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to give the true result. For surveying work an accurate measure of the height is of special importance.

Reduction of A stronomical Observations. The traditional method of maritime navigation is to employ logarithmic tables for the solution of the spherical triangle. The problem is: given the declination of the heavenly body, the latitude of the assumed position and the hour angle at the moment of observation, to determine the corresponding altitude of the heavenly body. The difference between the altitude

To make this calculation by means of logarithmic tables is simple enough on board an airship, but is not easily performed in an aero- plane. Nor is the degree of accuracy to which the existing tables are worked out necessary for air navigation. A method, which was tried in a Handley Page machine, was to use the rectangular nomo- gram devised by d'Ocagne, but it was found that within the limits of space available it was not possible to draw the diagram to a suffi- ciently large scale to ensure the final answer being accurate withfn the necessary one or two minutes of arc. (It is true that the deter- mination of position to within 10 m. easily suffices, but there is not infrequently an error of this amount in the sextant observations themselves; and to these unavoidable errors of observation it is not- desired to add any larger error due to the process of reduction of more than one or two miles.) Trial was next made of the ingenious method suggested by Veater of employing a Mercator projection of the sphere and using certain curves drawn thereon to solve the spherical triangle by the equivalent of a rotation of the sphere. This method gave, in small compass, a means of attaining the accuracy desired ; but it was difficult to use the curves without eye strain, and the method eventually gave place to the cylindrical slide rule devised by L. C. Bygrave. The whole procedure is by this last means made both simple and accurate. The advantage of the spiral scale of cylin- drical rules is that an immense length of scale is compactly housed ; an accuracy on this rule of one or two minutes of arc is easily attained.

Directional Wireless. During recent years wireless telegraphy has been made use of for the determination of the position of both sea- craft and aircraft. The invention followed from the discovery of a method by which the direction from which wireless waves were arriving could be accurately measured. An analogy would be afforded were it possible to determine, from the receipt of ripples at the margin of a pond, the direction of the spot at which a stone had fallen into the water. It was found that if a rectangular coil hap- pened to be placed so as to face the direction from which the wireless waves were travelling, no current would flow in the coil, whilst if the latter were placed " edge on," it was possible to detect an oscillating current in the coil. In intermediate positions, intermediate results were obtained. Once, therefore, a search coil of this kind is mounted on a vertical axis it can be turned until the current is either a maxi- mum or a minimum, and by these means the direction of the sending station be determined. It is true that a station N.E., say, could not be distinguished from one to the S.W., but other considerations usually enable a right choice to be made from these two alternatives. In practice various electrical improvements have been made on this simple circuit but the principle is the same; and it is the results obtained by such means which are of importance to the navigator. The navigator will of course require of the wireless officer that W/T bearings so given shall be " true," and that corrections due to any possible bending of the waves shall have been allowed for.

There are two methods by which " directional wireless " (as it is termed) can be employed. The first and simplest is by having suit- able search coils mounted in wireless beacons ashore. Two or more of such beacons take note of the direction of the calling aircraft, and communicate with each other so that one of them can plot on a map the several bearings which, by their common point of intersection, determine the position. This is then communicated to the aircraft. This plan has the double disadvantage that the aircraft is forced to disclose its position, and that the number of messages sent out " into the air " is thereby increased. The alternative is to mount the search coil on the aircraft, and for the latter to determine the bear- ings of two or more sending stations, and to do its own position- plotting on the chart. The latter alternative is usually preferred, but it suffers from the difficulty that the bearing of the wave is not infrequently altered immediately prior to receipt by the influence of the many flying, and other, wires forming part of the structure of the aircraft. These are called quadrantal errors, and they correspond to the errors which would be obtained in magnetic compasses if devia- tion were not allowed for. A difficulty common to both methods lies in the bending of the ray's direction when crossing a coast line, or the boundary of day and night such effects need to be allowed for. The plotting of wireless bearings, whether in the aircraft or ashore, requires care. If, as is usual, a Mercator chart is employed, it has to be borne in mind that straight lines on such charts are not great circles, and since the waves travel along the latter (except for the disturbances above mentioned) it is necessary to draw the path of the waves by means of a certain curve, the bending of which will depend on its distance from the equator. Approximate methods of doing this are in use, but the best method (following Veater) is to make use of the Littrow projection of the sphere (more familiarly known as the " Weir diagram ").

Much work has still tobe done before it can be determined how accurately the position of an aircraft can be found by means of directional wireless. But it has a great use apart from position find- ing, since it enables a straying aircraft to fly back to its parent ship by flying " home " along the wave path. Its path may not be a straight line, and it may take some time to make the flight, but if persisted in it is bound to bring the craft home sooner or later.

World Flights. The famous world flights of 1919 and 1920 were the transatlantic crossings by the American flying-boat NC4, by the Vickers-Vimy aeroplane, and the rigid airship R34 (not forgetting the gallant attempt of the Sopwith aeroplane) ; the flight to Australia by a Vickers-Vimy aeroplane, and the several attempts to fly an aeroplane down the length of Africa.

In the case of the Australia flight the coast line was usually followed and methods of air pilotage, as distinct from air naviga- tion, sufficed. The African flights were in part over uncharted territory, and pilotage alone did not suffice; both there and, of course, in the transatlantic flights the course was steered by navigational methods. In the case of the R34 the operations were carried out by officers accustomed to the navigation of naval ships, and in so roomy a craft the work was much more easily arranged than in the more compact aeroplanes and flying- boats. Comm. Mackenzie Grieve, the navigator of the Sopwith, stated that even in his tiny aeroplane he navigated by celestial observations and found that his position, as given by his ob- servations of the stars, when picked up after the forced landing in the sea was " practically correct."

The instruments available in 1921 for navigation were much more satisfactory than those in use prior to 1920. In future world flights the determination of position, course and speed will not only be simpler and more speedy, but will also be very much more accurate than anything hitherto known in the history of air navigation.

BIBLIOGRAPHY. S. F. Card, Navigation Notes and Examples (igif), and Air Navigation Notes and Examples^ (1919); J. E. Dumbleton, Aerial Navigation (1920); H. E. Wimperis, Primer of Air Navigation (1920) ; Hawker and Grieve, Our Atlantic Attempt (1920).

(H. E. Wi.)

VII. CONTROL OF AIR TRAFFIC

The pre-war legislation of individual States generally pre- sumed sovereignty of the air, but the doctrine was not finally accepted until the World War. Thus in 1911, at the Madrid session of the Institute of International Law, a resolution was passed that " International aerial circulation is free, subject to the right of States to take certain steps, which shall be fixed, to ensure their security and that of the persons and property of their inhabitants." This principle was modified in the Report of the Committee on Aviation of the International Law Asso- ciation in 1913:

" It appears to the Committee impossible to contend that accord- ing to existing International law the air space is free, nor do they think that States would be willing to accept or to act on that view of the law. But they are of the opinion that, subject to such safe- guards as subjacent States may think it right to impose, aerial navigation should be permitted as a matter of comity.'

Though in some quarters the assertion of state sovereignty only up to some prescribed height was advocated, individual States, and among them Great Britain, asserted, mainly for military reasons, their right to close their atmosphere ab- solutely (usque ad coelum) to the aircraft of other States. It was the conflict of opinion between the British and German delegates, as to the right of each State to the exercise of control and juris- diction in the air space over its territories, that prevented the completion of an International Convention by the conference held in Paris in 1910. By the first British Aerial Navigation Act (1911) power was taken to prohibit the navigation of air- craft over prescribed areas. In the Act of 1913 this power was extended for the purposes of the defence or safety of the realm to the whole or any part of the coastline of the United Kingdom and territorial waters, while the Statutory Rules and Orders of that year limited the landing areas for aircraft coming from any place outside the United Kingdom to a comparatively few strips of coastline, and forbade foreign naval or military aircraft to pass over or land within any part of the United Kingdom except