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of failure made necessary for all employed on this arduous service. That so few flying-boats were lost on such patrols says much for the care with which the instruments were attended to and the skill with which their indications were heeded. An error of only two degrees in the course made good would throw out the position by over 3 m. in each too flown: the consequences on a misty day for an aircraft trying to make, say, the Scilly Is. base can be imagined. There were then no facilities for astronomical navigation, and dead reckoning had to be relied upon.

Not only had the flying-boats on war service to be navigated but the pilot and observer had also to " navigate " a bomb to its desired target. Since a bomb, or any other heavy body, maintains the course and speed of its carrier aircraft substantially unaltered during its fall to sea level, the sighting problem is the same as the dead-reckon- ing navigation problem: in fact, one observing instrument can serve both purposes. The horizontal motion of the bomb is com- pounded of the wind velocity and the air speed of the craft. The distance it will travel horizontally will be the product of the resultant of these two velocities and the time taken to fall from the height at which the aircraft is operating. This then must be the horizontal distance of the craft from its target at the moment of release and the line of attack must of course be that of the course being made good. The angle ahead of the vertical which the target subtends at the moment of release is called the sighting angle, and obviously it will vary with the direction in which the target is attacked unless the wind velocity happens to be zero. This requires that the instru- ment should be set for height, air speed, wind velocity and wind direction, and further that it should make automatic provision for the right combination of these elements for any direction of attack.

FIG. 23 Course-Setting Sight

The best known instrument for doing this is the course-setting sight shown in the illustration (fig. 23), and much used on flying- boats; in its navigational use it enables the velocity and direction of the wind to be measured whilst in flight, and it indicates the course to be steered for any given track, and the time taken in flying any desired distance in that direction. Towards the end of the war the French made some use of navigational bomb sights, and the United States Government had a large number constructed, but so far as is known no such efforts were made elsewhere.

For D.R. navigation on land aircraft use is often made of an instrument called an aero bearing plate. This was an adaptation of a marine bearing plate, or pelorus, having a transparent centre to admit of vertical observations of the ground, and having one or more longitudinal rods or wires which could be aligned parallel to the apparent earth flow so as to enable the drift angle to be read off. A graduated height bar also permitted the ground speed to be measured by noting the time taken for an object on the earth to pass through the vertical angle corresponding to a distance of flight of half a mile, or other convenient distance.

New Navigational Instruments. One of the first instruments known to have been used for the determination of latitude in mari- time navigation was the astrolabe. This device consisted of a pendulous disc graduated round its circumference in degrees and carrying at its centre a rod fitted with back and fore sights the inclination of which to the horizontal could be read off on the degree scale. A sight on a star would therefore give a measurement of its altitude. The use of a pendulum or " plumb bob " is, of course, a familiar way of obtaining a vertical line, but it suffers from the disadvantage that it no longer indicates truly if its point of attach- ment is not kept still. On board ship the point of support is neces- sarily in general motion and in consequence the pendulum con- tinually oscillates: its average position still gives the vertical, but it is a tedious business to find what the average position really is. Seamen turned, therefore, to the visible horizon as a more satis- factory datum from which to measure the altitude of heavenly

bodies; the early cross-staffs were inaccurate, but a nearly perfect form of instrument for this purpose was discovered in the Hadley sextant of 1731. It depended on the very important fact that if a beam of light be reflected from two plane mirrors in sequence, the total angle through which the beam is turned depends only upon the angle between the two mirrors and not on the angle between the rays of light and the mirrors themselves. Thus, if the two mirrors are fixed at an angle of 40 to one another, the angle through which the ray of light will be turned after the double reflexion will be exactly 80; if this reflecting system be now used to view a star having an angular elevation above the visible horizon of 80 then the star will appear to be " brought down " to the horizon and its apparent position will not be affected, however much the frame carrying the two mirrors may be rocked in a vertical plane. It will easily be seen that for use on a rolling platform, such as the deck of a ship, this is a most valuable property. The seaman will see the horizon rising and falling relative to the ship, but the image of the star will rise and fall with it. If the two images only came into coincidence when the deck was level, the instrument would be useless. It is the fact that star image and horizon appear to move together when the ship rolls or pitches which makes the sextant the valuable instrument it is. Inasmuch as the pitching and rolling of an aircraft is sometimes just as bad as the pitching and rolling of a seacraft, it might be thought that the Hadley sextant would equally be of use in the air. Indeed, the instrument is equally available, but the horizon is not. At 10,000 ft. height the horizon is about 90 m. away, and unless the day is exceptionally clear there will be sufficient mist to prevent so distant a horizon being visible as a clear line. If the horizon has therefore to be abandoned as a datum line, it be- comes necessary to fall back once more on the method of the mediae- val astrolabe and to employ plumb-bob methods of obtaining the vertical. This, of course, has the great disadvantage that it is only the average of a number of such observations that can give the true answer.

There is, however, a half-way house, though not a good one. Although the true horizon may be invisible there will often be false horizons given by the upper surface of cloud layers or banks of mist. These false horizons are not so far below the level of the aircraft as is the sea, hence their distance is much less and the line of separation between cloud level and sky is often sufficiently sharp to be of use. The great drawback is, however, the absence of definite knowledge of the height of such cloud levels, and therefore of their value as datum lines for sextant observations. A wrong guess at the height may give a totally false value to the sun's altitude, and therefore to the position line deduced from it. Attempts have been made to avoid such errors by assuming that the false horizon on the port side is of the same altitude as that to starboard, and then, by taking a point half-way in between as the zenith, to make all measurements from that as datum. This is correct just as often as the two horizons do happen to be of the same height ; but it does not appear that this is always the case, nor in fact is a second horizon always visible, and at night time neither the one nor the other. Moreover, such level cloud or mist layers can only be expected when the temperature lapse rate is small and the air is very stable. On very many occasions these conditions do not hold, the air is frequently " bumpy," and the cloud masses heaped and tumbled. Speaking generally, the condi- tions in which large flat cloud sheets extend are conditions favourable to navigational measurements, and they are also the conditions in which accurate knowledge of position is most essential. Such conditions arise when the temperature falls but slowly with altitude. When this lapse rate (as it is called) is much lower than the 10 C. per km. which marks the condition of instability, there is little atmos- pheric turbulence, and the aircraft is comparatively steady; even a plumb-bob instrument is then a convenient method of making measurements. A spirit level is of course a form of plumb-bob, in that the bubble is a kind of inverted " bob," which tries to get as high up as possible instead of as low down. Such levels have long been used in inclinometers for surveying, witness the well-known " Abney level." They suffer, however, from the disadvantage that when the instrument rocks, the image and bubble move in opposite directions. No such device could be a success in the air, and it is necessary to incorporate the double reflexion method or its equiva- lent of the Hadley sextant. This has been done by the staff of the Royal Aircraft Establishment, Farnborough, in England, and by Prof. Wilson in America.

The principle of action of the R.A.E. instrument is shown in fig. 24. la this instrument known as the R.A.E. bubble sextant the vertical is given by the position of the bubble in a spherical level, capable of being illuminated at will by a little electric lamp. The eye may take up either position (i) or position (2). The former is best for star or planet observations, and the latter for those on the sun, though theoretically there is no reason why either position should not be used for all observations. It is a matter of convenience which is used ; a star is more easily identified and held in view by the method of direct vision, whilst for observations of the sun there is no risk of confounding it with any other heavenly body, and it is much more comfortable to the eve to look downwards and so avoid the glare of the sky in the neighbourhood of the sun. The lens is chosen to have a focal length equal to its optical distance from the bubble, and since the curvature of the upper surface of the latter is