Range

"Range \- FINDERS AND POSITION-FINDERS (see 22.888).- Recent improvements have rendered many of the earlier types of range-finders obsolete, and the following features are common to all modern coincidence range-finders. The range-finder usually consists of two main parts, viz: - a strong outer tube and an inner frame which supports the delicate telescopic system, any slight derangement of which would seriously upset the accuracy of the range-finder. The outer tube is made as strong and rigid as possible, having regard to the weight which can be allowed. The inner frame is supported in such a way that any slight bending of the outer tube will not affect it.

Some form of double end reflector is always used. This at one time consisted of a pentagonal prism, but large pentagonals are very costly; they absorb a good deal of light and are liable to slight distortion with changes of temperature. There is therefore a tendency to replace them by a combination of two silvered plane mirrors inclined to one another at 45°, and either fixed in a mount made of a metal having the same coefficient of expansion as glass, or rigidly attached to an upper and lower glass support, to prevent change in their relative positions.

The central reflectors usually take the form of two or more prisms balsamed together, and are known as the centre prism combination. Their object is to deflect the rays received through the two ends of the range-finder into the eye-piece, and to present the two images of the target in the field of view immediately above and below a thin separating line. Their construction is usually rather complicated. The fine separating line is as a rule obtained by means of a special separating prism; or by the edge of a silvered surface on one of the prisms, so arranged that the rays forming one image pass through the prism, and those forming the other image are reflected by the silvered surface.

The centre prism combination is also used for erecting or inverting the images, and for defining the limits of the fields of view received from each half of the range-finder. The arrangements of fields of view usually met with are the following: - I. The field of view is divided into two equal halves and the images in both are erect. When a coincidence has been made, the separating line cuts straight through the image of the target. This system is used with naval and coast defence range-finders which have to deal with targets having long vertical features, e.g. masts and funnels. It is known as the " erect " system.

2\. The field cf view is divided into two parts by the separating line. One field (in field range-finders usually the lower) is erect, and the other one is a replica of it, being inverted up for down but not right for left. With this system it is much easier to make an accurate coincidence on small targets, but it has the slight drawback that the total actual field of view is necessarily considerably smaller than with the erect system, and a slight elevation or depression of the range-finder may cause the target to pass the separating line and disappear. This, however, is not of much importance if the target is a stationary or slowly moving one. The upper field is often made smaller than the lower, so that as much ground as possible may be seen in the field of view. This system is known as the " invert," and is used in many field range-finders.

3\. The whole field is erect with the exception of a small central rectangle in which the image is inverted. The advantage of this system is that the field of view is as large as that of a range-finder of the erect type, except that the part covered by the rectangle is missing. It is known as the " invert rectangle " and is used in many field range-finders, especially in foreign armies.

4\. The whole field is erect with the exception of a narrow horizontal strip which passes right across its centre. The field in the strip may be either erect or inverted. This system, known as the " strip " system, is used in the British heightand range-finder.

In early range-finders the axis of the eye-piece was horizontal when targets in the horizontal plane were being viewed. It is now usually inclined downwards at angles of 45°, 60°, or even 90 for anti-aircraft work, so that the range-taker can observe from a more comfortable position. Eye-pieces can be focussed for individual observers, the two images of the target and the separating line coming to focus simultaneously. Coloured and neutral tinted glasses are useful in cutting out excessive glare, haze, etc. In some range-finders, the magnification of the eye-piece can be altered so as to obtain the best effect under various atmospheric conditions. Astigmatisers are sometimes used for drawing out a point of light or small object into long lines or bands. Coincidence, which without their use would be almost impossible to effect, can then easily be made. They consist of two negative cylindrical lenses with horizontal axes, one being placed at each end of the range-finder between the pentagonal and the objective.

Range-finders are provided with halving and coincidence adjustment heads, which, when turned slowly, move the optical systems mentioned above. Correct adjustment is of course essential for accurate work.

## Accuracy of One-man Range-finders

The accuracy of the range-finder, other things being the same, depends upon its base length and magnification; but there are limits to the magnification which can be conveniently used. It is usually between Io diameters (for the smaller range-finders) and 30 (for the largest). Under good conditions, two images can be aligned across a fine separating line, with an error of only a few seconds. There is little doubt that this degree of accuracy can be obtained under the best atmospheric conditions and when the target is stationary, as the mean result of several observations being taken as the range. If, however, the atmospheric conditions are bad and the target is moving rapidly, such accuracy cannot be expected.

The base lengths of range-finders used in the field usually vary between half a metre and two metres. The Barr and Stroud range-finder with a base of one metre, which is used for field artillery by the British and other armies, is typical.

German field coincidence range-finders, such as the Zeiss and Goerz, are used in a similar way to the Barr and Stroud, although their construction differs materially in details. Many of these were introduced to avoid infringements of earlier patents. The chief features of Zeiss coincidence range-finders are that they have only one eye-piece in which are seen a small rectangular inverted field in the centre of a large erect field and on the left of these a range scale. Coincidence is effected by revolving a working head which rotates two wedge-shaped prisms in opposite directions.

## Stereoscopic Range-finders

The principle of the stereoscopic range-finder is entirely different. Stereoscopic range-finders have not found much favour in the British services; but they have been extensively used by the Germans. Speaking generally, a stereoscopic range-finder contains the elements of a stereoscopic telescope rigidly mounted in a tube. It is very similar in outward appearance to a coincidence range-finder with two eye-pieces. Objects viewed through a stereoscopic range-finder are seen to stand out in stereoscopic relief; and it is comparatively easy for the observer to judge their relative distances. The actual distance of a target is obtained with the assistance of one or more marks which are seen in stereoscopic relief in the field of view. By means of suitable optical arrangements the stereoscopic relief of either the objects in the field of view or of the mark can be varied until the target and mark appear to the observer to be the same distance away from him. The range of the target can then be read off a range-scale attached. The mark which is seen in stereoscopic relief, really consists of two similar marks which are photographed on glass diaphragms mounted in front of the eye-pieces of the range-finder. If the two marks are on the optical axes of the two halves of the range-finder, they will appear to the observer as one mark at an infinite distance. If the two marks on the diaphragms are made to approach one another, the resulting single mark will appear to come towards the observer. In the later stereoscopic range-finders, marks in the eye-pieces are adjusted so as to appear to be at a fixed distance when seen stereoscopically. The view containing the target appears to approach or recede from the observer when the working head is turned; and the range is read off from an external range scale or drum.

Stereoscopic range-finders suffer from the disadvantages that very few people are able to see stereoscopically with sufficient exactness to obtain good results and the degree of accuracy obtained by a range-taker appears to vary from time to time. Under the same atmospheric conditions, stereoscopic range-finders do not appear to give such good results as coincidence ones. Owing to the marks on the diaphragms in the eye-pieces being more distinct than the image of the target, there is difficulty in deciding when they are at the same apparent distance. On the other hand, owing to both eyes being used, the target should be seen more distinctly than through a coincidence range-finder. Ranges of targets with the sky as a background, e.g. aircraft, masts of ships, and trees on a crest line, are comparatively easy to take with a stereoscopic range-finder; but those of comparatively indistinct objects, objects with near backgrounds and objects in a shadow, e.g. a gun under a tree, are very much more difficult to take.

## Directors

The director is an instrument employed chiefly for the measurement of azimuth angles and angles of sight. There are numerous patterns of these instruments. Some are of simple form; while others are complicated and are provided with quick and slow motion movements for their azimuth and altitude movements and for laying on a gun or target without the setting of their azimuth scales being altered. Some are used as directors pure and simple, whilst others are provided with powerful telescopes for observing fire. British directors are graduated in degrees and minutes, whereas those of nearly all other powers are graduated in milliemes. Instruments graduated in milliemes can be made much more compact than those graduated in degrees and minutes, as the main azimuth plate has only 64 divisions instead of 360. The azimuth scales of some German directors are graduated in 16ths of a degree and 16ths of a degree are also sometimes used for angle-of-sight scales.

The German director for field artillery is a good example of modern types of this instrument. Powerful telescopes like the stereoscopic or scissors telescope are often provided with fittings which enable them to be used as directors as well as for observing fire. Azimuth angles can be measured by means of an azimuth scale, and angles of sight by means of a small bubble and scale. In one pattern of German stereoscopic telescope, the angle of sight is measured by means of a device which is compactly pldced between the two arms of the telescope, above its elevating gear.

The Field Plotter is an instrument used for obtaining the gun range when the range-finder is not near the gun. It consists of two similar nickel-plated steel plates, having azimuth scales and a scale of yards (upon which the distance of the gun from the range-finder can be set) engraved upon them, and two range arms which are pivoted at the centres of the azimuth scales and connected by means of a slider. The two plates are slid along one another until the distance between the gun and the range-finder is opposite the reader. The slider is then moved until an arrow upon it reads on the arm the distance from the range-finder to the target. The arm is then moved until another arrow reads the angle, recorded by the director, between the target and the gun. The plotter is then turned over, and the range from the gun to the target and the angle at the gun between the target and the director are read off. When fire has been opened, it is necessary to observe the results, so that corrections for both range and direction may be made. Also if time fuzes are used, the angular height above the target at which they burst the shell must be observed and corrected if necessary. Various instruments, e.g. graticuled binoculars, stereoscopic telescopes and periscopes, are used for this purpose.

The binoculars used in the British service are of the prismatic type having a magnification of six diameters and are fitted with a glass diaphragm in front of the right eye-piece on which are engraved the vertical lines 2° apart; their heights above the horizontal line being alternately 2° and z°. The central line is longer, extending x2° above, and z° below the horizontal line. When observing fire, the point of intersection of the centre vertical line with the horizontal line is laid on the target; and, when the burst of the shell is observed, its angular distance to the right or left of the target and above it can be ascertained by noting its position with reference to the lines on the diaphragm. Graticules used by other continental powers vary very much in design and often consist of a very large number of short lines at definite distances from the axis of the telescope.

The stereoscopic or scissors telescope was very largely used in the World War, especially by the Germans. The British pattern has a magnification of io diameters and a field of view of 4°. The two arms can be used either vertically for observation from below cover, or in line with one another for observation from behind vertical cover.

FOR Coast Defence Coast defence range-finding instruments are usually either range-finders or position-finders. A range-finder measures ranges from itself to the target and may also record the bearing of the target. A position-finder measures ranges and bearings to the target from the point for which it has been adjusted. This would usually be a gun which may be many hundred yards away from the position-finder. The position-finder sometimes also records the range and bearing of the target from its own position. Coast defence range-finding instruments may be divided into classes, depending upon the nature of their bases, as follows: Depression instruments, having vertical bases (either rangefinders or position-finders) the accuracy of which depends upon their height above the sea-level. They measure ranges with equal accuracy in all directions; and, if sufficient height is available, they are most reliable instruments. It is usually considered that, to obtain ranges with an error not exceeding i %, loo ft. of height is required for every 5,000 yd. of range. All that the range-taker has to do is to keep a cross wire in the telescope of his instrument laid on the water line of the target.

2\. Instruments having a fixed horizontal base (usually positionfinders). Each usually consists of two instruments installed at the ends of a base which may be several thousand yards in length, the length required depending upon the range and arc of fire of the gun for which the instrument has been installed. The instrument at one end of the base is known as a transmitter and usually consists of a telescope mounted above an azimuth circle. It measures the bearing of the target and transmits it to the instrument at the other end of the base which is known as the receiving instrument. The bearings may be transmitted by telephone; or, as the telescope is traversed, electric impulses may cause some portion of the receiving instrument, e.g. a metal arm or a dial, to move automatically. The receiving instrument is usually an accurate, solidly constructed plotter, made to a certain scale, e.g. 500 yd. to an inch. In its simplest form it would consist of a base plate upon which two straight arms were pivoted, the relative positions of the pivots being, to the scale of the instrument, the same as those of the transmitter and receiving instru ment. The first arm would be kept set to the azimuth angles received from the transmitter, and the second arm would be kept in line with the target by means of a telescope attached to it. The point where the two arms intersect would represent the relative position of the target. The arms being graduated in ranges and moving over azimuth scales, the range and bearing of the target from either end of the base could be read off. By means of a third arm, pivoted to the base plate in the position representing the position of the gun, the range and bearing of the target from the gun could be ascertained if the arm were brought above or below the point of intersection of the two other arms. Horizontal-base range-finding instruments are often designed to allow of several alternative bases being used, the pivots of the arms in the receiving instrument being set for the base which is most suitable for the conditions prevailing at the time. Thus for very long ranges a very long base would be used; but, if the visibility were bad, a much shorter one might be preferable. Horizontal-base instruments have certain disadvantages. For a definite range, their accuracy varies with the position of the target. It is greatest when the target is opposite the centre of the base, decreases as the target moves to the right or left, and disappears altogether when the target is in line with the base. It is somewhat difficult for the receiving instrument to indicate to the transmitter the target whose range is to be found. There are difficulties in passing azimuth angles from the transmitter to the receiving instrument. If they are telephoned, delay and errors are involved, and owing to the fact that they may alter at greatly varying rates there is usually some uncertainty as to the most suitable intervals in which they should be called out. If they are electrically transmitted, so as to move some part of the receiving instrument, the mechanism must be capable of moving in small steps of, say, one minute, in order to obtain the required accuracy, and at the same time it must be capable of moving quickly through a large angle when getting on to a target.

3\. One-man Range finders used for coast defences are constructed on the same general principles as those used in the field; but, as their weight and size must not be limited to the same degree, many modifications to make them as accurate and convenient as possible are introduced. Their base lengths are usually between 9 ft. and io metres, but even longer bases have been considered. They are practically always of the coincidence type with both fields erect.

The Mark III Depression Range finder (fig. 2) will be taken as a type of a depression instrument. In this range-finder the rangefinding triangle is reproduced in the instrument on a small scale. Figure I shows diagrammatically how this is effected by means of two arms. AB represents the height of the axis of the telescope above the surface of the sea BC. Ab represents the distance between the pivot of the telescope arm Ac and the range arm bc, and this to the scale of the instrument, represents the height AB. When the instrument is level, the arm cb is horizontal, and therefore parallel to the 2. - Depression Range-finder Mark III.

surface of the sea. cb is subdivided and graduated in equal divisions to the scale of the instrument. Ac, which has a telescope mounted on it, is pivoted at A and can be directed on to the water-line of a target at C. The triangles ABC and Abc are similar, and the length of bc therefore represents to the scale of the instrument, which is i,000 yd. to an in., the actual range BC. Similarly bd will represent the range BD of a target at D. If the instrument is required for use at any other height than AB, the telescope arm pivot A would be raised to a height above cb corresponding to the new height of the range-finder above the sea. In the foregoing, the surface of the sea has been considered as a plane surface, whereas it is really the surface of a sphere with its centre at the centre of the earth. Allowance for this curvature could be made by making the arm bc the arc of a circle instead of a straight line. It is, however, found to be more convenient to curve the telescope arm Ac in the opposite direction, the effect being the same. Corrections for mean refraction are made in the same way as those for the curvature of the earth, but in the opposite direction; the arm Ac being curved to allow for the combined effect of curvature and refraction.

The Small German Position finder may be taken as a typical position-finder. It was used during the World War for coast artillery on low sites. Very much larger instruments based on the same general principles were also used. Air communication was by telephone. Other nations often use automatic electrical transmission for moving parts of the receiving instrument when the transmitter telescope is traversed, and for actuating range and bearing dials on the gun mountings when the gun arm is traversed.

The Barr and Stroud Range-finder having a base-length of 30 ft. is typical of the one-man range-finder used for coast defences.

None of the range-finders or position-finders mentioned above is of any use if it cannot see the target; the position of a moving target can then only be ascertained by aerial observation.

Naval Range-finders, which must necessarily be of comparatively small size, are nearly always of the one-man type. They are generally similar to those used in coast defences, but in order to obtain better illumination their optical parts are often made larger. Their mountings are designed to enable the range-finders being kept on the target in a sea way. They are nearly always of the coincidence type with both images erect; but some stereoscopic range-finders have been used by the Germans. It is thought by some that a range can be more rapidly taken from a ship having considerable motion with a stereoscopic range-finder than with a coincidence range-finder; as with the latter it is difficult to keep the separating line across the target. The coincidence range-finder will, however, give more accurate results. Range-finders with a base-length of to metres are the largest which can conveniently be used on board ship. Base lengths vary with the size of the ships on which the range-finders are employed and the uses for which they are intended; one of less than a metre being employed for navigational purposes. Antiaircraft range and height-finders used on ships must be provided with some form of pendulum to keep certain of the parts horizontal, as the mountings cannot be kept level. Certain small range-finders have been made which can measure the range to a ship if the height of its mast or funnel is known. This height is used as the base of the range-finding triangle, the angle of parallax being measured by the instrument and read off it as a range. Such a base is obviously longer than that of a range-finder which could be carried on a ship. This type, however, has not been generally adopted.

FOR AIR Defence Range-finders and height-finders used in connexion with anti-aircraft guns have a much more difficult task to perform than the range-finding instruments used in the field or in coast defences. In the latter cases the target, if it moves at all, will move in one plane only and its speed will not approach that of aircraft. As the result of experience, the range of an aerial target which may alter by several thousands of yards in a minute is not taken into account; but its height, which will not vary to the same extent, is used as the basis of laying S and is measured by a height-finder. The rate of burning of the fuze has also to be considered, as it will not be the same for a definite range if the target is at different heights.

When laying a gun on aircraft, the setting of the sight is therefore based on the height and angle of sight of the target and on the setting of the fuze. At the beginning of the World War, no height-finders were available, so existing one-man range-finders, e.g. the Barr and Stroud, were used, and long base height-finders which could be rapidly made were introduced.

Q 3.

One-man range-finders were usually of two metres base length, and coincidences were made on the target in the usual way. In order to convert the ranges into heights, a slide-rule attached to the rangefinder was employed. One scale of this slide-rule was automatically set to the angle of sight of the target, by means of a cam, as the elevation of the range-finder was altered. The other scale was set to the range recorded by the range-finder, and the height of the target could then be read off.

Long base height-finders usually consist of two instruments at the ends of a base about a mile in length. Sighting planes in these instruments are kept laid on the target; the triangle formed by the intersection of a vertical plane with three planes, one of which is a horizontal plane passing through the base and the other two are extensions of the sighting planes, is mechanically solved; and the height of the point where the two planes of sight intersect (i.e. the height of the target above the base) is plotted at the same time.

The principle of this method is shown in fig. 3. AX and BY are two horizontal lines, parallel to each other. The sighting planes of C 0 ?' B 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 horizontal, 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 ascertained by noting against which of the horizontal lines on the board the intersection of the two straight edges comes. Such heightfinders have serious disadvantages, the principal one being the difficulty in getting the two instruments on to the same target.

## Heightand 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 rangefinder, 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 horizontal strip in which an inverted image is formed by the rays entering 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 1 5 and 25 diameters, and also with light filters for varying atmospheric 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 corresponding 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 formula r sin a =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 logarithmic 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 logarithmic 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 constant 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 working head. The movement of the instrument in elevation automatically 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 coincidence 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.: (r) 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 accurately laid for line on the target; and (3) the scale reader, who, standing 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 diagrammatically 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 telescopes 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 alteration 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 cables to the " fuze indicator and time rheostat " and thence to the " deflection voltmeters." As the body of the " double telescope " traverses about a vertical axis, but laying is done in the plane of sight, it is necessary to multiply the angular velocity of the body of the instrument by the cosine of the angle of sight in order to obtain the angular velocity of the target. This is effected electrically by passing the current from the lateral magneto through a rheostat, whose resistance is varied by a rubbing contact passing along it, as the telescopes are elevated or depressed.

Another rheostat and an accumulator (connected to the fuze indicator and time rheostat) cause an angle of sight needle in the fuze indicating voltmeter to move to the same angle of sight as that of the telescopes; this needle is controlled by another circuit.

2\. The fuze indicator and time rheostat consist mainly of the time rheostat, a fuze indicating voltmeter, a microphone and an external accumulator of three cells.

As explained above, the currents generated by the magnetos pass through rheostats on their way to the deflection voltmeters. These rheostats are situated beneath the time adjusting dial, and their resistance is altered as the dial is turned. The setting of the dial is dependent upon the height of the aircraft and the setting of the fuze, and is effected as follows: - A graduated height arm is moved by means of a milled head until it reads the height obtained from a height-finder. On its right-hand upper edge is a reader for reading the fuze curves on the time adjusting dial. The latter is turned until the reader of the height arm is on the fuze curve representing the length at which the fuzes have been set.

FIG. 4. - Arrangement of Brocq apparatus.

The angle of sight needle in the fuze indicating voltmeter is controlled by two circuits, viz,: that referred to in (I) which tends to set it at the angle of sight of the telescopes, and another in which are the vertical magneto armature in the double telescope, the rheostat beneath the time adjusting dial and another rheostat which automatically adds eight seconds to the time of flight. This eight seconds is an allowance for the time taken to set the fuze, load, lay and fire the gun. The angle of sight needle therefore makes with its zero or horizontal line an angle equal to the angle of sight to the predicted position of the target at which the shell will burst. When the height arm is moved, a height strip inside the fuze indicating voltmeter is also moved. Its height above the zero line of the angle-of-sight needle represents, to the scale of the instrument, the height of the target. The intersection of the needle and strip therefore represents the position of the target at the moment of the shell burst. Fuze curves are marked on the glass cover of the voltmeter, and the curve which is nearest to the intersection of the needle and strip will indicate the length at which fuzes are to be set. This fuze length is called down the microphone to the fuze setters, and is transmitted to the sight setter by the man taking up the shell.

3\. The deflection voltmeters are of the dead-brat type and read to 10° on either side of zero. Two are provided for each gun; one for lateral and the other for vertical deflection. As a rule, two guns can be worked by one Brocq equipment, four deflection voltmeters being provided. The required deflection is read by the upper pointer. Corrections for wind are applied by moving the scale by means of a knob beneath the voltmeter, the amount of correction being indicated on the scale by the lower pointer.

Stereoscopic range-finders were extensively used by the Central Powers for anti-aircraft work. (A. C. W.) Sound-Ranging The method of locating hostile guns by the sound, or sounds, consequent on their discharge was introduced on the British front in France during 1916. It had at that time already been in use in the French army for many months. It speedily proved its usefulness, especially in circumstances which rendered other methods of location very difficult or impossible. The system of concealment known as " camouflage " added considerably to the difficulty of finding the position of gun-pits on photographs taken from the air, and, further, these photographs offered no certain method of deciding whether a gun position, once identified, were occupied or no. The locations given by soundranging frequently enabled well-concealed positions, which had previously been missed on air photographs, to be detected, and offered a sure index as to whether known positions were active at a given time. Although air photographs always offered valuable confirmation of the sound-ranging locations, and were, when available, consulted with this object in view, the method is, of course, quite independent of such support. It works as well at night, or when, owing to fog, mist, or smoke, the visibility is poor, as on clear days; it can detect batteries so well hidden as to be invisible from the air or on air photographs; it is always ready when once the apparatus has been installed; and a location can be obtained, under favourable conditions, within a minute or two of the arrival of the report of the piece. On the other hand the instalment of the apparatus necessitates the laying of several miles of wire, and involves considerable preliminary labour in other ways; the method will not work during a heavy bombardment; and certain weather conditions, to be discussed later, render locations almost impossible. The difficulty first mentioned will quite possibly be surmounted or diminished; the other two seem, at present, insuperable.

The method has been elaborated to permit the directing of fire on a hostile piece by comparing the record of the sound of discharge of the piece with that of the burst of the shell directed against it. With 1 2-in. and 9.2-in. howitzers destructive shots have been directed very successfully by sound-ranging.

## Principles

The method generally adopted in the British, French, and American armies is to record the instant of the arrival of the sound made by the hostile piece at certain fixed and carefully surveyed posts, spaced at intervals varying from 1,000 to 2,000 yards. If it be assumed that the sound spreads out from the source with a known velocity, the same in all directions, then a known interval between the arrival of the sound at two fixed posts will determine a curve on which the source must lie. This curve is a hyperbola with the two posts P I and P2 as foci, for the determining condition is that the difference of the radii vectores SPI, SP 2 be constant. If, in addition, the time of arrival at a third post be known, then the interval between this and the time of arrival at either P i or P2 will fix a second hyperbola on which the source must lie, and so determine the position of the source. In practice three posts are not sufficient, since any uncertainty caused by the recording of a spurious sound at a post would falsify the location. In general six posts are used, which, taken consecutively in pairs, give five lines which should all intersect. Any accidental selection of the record of a spurious sound at one or more of the posts is then at once detected by the non-intersection of the curves. Records of the sound at five, or indeed four, of the posts are generally sufficient for the experienced sound-ranger, even when several guns are being recorded at short intervals, so that the use of six posts allows for the sound not being successfully recorded at one or two of the posts.

## Nature of Sounds from High-Velocity Guns

In the preceding argument it has been assumed that the sound spreads out with uniform velocity in all directions from the source. There is little doubt that this is true, in a still atmosphere of uniform temperature, of the sound of the discharge of the piece. With the modern highvelocity gun, however, a second sound, originating in the motion of the shell through the air, always accompanies the sound of discharge. This second sound is due to a pulse of compression set up by the shell, known as the " shell-wave," or " onde de choc." It is perceived by an observer in front of the gun as a sharp crack, which is followed after an interval depending on the type of gun, the elevation of the gun, and other factors, by the duller, heavier sound of the discharge, or gun-wave. To examine the formation of the shell-wave by the passage of the projectile, consider the resultant disturbance produced by the pulses of compression travelling out with the velocity of sound from every point of the path of the shell. For simplicity take in the first case a projectile travelling horizontally with a uniform velocity greater than that of sound; let G be the position of the gun, S i, S2,. .. S10 be the positions of the projectile at the end of the 1st, 2nd,. .. 10th second (fig. 5). When the shell is at Sio the compression originating at G has travelled out as a spherical shell with G as centre for 10 seconds, that originating at S i has travelled out as a spherical shell with S i as centre for 9 seconds, and so on. The envelope of all these spheres is a cone with its apex at Sio; if the shell be travelling close to the surface of the earth the trace of this cone on the surface is AS IO C, which represents the pulse of compression under discussion. If the velocity of the shell be considered to decrease with time, as in any actual case, the interval of space between centres of successive generating spheres will decrease as the shell travels, and the enveloping cone will be modified (fig. 6). The form of the shell-wave will resemble roughly a paraboloid of revolution, the vertex being at the shell as long as the latter has a velocity exceeding that of sound, and consequently travelling with a velocity greater than that of sound. After the velocity of the shell has dropped below that of sound the shell-wave travels out in all directions with the velocity of sound normal to the surface.

FIG. 5.

The exact form of the shell-wave will depend upon the range table of the gun and the interval since the shell left the gun, and cannot be specified as being any familiar surface. The trace of the wave on the plane of the earth's surface, with which the observer is in general concerned, depends further upon the elevation at which the gun is firing. Since the sphere representing the position of the gun-wave is one of the generating spheres the shell-wave will touch this sphere. In fig. 6 where G is the gun, ABC the trace of the gun-wave on the horizontal plane, ASC the trace of the shell-wave, within the cone represented by AGC both sounds will be heard, outside the cone only the sound of discharge. The interval between the two sounds is FIG. 6.

clearly greatest on the line of fire, decreasing as the observer moves to a flank. As the gun is elevated the interval detected by a listener in a fixed position decreases, the trace of the shell-wave approaching that of the gun-wave. This is illustrated in fig. 7. If the gun be sufficiently elevated no shell-wave is heard by a listener at any position on the ground, though it may be heard in an observation balloon. Thus the double sound has been heard by an observer so situated in the case of a 9.2-in. howitzer, firing with full charge (M.V. 1,500 f.s.), while observers on the ground heard only the single sound.

Owing firstly to the selective sensitiveness of the human ear, and secondly to the fact that the shell-wave is generated well above the surface of the earth, and travels down to the ear without meeting obstacles and without being hindered by refraction effects, the shellwave alone is usually heard when the hostile piece is distant, and is spoken of as the sound of the piece by the casual listener. Any attempt to take rough bearings on a gun by estimating the direction from which the sound appears to be coming then leads to a very erroneous result, since it is the normal to the shell-wave that is selected. Unless the listener is on the line of fire such a bearing will pass considerably in front of the piece. To calculate the position of a gun from the intervals between the arrival of the shell-wave at different posts requires a knowledge of the exact form of the wave in question at various times of flight, and this presupposes a knowledge of the range table of the gun, and the elevation at which it is firing (given by the approximate range). It is clear that to apply the soundranging method to records made by the shell-wave is a matter involving information not always available, and considerable preliminary work on the construction of curves representing shell-waves for different hostile guns firing at various elevations when it is available.

FIG. 7.

In the case of howitzers the horizontal component of the muzzle velocity is less than the velocity of sound in all ordinary cases, so that only one sound, the gun-wave, is heard on the ground.

## Instruments

The instruments comprise: (a) detectors, placed at each of the six surveyed posts, which give an electrical response to the arrival of the sound, and (b) a recording instrument, placed at a central station and connected by a separate circuit to each detector, which registers the exact time at which each detector responds.

When the method was first tried by the French the detector used was a soldier, who pressed a key when he heard the sound of a hostile piece, the key closing a circuit which actuated a pen on a smoked paper chronograph at a central station. This method C FIG. 8. - Hot-Wire Microphone.

involves inevitable errors due to the personal equation of the observer, and is further invalidated by the fact that, in the case of guns, the observer frequently hears only the shell-wave. The difficulties of working from records of this kind have already been discussed. Later, carbon microphones with large wooden diaphragms were introduced, small cells being included in circuit with the microphone and a primary coil, all at the post; the circuit leading back to the recording instrument included a secondary coil wound on the primary. These microphones suffered from the fact that they had a range of sensitiveness similar to that of the human ear; they responded readily to chance sounds, such as the clatter of equipment, or to shaking, and they registered the shell-wave in preference to the gun-wave. They were superseded (first in the British army, and ultimately in all the Allied armies) by the hot-wire microphone invented by Maj. W. S. Tucker (British patent No. 13123 of 1916, and No. 8948 of 1918: see also Phil. Trans. Roy. Soc., A, vol. 221, p. 389). This depends on the principle utilized in the hot-wire anemometer, i.e. the change of electrical resistance consequent on the change of temperature of a heated wire which ensues when the air round it is set in motion. A very fine wire of platinum, whose resistance at atmospheric temperature approaches loo ohms, is mounted in the form of a grid over a circular hole some 7 mm. in diameter (fig. 8). It is provided with terminals. It is included in one arm of a Wheatstone bridge, and sufficient current passed through the network to heat the wire to a dull red. The bridge is balanced so that when the air round the wire is undisturbed no current passes through the galvanometer. Motion of the air causes the resistance of the wire to decrease, upsets the balance, and so causes a current to pass through the galvanometer.

The microphone wire is mounted in front of an air container of some 16 litres capacity. Resonance effects in this container may be partly eliminated by small openings made in the wall. The instrument so completed is insensitive to all sounds of speech, musical sounds, traffic, or even rifle fire. It responds readily, however, to gun sounds (which are low frequency disturbances), even when they are inaudible, and records also the shell-wave. Its reaction is very rapid, and the small lag which does occur appears to be the same for all similarly constructed instruments.

An essential part of the recording instrument is a galvanometer for each circuit which shall respond very rapidly to the current caused by a sound reaching the microphone. For rapid response it is necessary that the moving part of the galvanometer shall be very light indeed - the moving coil or moving magnet type is out of the question. The condition is satisfied by the Einthoven galvanometer, in which the moving part is a very fine wire (through which flows the current to be detected) mounted in a magnetic field. The wire moves in a direction normal to its length and to the direction of the field. Six wires, insulated from one another, and provided with separate terminals, can be mounted side by side in the field produced by, a single small electromagnet. This provides in a small space what is essentially six independent galvanometers, one of which is included in the bridge belonging to each microphone. As the sound reaches successively different microphone posts the corresponding galvanometer wires move in rapid response.

The instant at which each wire begins to move is registered on a moving photographic film. The camera in which the film runs verticall y is furnished with a horizontal slit, a cylindrical lens in front of the slit reducing its effective breadth. Shadows of the perpendicular galvanometer wires, cast by means of an electric lamp and an optical system mounted in the pierced poles of the galvanometer magnet, fall on the slit, and are focussed on the film, appearing there as six points of shadow on a horizontal line of light. As long as the wires are still each point leaves on the running film a straight line; the movement of a wire registers itself as a break in this trace.

If the film ran at a uniform speed measurement on the developed film of the distance between the breaks would give the required time intervals. As this is not the case the following device is adopted: a wheel provided with ten flat spokes, one of which is somewhat wider than the others, is mounted in the case containing the lamp, so that, when it is rotated, the spokes successivel y interrupt the light which illuminates the galvanometer wires. The wheel is actuated by a synchronous motor controlled by a tuning fork, and rotates ten times a second. As a result of this arrangement there appear on the film lines perpendicular to the direction of the motion, the intervals between which correspond to hundredths of a second, every tenth of a second being marked by a wider line. This recording apparatus was devised by Dr. Lucien Bull, of the Institut Marcy, near Paris.

Originally the film was cut off after the required record had been taken, and developed in a small dark room adjacent to the instrument. Later a method of automatic development was devised, by which the film passed successively through developer and fixer while running, and emerged ready for interpretation.

Fig. 9 shows some typical records. (a) and (b) are records of two differently situated 5.9-in. howitzers taken by six posts in each case. The burst of the shell was also registered on these films, but as it occurs several seconds later space does not permit the inclusion of the part of the record in question. (c) is a record of a field gun, showing both shell-wave and gun-wave. Only five posts were used for this record. The varying interval between the two sounds at the different microphones is well shown: at the flank microphone, corresponding to the lowest trace, only one sound is heard. (d) is a record of the burst of a British shell on a German position.

## Influence of Weather Conditions

The method in use demands that to every time interval shall correspond an exact distance, a standard velocity of sound being assumed, which corresponds to some standard temperature, and still air. (The velocity of sound does not, of course, vary with the pressure, and the effect of humidity is in general negligible.) Hence the time interval read off from the film has to be corrected for temperature and wind before it is used on the board prepared for location. For the temperature variations which occur in ordinary circumstances the increase of velocity of sound may be taken as proportional to the increase in temperature, so that the temperature correction is easily applied. Simple geometrical considerations show that the correction for wind depends only on the velocity and direction of the wind and the position of the microphone, and not at all on the position of the gun. With given microphone positions a diagram can be prepared which allows the rapid graphical determination of the correction for a known wind.

It has been found by experiment that the temperature and wind which are concerned in these corrections are not those prevailing at ground level, but at a height of between 250 and 500 ft. up.

Owing to the refraction of sound by wind the record of a given sound at ground level is greatly influenced by the variations of wind velocity at different heights above the ground. This wind gradient determines largely whether the conditions are favourable or unfavourable for the detection of sounds. In the case of a wind increasing in velocity with height, a following wind, besides increasing the velocity of the sound, tilts the wave front so that the sound converges on the listener or instrument on the ground, and is well heard. An opposing wind causes the sound to tend to pass upwards and leave the ground. Hence a wind blowing from the instruments towards the hostile piece often renders sound-ranging almost impossible if it be of any strength. The temperature gradient also plays a part in the refraction of sound.

FIG. 9. - Typical records of Bull apparatus.

## Location from Record

Having seen how the intervals between the arrival of the sound at different posts can be accurately obtained and corrected to standard conditions it remains to discuss how these intervals can be made to supply the position of the gun with as little delay as possible. A map board is prepared with an accurate " grid " (coordinate system of squares) covering the region in which locations are expected. On this the microphone positions are accurately marked. The posts are usually taken consecutively in pairs; with each pair as foci a family of hyperbolae may be drawn giving the loci corresponding to various time intervals (at standard velocity of sound). In practice, however, to avoid the labour of preparing the hyperbolae it is usually preferred to use the asymptotes instead of the curves themselves: for these it is onl y necessary to have a thread attached to each mid-point between pairs of consecutive posts, and a scale plotted round the edge of the board for each base, graduated in time intervals, so that when the thread is placed to pass through a given graduation it is the asymptote to the hyperbola corresponding to the interval. To allow for the divergence of the asymptote from the hyperbola, which becomes serious as the base is approached, tables are prepared giving the corrections (always additive), in terms of the length of the base and the distance from the mid-point of the base, to be applied to the time intervals obtained from the record. The asymptote corrections having been applied to the various intervals, already corrected for temperature and wind, the asymptote corresponding is laid out for each base. The various lines should all intersect at a point: in general they do not, but form a small polygon from which the position of the gun can be estimated.

## Estimation of Calibre

The position of the hostile burst may be obtained from the record of its sound in the same way as the position of the piece, and the interval between the departure and burst of the shell, i.e. the time of flight, can be computed from the record on one microphone. Thus the record gives the time of flight corresponding to a given range, which affords an indication of the calibre of the piece. In the case of guns, as distinct from howitzers, a further indici) cation can be obtained from the interval between shell-wave and gunwave at the different posts.

## Work in the Field

It is not feasible to have the film running continuously during any period when records are expected. It should he started a second or two before the sound reaches the first microphone. In the field this is effected by having two forward observers in front of the line of microphones, so placed, one to each flank, that either the one or the other of them must hear the sound of the hostile piece a few seconds before it reaches any of the microphones. These observers are provided with keys, the depression of which starts the film running. They also report by telephone informations judged useful as to the estimated calibre, the approximate location of the burst, if seen, and so on.

The line of microphones in general covers a front of some 8,000 yd. and is some 2,000 yd. or more from the front line. It is usually preferred to place the instruments at approximately equal intervals on a smooth curve, which may be a straight line, or the arc of a circle either convex or concave towards the enemy, according as guns well to a flank have to be located, or attention is concentrated on a more central group of guns. Such arrangements lead to greater ease of identification of a record than is possible if the microphones are very irregularly placed.

The microphones may be placed anywhere where the hearing is good: the only obstacles which seem to cast sufficient sound shadow to affect them are high hills just in front of them. They may be put in shallow depressions dug for them, and should be protected from splinters, and also from wind and draughts. Canvas and hurdles may be used for this latter purpose without appreciably affecting the sensitiveness of the instruments.

## Ranging on Hostile Pieces

A heavy burst near a hostile gun position will furnish a sound record of its position just as does the gun itself. Fire may be directed on a piece which is in action by comparing the records which it supplies with those of the bursts of one's own answering shell. Since both gun and burst are located by the same method all uncertainties introduced in an ordinary location by ignorance of the precise atmospheric conditions are eliminated.

A differential method is adopted, the difference of times of arrival of the sound of the hostile gun and of the friendly burst at each microphone being plotted as ordinates against a certain simple function of the relative positions of the microphones and the hostile gun as abscissae. A horizontal line then corresponds to a direct hit; a straight line sloping to left or to right to an error of line to one side or the other; a curve (approximately an elliptical arc) convex or concave downwards to an error of range. The magnitude of the corrections necessary is easily estimated from curves previously prepared. (E. N. DA C. A.)