sea navigation may be drawn on, and much of this experience is capable of direct application to the air. The earlier forms of marine navigation were of a rudimentary type and would now be included in the general term " pilotage." Whenever they could manage to do so the primitive sea voyagers were careful to keep in sight of the coastline, so that even a rough map sufficed to enable the position of the ship to be noted. The great voyagers of the middle ages were bolder and depended no longer on mere pilotage methods; then it was that scientific navigation had its birth. The compass came into use in Europe about the i4th century, and by its means, combined with a rough measurement of the speed of the craft through the sea, it was possible to keep a reckoning on the chart called a " dead reckoning," or briefly D.R. of the position from day to day. This allowed nothing for drift due to tides or currents or leeway, but since in the early voyages these were quite un- known in amount no allowances could be made. Experience showed that the D.R. position thus obtained was often con- siderably in error, and some check upon it became very neces- sary. For this the simple cross-staff and the astrolabe were em- ployed. With these instruments a rough measurement of the altitude of the sun at midday, or of the pole star at night, enabled the latitude to be determined to perhaps half a degree, or 30 nautical miles. But a simple latitude observation like this did not suffice to ascertain the ship's position, since it merely gave the information that it must lie somewhere on an east-west line drawn so many degrees N. or S. of the equator. If the course were N. or S., this measurement gave the run, but no check on the estimated course; whilst if the course were E. or W., the latitude measurement gave no information as to the run. Later on, when better instruments were available the introduc- tion of the Hadley sextant in 1731 marked a very real advance methods were adopted to enable longitude as well as latitude to be measured, but the necessary calculation of lunar distances was troublesome, and it was not until the perfection of the marine chronometer in the latter half of the i8th century that it became open to the average sea navigator to work out his longi- tude as well as his latitude, and so obtain a check on both run and course.
Experience with air navigation has followed a generally sim- ilar path; compressed of course into a very few years. When air craft were first navigated they followed pilotage methods only; the earth was continuously, or almost continuously, in sight, and the position from time to time was ascertained by the recognition of landmarks, or, where these were scarce, by a system of dead reckoning based on the compass course and the speed through the air. Here, however, arises the great difference between sea and air conditions. Currents in the sea rarely exceed a few knots, but in the air are quite commonly of 20 knots, velocity, and may be even four or five times as much ; moreover, whilst the former may be charted the latter cannot. This would tend to make air navigation the more difficult, but its effect is mitigated by the fact that the air ocean has the great merit for this purpose of being transparent (except for occasional cloud sheets) and of enabling the direction and course of air currents to be measured by watching the apparent motion of objects on the earth's surface. A wind of 50 knots opposing an aircraft having a speed through the air of 100 knots will re- duce its speed over ground by one-half, while if favouring it will cause the ground speed to exceed the air speed by 50%: neither, however, will cause any apparent sideways drift of the craft. If, in either of these cases, the speed over the ground be measured in some convenient way, it is possible to determine both the velocity and direction of the air current, i.e. the wind. A similar but slightly more troublesome measurement gives the wind velocity, and direction, when the flight is oblique to the wind. This ability is not shared by the sea navigator, who cannot see the bottom of the ocean on which he sails, and has instead to assume the accuracy of the information given on his charts and in his sailing directions.
The fact that an aircraft, when flying with the wind, may have a ground speed of as much as 1 50 to 200 knots, makes it essential
to determine the position with rapidity. An observation which took 10 minutes to reduce would afford information of a position some 30 nautical m. to the rear. Hence speedy methods are essential; and fortunately owing to the absence of aerial rocks and shoals, and the extensive field of view much less accuracy of position-finding is required in the air than at sea. An accuracy of determination of 10 m. suffices for almost all air purposes; whereas the sea navigator aims hopefully at "an accuracy within a mile or less.
Dead Reckoning. Hakluyt, recording in 1580 " instructions and notes very necessary and needful to be observed," points out that " in keeping your dead reckoning, it is necessary that you doe note at the ende of every foure glasses what way the shippe hath made (by your best proofes, to be used) and how her way hath beene through the water, considering withall for the sagge of the sea, to leewards, according as you shall finde it growe. Doe you diligently observe the latitude as often, and in as many places as you may possible; and also the variation of the compasse. . . ." These instructions, so necessary and needful to be observed at sea, are for air navigation not less so. But in the latter case special difficulties arise. The course over the ground is determined by the apparent motion of objects on the earth relative to the fore-and-aft line of the craft ; but owing to the rolling, yawing and pitching of the latter, and of all instruments carried upon it, such measurements are far from simple. However straight the pilot may try to fly he will yaw slightly from side to side, and this will cause the flight path to be more or less sinusoidal, with an accompanying lateral acceleration tending to cause the machine itself, and all instruments fastened to it, to roll periodically to port or starboard. This will cause any objects below the craft to appear to follow an oscillatory path instead of a straight line, and so make the determination of the angle of drift much more difficult. Nor is it possible to surmount this obstacle by making the observing apparatus pendulous in the hope that it will remain vertical. The lateral acceleration due to the slightly curved path will cause the centre of gravity of the pendulous mass to seek a position such that the moments about the point of support of the weight will balance; in other words, the instrument tends to set itself not to the true vertical but to the " apparent vertical " given by the resultant of the gravitational and the lateral acceleration. If the pendulous instrument has a substantial amount of inertia, it will not have time to pick up this direction before the aircraft will have entered on a fresh part of its sinusoidal path corre- sponding to a fresh position of the apparent vertical. The instrument therefore continually hunts the apparent vertical, but is always in arrear to the one side or the other. It may appear that by making the inertia sufficiently great the motion of the instrument would be so slow and so slight as to be negligible, but calculation shows that unless gyrostatic forces, with their attendant complication, are brought into play it is not possible, within the necessary limits of dimensions of the craft, to achieve this. These ever-present oscilla- tions are of great importance in the study of aircraft instruments. Not only is the apparatus for measuring the angle of drift of the ground affected by them, but equally any apparatus for getting a reading of the ground speed, and, by no means least, the magnetic compass itself. Compasses fitted to ships usually have a period of oscillation much longer than the period of roll of the ship, hence the compass has not time to be very much disturbed by such movements. In aeroplanes, however, the period of roll is longer and the early types of aircraft compass by an unlucky coincidence had just about the same period, hence resonance was a frequent occurrence, and wild oscillations of the compass needle were all too frequently reported. Later on the cause of the phenomenon was recognized and a remedy was found.
That a magnetic compass points magnetic N. instead of true N. gives rise to the correction called " variation," and this applies equally to sea and air craft. Variation charts are equally available and no difficulty is presented. With the correction known as " deviation " due to the magnetism residing in the structure of the craft itself, air conditions are simpler than those at sea, in that the masses of magnetic material near the compass position are much less in amount; but on the other hand the value of the deviation on each point of the compass is rather more troublesome to determine and much more likely to vary with the life history- of the craft itself.
The measurement of the speed through the air fortunately pre- sents none of these difficulties since the forces produced by the relative air stream are dependent only on velocity and air density, and the latter being known for any given altitude of flight it is possible to obtain a measure of velocity through the air free from any complication.
Except for flying-boats engaged on anti-submarine patrol scarcely any aircraft prior to the end of the World War had need to employ navigational methods of flight: ordinary pilotage sufficed for their journeys. The work of the flying-boat patrols, however, required meticulous care in navigation since their duties carried them far out of sight of land and it was imperative that they should make a landfall before the petrol supply ran out. The method employed was dead-reckoning navigation carried out with that care which the risk