In all sciences, the experimenter is constantly seeking to improve both the accuracy of his observations and the speed with which they can be obtained. He wishes, further, to use the minimum of basic equipment, and to obtain the maximum simplicity in collecting his results. Unfortunately, these factors frequently act in opposite senses: an expensive apparatus, for example, may be required to collect accurate data quickly. In certain fields, it is even worth while deliberately to sacrifice accuracy in order to gain advantage both in speed and simplicity. Thus, in astronomical navigation, it may be possible to simplify sight reduction, to cut down on the bulk of tables carried in the air, and to reduce the time taken for observation and reduction of a sight. The penalty will be a loss in accuracy, but, provided this is not reduced beyond a certain level, it may well be worth while. A review of the requirements for air navigation, and an examination of the problems of position finding by the stars against these requirements may lead to some conclusions as to whether an advantage is to be obtained by simplifying the methods.

Astro-navigation cannot be regarded at present as one of the principal aids to air navigation. It suffers, by comparison with radio aids, in that it is slow in use and much more subject to interruption by bad weather. The average navigator needs at least 15 minutes to take and plot a two-star fix with present methods. This is quite a long time in the air, though not prohibitive with present-day aircraft, and in consequence astro-navigation is now used extensively only on long flights over sea or desert where radio aids are lacking.

It is generally agreed that the increasing speed of modern aircraft, together with the availability of short-range radio and radar aids, necessitates a fresh approach to astronomical methods; less accuracy can be tolerated in the calculations but greater speed is essential. There are three stages after observation : the derivation of the position of the heavenly body observed, usually from the Air Almanac; the solution of the astronomical spherical triangle, usually by means of reduction tables ; and the resulting plotting of the position lines and fix.

Hitherto it has been the practice to compute the altitude and azimuth of a celestial body either for a D.R. position or a chosen position in the vicinity of the D.R. position and to compare the computed altitude with the observed altitude, the difference (the intercept) being marked off along a line drawn in the direction of the computed azimuth from the position used for computing, either ‘from’ or ‘towards’ the object; a perpendicular drawn at the end of the intercept is the position line of Marcq. St. Hilaire.

The method proposed consists in measuring by means of a specially designed sextant the altitude and azimuth of a star simultaneously and using these two quantities with the declination to solve the astronomical spherical triangle. In this way, both the latitude and, by means of certain simple additions and subtractions in terms of the local hour angle which is found directly, the longitude are determined.

If astronomical navigation is only required to give a ten-mile accuracy, as Mr. Parker has suggested in his paper, then its use will be mainly that of a last-aid in emergency. Radio, however, will give this degree of accuracy and, since a radio operator will in any case be carried, will naturally be more popular. On the other hand if astronomical navigation can be made to give a ½-mile accuracy it will become immensely more valuable than any other long-range aid. In the first place the signal received from the stars is completely reliable (at the heights which concern the air navigator, variable refraction can be ruled out) ; it is wholly independent of the ground; it provides a universal coverage which is free and is controlled by a non-political Body; and it can provide an accuracy greater than that of the long-range aids except the limited-purpose systems such as Oboe.

In this note, we propose to enquire into how far it may in principle be possible to employ zenith-photography for astro-navigation in the air, also to touch on the question of whether the mechanical difficulties can be adequately overcome. The question of principle seems in fact quite clear, but the practical side will undoubtedly demand much care and study by engineers and by practical navigators if the method is ever in fact to be adopted; we hope to show that the method has advantages sufficient to make the problem worthy of attention.

If astronomical navigation can be made to give its results in as simple a manner and as quickly as do the modern electronic systems, then clearly it can provide an aid whose usefulness will remain undisputed. The aim, then, should be to develop a system of astro-navigation which will give an immediate and continuous reading of, for instance, latitude and longitude; and it seems quite possible at the moment to envisage the nature of such a system. Its realization is perhaps another matter; and this may take time that perhaps the development of other systems will render ill-spent.

The ideas put forward in this paper are only concerned with the fundamentals of what, in the writer's opinion, is a possible solution to the problem; they are also not all new.

For the purpose of comparing results with the two wavelengths, 3 cm. and 10 cm., generally used in navigational radar, the Defence Forces Research Institute, in collaboration with the Swedish Admiralty, the Royal Pilot Service and the Marine Cartographical Institute, carried out systematic researches and experiments under various conditions, in view of the special meteorological and navigational circumstances prevailing in Swedish waters. Two radar equipments covering these wave-bands were obtained from the Research Institute and installed on board the marine survey ship Gustav Av Klint during the summer of 1947. A separate report has been issued on the results obtained during the summer months.

This paper first gives a brief account of the deviation theory applicable to magnetic compasses and a unified theoretical treatment of the principal heeling-error and pitching-error effects. Consequences of symmetry in soft-iron correctors are then considered, and a system of six equal soft-iron spheres at equal distances along three mutually perpendicular axes is shown to have no effect at the compass position, any diametral pair thus having a complete negative counterpart in the remaining four.

This leads to the deduction of the possibility of a simple form of corrector system in which soft-iron correctors remove those parts of the principal inclination errors which are due to induced magnetism. If the remaining part due to permanent magnetism is assumed to be removed by vertical magnets in the usual manner, the correctors when once adjusted would then require no readjustment on change of locality, in distinction from all known correctors at present in use or in course of manufacture, which require continual readjustment in these conditions.

I wish to thank Dr. Clemence for pointing out1 the flaw in the interpretation drawn in my paper that the error in observed altitude due to tilt of the sextant is a maximum when the altitudes are in the neighbourhood of 45°. The purpose of a correction table is either to supply the correction or to indicate the most favourable or unfavourable circumstances. I agree that my table does not fulfil this purpose; the argument β is unknown. Moreover the table gives corrections for all combinations of altitude and β this is incorrect, as some values of β are impossible for some altitudes, and a square form of table is therefore not permissible.

In a paper under the above title (Journal, Vol. 1, p. 266) J. P. G. Worlledge has made the useful suggestion that sextant certificates should give a critical table for the corrections instead of the present practice of giving the corrections at a few equally spaced readings. Unfortunately the method which he gives of deriving the proposed form from the present form is unsound. The centring error is correctly stated as

where Z is the sextant reading (the difference between Z and the true angle in this formula is negligible). But part of the centring error is included in the index error, so that to obtain the part of the centring error shown on the certificate the value of C for Z= 0 must be subtracted. This yields

for the formula of the correction.