conditions. Though exact spectroscopy would not be possible, any change in the relative activations of the detectors would be a quite sensitive indicator of a change in the incident neutron spectrum.

In 1914 Carathéodory defined m–dimensional measure in n–dimensional space. He considered one-dimensional measure as a generalization of length and he proved that the length of a rectifiable curve coincides with its one-dimensional measure.

1. The boundary value problem of Laplace's equation for two spheres is a classical one, and has been the subject of discussion by many mathematicians (1). The earliest attempt to solve a boundary value problem of this type is due to Poisson (2), but his analysis is applicable only to the electrostatic problem. The first of the methods which can be successfully applied to both electrostatic arid hydrodynamical problems was developed later by Lord Kelvin (3); this procedure, which is known as the ‘method of images’, was first applied to the problem of the motion of two spheres in a perfect fluid by Hicks (4). Another method of great generality, that of transforming Laplace's equation to bipolar coordinates and studying the solutions in these coordinates, was developed about the same time by Neumann (5) and much later by Jeffery (6). More recently a new method has been developed by Mitra (7) for the solution of the problem of two spheres in a potential field. It makes use of two sets of spherical polar coordinate systems; the solution is expressed in terms of infinite series whose coefficients satisfy an infinite set of linear algebraic equations. The chief interest of Mitra's method lies in the fact that he has found it possible to derive exact solutions of this infinite set of equations. All of these methods suffer from the disadvantage that the potential function is obtained in the form of an infinite series so that any numerical calculations are rendered cumbersome.

Recent papers by Néel (8) and Lawton and Stewart (7) have provided an explanation of the process of magnetization in a single crystal, using the well-known ideas of the domain theory but bringing out the important role played by the demagnetizing field. These authors applied their ideas to two shapes of single crystals of iron, long rods and oblate spheroids, but in the latter case the only crystal orientation worked out in detail was that in which the equatorial plane was (100). The case of oblate spheroids of iron and iron-silicon where the equatorial plane is a (110) plane of the crystal, and the magnetic field is applied in this plane, are considered in detail in this paper. Calculations are made for In, the component of magnetization perpendicular to the applied field He, and comparison made with experimental measurements. This particular problem was considered by Bozorth and Williams (4) who calculated the torque per unit volume (i.e. the product InHe) experienced by the crystal in a magnetic field. Their calculations are, however, incomplete, because their picture of the magnetization process is not a valid one in moderate fields. Moreover, the demagnetizing field was taken into account only in assessing the size of the field H acting within the crystal, but not its direction.

A sequence of papers by P. Hall ((1)–(4)) on some fundamental properties of soluble groups was followed in 1940 by his account of a new construction theory for such groups (5). We shall have frequent occasion to refer to these papers, and we begin with a brief account of their contents.

A method is given for the solution of transient differential equations of the type

where D is a differential operator in one or more dimensions. These equations arise in vibrational problems and problems on the conduction of heat. Some examples on the application of the method are given.

In present designs of radar sets for merchant ships, the radar-equipped ship is represented as being at the centre of its own P.P.I. picture. But there is a case for having an off-centre display. In this article are discussed possible advantages to be obtained from such a display, when the set is being used for collision warning away from a coast-line. The author recognizes that some of the opinions expressed are of a controversial nature.

The method described provides glide-paths for climbing and descending aircraft by combining in a single instrument information from the barometric altimeter and radar distance measuring equipment. Preliminary flight tests have shown that the method provides a smooth path along which an aircraft can be flown within close limits, and is one that appears sufficiently promising to justify further development.

Height separation has for years been a fundamental concept in the control of air traffic. It is the basic method of preventing collision during en-route navigation and in some holding procedures. The main reason for this is that a suitable instrument already exists in the form of the barometric altimeter, aninstrument which is intrinsically more accurate and reliable than any of the usual navigational aids.

1. This paper and an earlier paper (l) were written at the suggestion of W. L. Bragg in connexion with his theory of yield in metal crystals (2).

1. Introduction. Modern computational machines and methods are conveniently divided into two classes:

(A) Those depending on physical analogues, and therefore restricted in accuracy.

(B) Those depending on digital processes, and so capable of giving any desired accuracy.

In this paper, the general hydrodynamic theory of visco-inelastic, incompressible, non-Newtonian fluids, developed in a previous paper (l), is applied to the problem of the flow of such a fluid through a tube of circular cross-section. It is found that the absolute values of the normal stress components are no longer uniform over a cross-section of the tube normal to its axis, as in the case of Newtonian fluids obeying the laws of classical hydrodynamics.

However, the pressure difference, between points at equal radii on two planes normal to the axis, is independent of the position of these points on the planes.