Soon after the introduction, in March 1947, of GCA to London Airport, it was realized that the advantages which it had brought to approach control could be greatly increased if the range of the radar could be extended to give earlier and more accurate information to the flight information controllers, and eventually the airways controllers, on the position of aircraft. At the time when the Ministry of Civil Aviation had installed and were testing an MEW type radar at the west end of London Airport, the question of the extended cover required from radar in this country was under active consideration. It was thus planned to develop long-range radar control techniques and procedures to be used in conjunction with the MEW radar. The work was planned to fall into three separate stages: (1) experiments in combined MEW/GCA working (termed long-range GCA); (2) operational trials; (3) operational service.

The geometrical configuration consisting of five straight lines tangent to the stream line (ψ = const.), isobar (p = const.), isocline (θ = const.), isovel (q = const.) and isopycnic (ρ = const.) at a point P of the physical plane in the plane flow of a fluid has a number of interesting properties. The study of this geometric configuration for a wide class of ideal fluids (which includes polytropic gases and incompressible fluids), in particular its properties at sonic points, is the purpose of this paper.

1.1. This paper is a theoretical investigation in the real domain of the existence of subharmonic solutions of non-linear differential equations of the form

where F is analytic and of least period 2π/ω in t; ε = (ε1, …, εn) is small; and F(x, ẋ, 0, t) is not linear in x and ẋ.

The seaman requires of radio aids to navigation that they should be effective substitutes for astronomical and terrestrial methods of fixing when these fail him, either wholly or in part. For normal peacetime voyaging there has been no firm demand for a radio system that will improve on the performance of the other methods at their best. The requirements for radio aids can therefore be related to the facilities which these other systems afford. This does not, of course, imply that circumstances do not exist in which radio aids can provide a degree of assurance that the other methods might not.

Reference to a chart of the Thames Estuary will show that the dominant feature of the submarine morphology is the series of elongated banks, of which the Barrow, Sunk and Long Sand are the most important. Between these banks, and with the same north-east to south-west trend, are the navigable channels of the Swin, Barrow and Black Deep (Fig. 1).

The alignment of the channels suggests that they originated as a result of tidal-stream scour of a fairly uniform sheet of fine silt and sand. In each tidal period, streams enter the estuary from the north and flow on the flood in a south-westerly direction parallel to the Essex coast. After about six hours they slacken, turn and flow out of the estuary in the reverse direction. This continuous flood and ebb stream action, with a maximum velocity varying from 2·3 to 2·9 knots depending on whether the tide is neap or spring, has apparently scoured out channels to depths which exceed 10 fathoms in places. If the channels largely arose in this way, the banks represent the modified remnants of the initial surface. These banks are constantly being extended seaward as more riverine silt is emptied into the estuary by the Thames, Medway and the rivers of Essex. The distal end of Long Sand alone has grown almost ½ mile in the past 100 years (see Figs. 1 and 4).

Summary of a paper presented to the Canadian Institute of Navigation at a meeting held in Montreal on 22 September 1950.

In 1946 and 1947 a great deal was learned about scope interpretation and the use of search radar as an aid to air navigation in the Canadian Arctic. New techniques, differing from those used during the war, when search radar was considered primarily as an aid to bombing and for pin-pointing, were developed and a great deal of information on interpreting the radar presentation of topography at different seasons was obtained. The use of search radar for navigation in the Arctic is described in this paper, which also gives information on the probable appearance of topographical detail on the display at different times of the year.

Presented at a meeting of the Institute held at the Royal Geographical Society on 15 June 1951.

Shore-based radar stations to supervise or assist the navigation of ships have now been employed for at least a decade. Such stations were more extensively used during the war than they have been since, principally because there had to be large convoy movements along heavily mined coastlines under conditions when, because of wartime limitations, many of the more conventional navigational aids were not available. The most important wartime development in the use of radar in this direction was undoubtedly the introduction of high power centimetric equipment and the plan position indicator. Since the war the use of shore-based radar to assist navigation of merchant shipping has been extremely limited and the only outstanding installation of this type is the Liverpool Harbour Supervision System, which was brought into service in 1948. This system has now been in operation for three years and has provided a great deal of information and has created a world-wide interest.

1·1. Let van der Pol's equation be taken in the form

where ε1, ε2, k1 and k2 are small, and ω ≠ 0 is a constant, rational or irrational, independent of them.

The Abridged Nautical Almanac in its revised form, for the year 1952, has now appeared. In place of right ascension and the familiar quantities E and R which were adopted in 1929, it tabulates Greenwich hour angle in arc for the Sun, Moon, planets and Aries, and sidereal hour angle (or versed ascension) for the stars.

Greenwich hourangle has been used in air almanacs for a number of years, and several surface almanacs have tabulated it as an alternative to right ascension; it is only recently, however, that it has been given exclusively in surface almanacs. Among the surface almanacs which tabulate G.H.A. at present are the American, Spanish, Argentine, Brazilian and Yugoslav.

The redesign of the Abridged Nautical Almanac has been under consideration for many years, but the change was delayed first by the war, and then by the desire to avoid a transitional period during which the new G.H.A. and E and R were given together; it was also decided to give as much notice of the proposed changes to users as possible. The design in substantially its present form was in fact accomplished in 1947, though the arrangement of the daily pages and much detailed work was carried out later.

In two classical papers (1, 2) J. M. Whittaker introduced the study of integral functions bounded at the lattice points m + in(m, n = 0, ± 1, …,). He succeeded in showing (cf. also G. Polya(3)) that an integral function of at most the minimum type of order 2 uniformly bounded at the lattice points was necessarily constant. This result was improved almost simultaneously by A. Pflüger(5) and V. Ganapathy Iyer(11), who showed that the result was true also for functions of type K<½12π of order 2. The example of Weierstrass's σ(z) function shows that theirs is a best possible result in this direction.

If the average spacing of the resonance levels is very small as compared with the range of energy in which the spacing or width of the levels changes appreciably on the average, one can speak of a statistical distribution of the level spacings and widths. The question then comes up naturally, whether the ‘distribution law’ for width and spacing is different for protons, neutrons, etc., i.e. whether it depends on the long-range interaction of the scattered particle. It is pointed out that while the average width must depend on the long-range interaction (on account of the penetration factor) the distribution of the widths, if these are measured in terms of their average, can be expected to be independent therefrom. In the case of the level spacings, not only the distribution about the average, but the average itself is also independent of the long-range interaction. It is pointed out, incidentally, that the logarithmic derivative of the wave function at the surface of the nucleus will have, on the whole, a positive value between resonances because of the greater effect of the high-energy resonances than that of the bound states.

A Letter published in the Journal (Vol. IV, No. 2, p. 211) from Captain Brett Hilder refers to the use of the phenomenon known as the green flash for obtaining longitude at sea, and an editorial comment on the letter suggests that accurate descriptions of what has actually been observed at different times at sea might be of value to meteorologists. The following notes, though they contain no reference to using the observations for navigational purposes, may be of some interest as they are the result of a great many observations of the phenomenon.

Numerous reports on observations of the green flash have been published in meteorological publications where, as a general rule, it is accepted that it is only seen under conditions of extreme visibility and clearness of the atmosphere. From numerous personal observations it has been ascertained that this is in fact not so, and that the green flash can be observed under conditions of extreme cloudiness, haze and humidity so long as the horizon is visible at the time of rising or setting of the heavenly body. Another factor affecting the actual sighting of the green flash is the intensity of light emanated by the body, for the flash is of very weak intensity when compared to the normal brilliance of the body observed.