This paper is concerned with two different problems. The first of these is to correct a magnetic compass so that the essential relationships for zero deviation are maintained even when the ship rolls and pitches. The Harvey-Raynes corrector is described and its advantages are explained. This corrector makes it possible to steady the compass at any time without affecting the accuracy of the existing deviation card.

The second problem considered is the automatic correction of deviation for transmitting magnetic compasses. A system of ‘point-by-point’ correction is developed, based upon the representation of the deviating force by a truncated Fourier series; it is shown that such a truncated series may be represented mathematically in a form immediately suitable for practical application, some such forms being described in detail. It is shown that by means of a small additional device the ‘point-by-point’ type of corrector may be made to correct both variation and deviation, so that for any given part of the Earth the transmitting magnetic compass may be made to point true north.

The paper is divided into two parts.

Part 1, under the heading of Non-standard Propagation, concerns variations in the apparent performance of marine navigational radar in its use for detecting shipping and land targets. The effects of changes in the density of the lower layers of the atmosphere on radar transmissions, their distortion of radar coverage for better or for worse, and resultant errors in the evaluation of echoes are here examined.

Part 2 describes the way in which weather echoes may influence and restrict radar-assisted navigation. The attenuation of field strength with various types and intensities of precipitation, and the effects of these factors on the navigational and collision-warning uses of radar are examined. The detection, tracking, and application of weather echoes as an aid to short-range weather forecasting are also covered.

It has been noticed by various authors that the use of the hodograph transformation for problems of compressible fluid flow leads to flows having singularities where the acceleration becomes infinite, streamlines have cusps and the solution of the equations of motion in the hodograph plane ceases to represent any possible physical flow. In this paper we investigate the nature of the singularities which can occur in the representation of one plane upon another and apply our results to the hodograph transformation. Finally, we discuss the significance for practical purposes of such singularities and in particular their connexion with the occurrence of shock waves.

A rubber molecule containing n + 1 carbon atoms may be represented by a chain of n links of equal length such that successive links are at a fixed angle to each other but are otherwise at random. The statistical distribution of the length of the molecule, that is, the distance between the first and last carbon atoms, has been considered by various authors (Treloar (1) gives references). In particular, if the first atom is kept fixed at the origin of a system of coordinates and the chain is otherwise at random, it has been conjectured that the distribution of the (n + 1)th atom will tend, as n increases, towards a three-dimensional normal distribution of the form

where σ depends on n. Thus r2 (= x2 + y2 + z2) will be approximately distributed as σ2χ2 with three degrees of freedom.

The effect of instrument errors in the basic pressure pattern formula (I) has been discussed. Calculations have been based on a 150 n.m. distance interval between altitude determinations, and the permissible instrumental tolerances are wider if the length of this run is increased. A particular latitude of N. 50° has been assumed, but this involves no loss of generality since ageostrophic errors and those due to the latitude term in the formula are believed to be compensatory. In general, both ageostrophic errors and pressure altimeter errors increase together with altitude, and if instrumentation is adequate for 10,000 feet (the level for which the probable error of 3 knots holds good) it will be so at higher levels. It appears that satisfactory results may be obtained by using a Mk. VI radio altimeter together with a Mk. XIV Kolsmann pressure altimeter, and taking the mean of four observations of D at the beginning and end of the run.

1. The problem to be discussed in the present paper arises when the finite resolving time of a recording apparatus is taken into account. Events are divided into two classes, recorded and unrecorded. Any recorded event is followed by a dead interval of a certain length of time, during which any other event which occurs will be unrecorded. A typical example is an α-particle counter; a recorded particle causes the chamber to ionize, and no other particle can be recorded until the chamber has deionized. In the case when the dead interval is of constant length τ, if the observation time t lies between (n − 1)τ and nτ, the number of recorded events must be 0, 1, 2, …, n − 1 or n. We shall assume that the probability of an event occurring in the interval [t, t + dt] is λdt, λ being constant; this is the case of most practical interest. The probability distribution of recorded events for dead intervals of constant length has been determined by Ruark and Devol (2). The explicit expression of this distribution is fairly complicated, and it is therefore difficult to manipulate. The method employed in the present paper leads naturally to the Laplace transform of the distribution with respect to the time t, and this is relatively simple. The method can easily be generalized to deal with the case of dead intervals which are not all equal, but follow a probability distribution u(τ) dτ. Finally the Laplace transform is very convenient for determining the asymptotic behaviour of the distribution of recorded events for large times of observation.

In the dynamical theory of the motion of the Earth relative to its centre of mass, the planet is usually regarded as a rigid or at most only slightly deformable body, and moments of inertia are adopted that are taken to refer to the Earth as a whole, while the motion itself at any instant is assumed capable of representation by a single angular velocity vector. This procedure, however, appears to involve unwarranted assumptions the recognition and removal of which may lead to conclusions of considerable importance. For it is well known from the theory of earthquake waves that the material of the central core of the Earth behaves like a liquid in that it transmits only longitudinal wave vibrations, while there is also other evidence suggesting that the material of the core is a true liquid (1). There is accordingly no a priori reason for supposing that the core will behave like a rigid body firmly attached to the surrounding shell if more or less permanent shearing forces are applied to it. In particular, in respect of any couple known to act on the outer shell, it is not permissible to assume, without examination of the assumption, that its effect will be transferred immediately to the inner core in a way preserving rigid-body rotation of the whole. If the material of the core behaves like a liquid where wave-motion is concerned, this suggests that it will probably also behave like a liquid whatever shearing forces act on it, and the extent to which changes in the rotatory motion of the outer shell can be communicated to the core, and what effects direct gravitational forces acting on the core may have, must in the first instance be questions of hydrodynamics and not rigid dynamics.

1. The half-life of Th C′ was determined by a new method of coincidence technique.

2. Previous investigators have recognized difficulties in regard to this investigation. These were: (a) random delays in the counters; (b) coincidences due to other disintegrations; (c) possibility of difference in delays in recording α- and β-particles. In this investigation the difficulties arising from these effects have been overcome.

3. From this type of experiment it is possible to determine the order in which the particles are emitted.

4. It would appear that the time of breakdown of a counter depends slightly upon the magnitude of the initialionization.

5. The value for the half-life of Th C′ was found to be 3.0 ± 0.15 × 10−7 sec.

The sailor will not be kept from the sea, even though empires fall and foreign invaders multiply. Yet we cannot expect to hear much of him in such troubled times. We know, however, that although European ships no longer sailed to India, yet, after the barbarian destruction of the Roman Empire, overseas trade did revive, and the foundations of such famous maritime states as Venice were laid. We know, too, that although the Arabs overran the whole length of the Mediterranean Sea, they were pushed back out of the islands by sea-borne expeditions from Italy and Catalan Spain, while when the Holy Places in Palestine were captured by the Turks (who were not ‘gentlemen’ like the Arabs), there were ships and sailors ready and able to carry crusading armies to the East, and to provision them while they were there.

1. Shastri (1) has shown that if and then

But (Goldstein (2))

hence substituting from (1·2) in (1·1) and changing the order of integration, which we suppose to be permissible, we find that if

then

assuming of course that the integrals converge.

A method is presented for the accurate numerical treatment of molecular vibration problems in which the potential energy function is of the form

The treatment is carried through in detail for the case V(q) = Aq2 + Bq4, which, in most instances affords an adequate description of the potential. There is no restriction on the relative magnitudes of quadratic and quartic terms so that the method is equally applicable to the purely anharmonic oscillations occurring in types of ring bending (1), where V(q) = aq4.

An approximate formula is derived for the energy levels in the general case. The case V = aq4 affords an illustration of the accurate treatment; the first five eigen-values and eigen-functions are computed and from them the associated transitionprobabilities. Numerical results are presented in a form convenient for further application. On comparison the approximate formula is found to yield results in error by approximately 1 %, the error decreasing for the higher levels for which the formula tends to a B.W.K. expression. In conclusion a ground-state eigen-function of simple analytical form is found to approximate remarkably well to the case of purely quartic vibrations.