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Rh th_> instrument would be attached to axles whose axes were on any parts of AX and BY. AXQZ and BYQZ represent planes of which the sighting planes form small parts. It is obvious that QZ is hori- zontal, and that ZK, PL or any vertical line between QZ and the horizontal line KL (which is parallel to the axes of the sighting planes) represents the height of an aircraft in the line ZQ, say at P. In the simplest form of height-finder, the plotting is done on a board fixed beneath B, the triangle AZB being reproduced there on a small scale and upside down. A straight edge is attached to the sighting frame at B and consequently moved round B in front of the board as the elevation of the frame is altered. Another straight edge is pivoted on the right of B at a distance from it which represents AB to the scale of the instrument. It is kept set to the altitude angle which is measured at A and telephoned to B. The point where the two straight edges intersect consequently represents the point Z. Upon the board below B, a series of horizontal lines are marked, their distance from a zero line passing through the pivots of the straight edges representing heights above the ground, to the scale of the instrument. The height of the target can therefore be ascer- tained by noting against which of the horizontal lines on the board the intersection of the two straight edges comes. Such height- finders have serious disadvantages, the principal one being the difficulty in getting the two instruments on to the same target.

Height- and Range-finder. Towards the end of the war Messrs. Barr and Stroud produced a most ingenious instrument which recorded both the height and range of aircraft, and which was at once adopted by the British Government.

It is used in a similar manner to an ordinary one-man range- finder, and the observer has only to keep the aircraft in the field of view and make coincidences. As will be explained later, if the height of the aircraft remains constant the coincidence will not alter as the range alters. The field of view is so arranged that the rays of light entering by the left window of the instrument form an erect image over the whole field, with the exception of a narrow central hori- zontal strip in which an inverted image is formed by the rays enter- ing by the right window. The lower separating line is the one on which coincidences are made. The advantage of this " strip " system is that it is considerably easier to keep the aircraft in the field of view than if the field were divided into two equal parts, one of them being inverted. As in field instruments, the inversion of the image in the field above the separating line is found to facilitate making accurate coincidences.

The eye-piece of the range-finder is placed at right angles to the plane of triangulation, so that if the angle of sight to the target is 60 the observer looks down at an angle of 30. It is provided with two lens combinations on a rotatable cap which give magnifications of 15 and 25 diameters, and also with light filters for varying atmos- pheric conditions. There is a window above and to the left of the eye-piece, through which the usual ivory range scale can be seen.

In a small casing on the top of the range-finder there is a most ingenious mechanism which converts ranges into the heights corre- sponding to them as the angle of sight varies. The ranges and heights can be read through two windows in close proximity to one another. This mechanism actually solves the trigonometrical for- mula r sin o = h; where r is the range of the target, a the angle of sight to it, and h its height. This formula may be written as: log r+log sin a = log h; and it is mechanically solved as follows: a differential gear is employed, the upper member of which is rotated in accordance with a logarithmic sine scale of angles of sight, and the lower member is rotated in accordance with a logarithmic scale of ranges, the jockey wheel accordingly revolving around the axis of the differential with a motion corresponding to a logarithmic scale of heights. It will be noted that the angle of elevation and the range are known, or rather are determined by the instrument, so that the duty of the gears is to convert the angle and range scales to logarith- mic form and then to add them together by means of the differential gear as explained above. The conversion of the reciprocal range scale motion of the range-finder deflecting prism gear into logarith- mic range scale motion, and the angular motion, of the range-finder in elevation into motion corresponding to a logarithmic scale of sines, is done in each case by means of toothed spiral gears.

The gearing is connected through three couplings to the working head, the elevation gear and the deflecting prism gear respectively. By means of suitable gearing the jockey wheel of the differential is driven from the working head, the upper member by the elevation gear, and the lower member by the deflecting prism gear. The range scale is connected to the lower member, and the height scale to a level wheel carrying the jockey wheel.

The advantage of arranging the working head to operate the jockey wheel is that in the frequent case of aircraft flying at a con- stant height the images in the field of view, when once set, can be kept in coincidence by simply elevating the instrument so as to keep the target in the centre of the field, without any rotation of the work- ing head. The movement of the instrument in elevation auto- matically controls the position of the deflecting prism, the height scale remaining unaltered so long as the working head is not rotated. When the target rises or falls, the images will move out of coin- cidence and must be brought back into alignment by rotating the working head, thus altering the reading of the height scale by the appropriate amount. The working head and elevating gear may, of

course, be worked at one time, in which case the combined effect of the spiral gears and the differential is that the two scales always read correctly as long as the coincidence is maintained.

The instrument has a base length of two metres, and is carried in the mounting forks in two eccentric bearing rings, the object of the eccentricity being to balance the weight of the height-scale gear box as the instrument is rotated in elevation. The elevating gear with a handwheel on the left of the observer, is of the worm-wheel type. The handwheel is provided with a two-speed clutch ; the speed being changed by merely pressing in or releasing, with the palm of the hand, a small lever connected with the hand grip.

The azimuth training gear is also of the worm and worm-wheel type and has a two-speed clutch. Its handwheel is on the right of the eye-piece, and in a convenient position for the man who, looking through a small prismatic telescope near the right-hand end of the instrument, keeps it laid for direction on the target.

The worm wheels for movements in both azimuth and altitude are mounted on friction slip-bearings, so that the instrument can be rapidly moved and the target brought into its field of view. An elevating lever is fitted near the left-hand end of the instrument to allow of rapid elevation. An adjustable azimuth scale and reader are provided; and a means of levelling the upper part of the mounting. Before using the instrument, its correct levelling must be attended to and checked by means of two bubbles attached to the upper part of the mounting. The lower part of the mounting is a very rigidly constructed tripod with pointed feet having discs to prevent their sinking into soft ground.

Three operators are required for working the instrument, viz. : (l) The observer who makes " coincidences " by turning the working head on the top of the instrument with his right hand, and who also keeps the separating line on the target by turning the elevation handwheel with his left hand. (2) The operator for line who, looking through the prismatic sighting telescope, traverses the instrument with the handwheel and keeps the cross line in his telescope accu- rately laid for line on the target ; and (3) the scale reader, who, stand- ing in front of the instrument, reads heights off the height scale; and, if required, also reads the range and angle of sight scales.

In anti-aircraft gunnery, where the target may move at a speed of two or more miles a minute, there is great difficulty in ascertaining what deflections are required to compensate for the travel of the target during the time of flight of the projectile. There is not only the lateral deflection to be considered, as with a ship moving in one plane; but also a vertical one. It is obvious that if an aircraft is flying at a constant height, the angle of sight to it from the gun will not remain constant. Vertical deflection equal to the alteration of the angle of sight during the time of flight of the projectile must therefore be allowed for. Another difficulty arises in connexion with the setting of the fuze. The fuze will not burn at the same rate if the projectile is fixed at different angles of sight, owing to the variation of atmospheric pressures at different heights. To help to overcome these difficulties a most ingenious apparatus was brought out during the war by Messrs. Brocq of Paris, and was adopted by most of the Allied Powers.

The general principle of the instrument is as follows: The height of the target must first be measured by a height-finder and set on the instrument. Two operators, who face one another, follow the target, looking through two telescopes which are rigidly connected. One keeps a vertical cross line in his telescope in line with the target by turning a traversing handle; and the other keeps a horizontal cross line in line, by turning an elevating handle. Connected with the traversing and elevating handles are the armatures of two magnetos which, when turned, generate electric currents, the voltages of the currents depending upon the speed at which they are turned. These currents are transmitted to two special voltmeters (attached to the gun mountings near the layers) from which the lateral and vertical deflections required can be read off, and then applied to the sights. On their way to the voltmeters the currents pass through rheostats which modify them in such a way that the deflections recorded are correct for the time of burning of the fuze. The exact length of fuze required to burst the shell at the target can also be read off another part of the instrument.

The general arrangement of the apparatus is shown diagrammati- cally in fig. 4. It consists of three main parts, viz. :

I. The double telescope, which consists of a metal drum upon which are mounted, on the same spindle, the two right-angle tele- scopes referred to above. The traversing and elevation handles are placed conveniently for the two operators. Each has a quick and slow motion (four to one), the ajteration from one to the other being effected by pushing in or putting out the handle. When a quick release knot at the top of the instrument is pressed down, the gears are put out of action, and the telescope can be quickly moved until the target is in their fields of view. Angles of sight and bearings can be read off conveniently placed scales, if required. When the handles are turned, the currents generated by the magnetos pass along