Chapter XIV (2)

663.--=The Sounding Sextant.=--This instrument is used for coast surveys. Angles are taken with it of objects, buoys, etc., from the land and also from a boat on the water for such objects or for others upon land. It is constructed upon the same principle as the ordinary nautical sextant; but as it is to be used as an all-day working instrument, and not for a few diurnal observations only, it is made much more solid, and its optical parts take a more extended field of view. The graduation is also stronger, such precision of reading only being required as may afterwards be plotted on a chart. This instrument is shown in perspective, Fig. 296. The index glass is large--about 2¼ inches by 1¼ inches. This is secured on all sides by a firm rim to the tray in which the glass is held at three points. The adjustment of the index glass is left under control, as it may occasionally be necessary to remove it from effects of spray upon and about it. The horizon glass is made about 1½ inches in width and ¾ inch in depth. This is entirely enclosed in a tray, the whole surface being a mirror without any plane part to the glass as with the ordinary sextant, so that it is entirely protected by the metal. By this arrangement the eye receives the direct ray from the object immediately before it, and the reflected ray from an object whose angular position is desired to be taken with it: but these images do not come exactly into contact, as the narrow frame interposes. It is, however, sufficiently near for terrestrial observations. The adjustment of the horizon glass to the perpendicular of the plane of the arc is the same as that shown in detail for the box sextant further on. The adjustment of the horizon glass to the index is by a stiff arm extended from the sole-plate projected into a loose opening, where it is held firmly by two opposing capstan-headed screws, as before described. The arc of the sextant is of 6 inches radius, graduated upon silver to 20′, and reading by the vernier to single minutes only by the microscope. The clamp and tangent are the same as those described for the nautical sextant. The frame is straight braced. The telescope has a wide field, with achromatic object-glass of 4½ inches focus, the clear aperture being 1-1/8 inches. The supporting ring of the telescope has no rising stem or collimating adjustment, but is solidly fixed in its true position by the maker. The ring carries a plain disc pin-hole sight, which takes the place of the telescope for near observations. The instrument in use is held in the hand by a firm oblong handle. The instrument rests, if required for reading, upon three legs as the ordinary sextant. Its weight is about 2¾ lbs., or when packed in its case, 5 lbs. Its examination and adjustment are of the same kind as those just described for the nautical sextant.

664.--=Box Sextant.=--This very neat and portable instrument was invented by the late William Jones.[50] It is used for taking angles within 120° upon the surface of the land to within a single minute of arc. It has become deservedly popular with British surveyors as a land surveying instrument, and is equally so as a military one. It is the same in principle as the nautical sextant already described, but it possesses the great merit--as a surveying instrument constantly in hand--that all its glasses and delicate parts are securely protected from accidental injury by being covered; whereas the nautical sextant, made for one or two diurnal observations only, has all these parts exposed. And it is not only that all parts are protected when the instrument is in use, but they are all doubly protected by the covering box when carried about out of use; so that it is found that a well-made box sextant set originally in perfect adjustment will retain this adjustment in average use for very many years. The author has seen an instrument twenty years in use still in perfect adjustment. The box which covers the instrument out of use forms also a most convenient handle or support for it when in use by attaching it in a reversed position underneath, as it appears in Fig. 297. This attachment is made either by a screw cut entirely round the body of the instrument, or, what is much better, by a bayonet fitting, for the reason that large screws of this description are liable to _cross thread_. The general description of the outer parts is as follows:--

665.--_C_ a covering box which inverts from the position shown in the figure and covers the instrument. This has a diameter of 3 inches and a depth of 1½ inches. _B_ box containing the optical and moving parts of the sextant. _A_ axis of index glass. This axis also carries a toothed segment fixed close under the front of the box, by which both the index glass and index are moved by means of a pinion to be described. The index carries a vernier divided into 30, which reads into the arc to single minutes; the arc is divided to half degrees on silver. The magnifier is centred by a swivel hinge joint over the axis, so as to permit it to be brought to focus upon the arc at any position. This magnifier is held down on the front of the box when out of use by a nib catch at a position of about 80° of the arc. _O_ a milled head, the axis of which carries a pinion which works into the segment above described under the index glass. The pinion is about 1 to 9 of the segment, so that the index traverses the arc of 60° (reading 120°) by one-and-a-half turns. This gives a conveniently slow motion to the index glass, and enables this sextant, if it be well made, to be set rapidly with great precision. _S_ two nibs, part of two levers for putting the shades in or out of action.

666.--In the closed form of sextant the shades block the reflecting position between the index and the horizon glass. For surface surveying they have therefore to be opened out, through an opening closed by a slide shutter which moves by a stud in a slot on the under side. The shades consist of one green and one dense red glass which must be worked parallel, as before described for the nautical sextant. These are used for taking altitudes of the sun, for adjustments only.

667.--_The Key K_ is a milled head which screws out, and carries a watch-key pipe at the end of its stem by which adjustments may be made from three square-headed screws fitting its pipe, two of which are close to _b_, the axis of the horizon glass. These adjust perpendicularly to the plane of the arc. One screw at a adjusts the parallelism of the index and horizon glasses when the index is at zero.

668.--_The Telescope_ is achromatic, with draw tube for focussing. It magnifies about 2½ diameters. It has a concave eye-glass, and therefore gives an erect image, Fig. 14. A sun-glass _E_ screws over the eye-glass when it is required for sun observations. The telescope is attached to the sextant by means of a crank-piece upon the telescope which is fixed by the mill-headed screw _T′_ and two steady pins. The crank-piece screws in reverse position upon the telescope for portability before putting it by in its case.

669.--By some makers the telescope is made to slide into the body of the sextant and thus become quite portable. This plan is a very neat one, but it requires care to see that the shades do not interfere before it is put by. The weight of the entire sextant with its solid leather case is about 18 oz. only. For close work the telescope is not generally used. A sliding shutter pierced with a small hole covers the telescope opening into the sextant, which is used as a sight hole.

670.--_The Interior or Optical and Mechanical part of the Sextant_ is shown Fig. 298. _I_ index glass, fixed over the toothed segment on the same axis. The pinion is shown working into the segment moved by the milled head _O_ of Fig. 297 on the face of the sextant. Fig. 298: horizon glass, cut by _ED_, adjusts to the vertical by screws _CC′_, which have square fittings on the face of the instrument, shown Figs. 299 and 300 full size. The differential adjustment between horizon and index glasses is made by a screw with a square fitting at _P_. This adjustment acts by screwing against a helical spring, shown at _Q_. The reflected rays enter by a wide window in the side of the box, Fig. 298 _d_, the direct rays by a small window _f_. The path of a ray is shown by fine lines from _R_ to _E_, for the positions in which the index and horizon glasses are placed. The pin-hole opposite which the eye is placed is shown white. _S_ shades with their axis are shown cut off, to prevent confusion of other parts. They are simply round discs of parallel glass on arms which rise from the back of the face by pressure of the nibs at _S_.

671.--_The Construction of the Box Sextant_ may be fairly inferred from inspection of the engravings. The face-plate is made of a casing in brass 1/8 inch thick, which should be well hammered to harden and stiffen it. The axis, which has a wide collar, is fitted into a hole in the plate, first by turning it as exactly as possible, and then by burnishing it in by friction, the hole being broached slightly conical with a D-broach. The careful fitting of the axis is an important part. The horizon glass frame, Fig. 300, is held down by a central screw which fits tightly both in its fore hole and thread. The flange of the tray _F_ is cut to an angle on its under side to permit adjusting to verticality by rocking over this angle, by tightening and loosening the adjusting screws _cc′_ which protrude in square heads to the face of the instrument. The horizon glass, _H_, which is half silvered, is fixed in a tray-piece which has two narrow fillets turned to the face of the glass, and a spring-piece at the back brought up by a screw _a_. This glass is entirely open at its unsilvered part. The toothed segment should be cut upon its own axis, and although fitted to the pinion without any looseness, it should not press the index axis. The silver is inlaid in the arc on the plan shown Fig. 127. The vernier is soldered closely on the index and should read down to a fine clean edge.

672.--_Examination of the Box Sextant._--The glasses should be cleanly silvered, with a sharp, clear cut between the silver and the clear glass of the horizon glass. The pinion should move softly and equally in causing the index arm to traverse the arc. If the pinion be moved in little jerks backwards and forwards there should be no shake, but the index should follow every slight motion. The magnifier rising joint should move rather stiffer than the traversing joint, so that the focus is not changed by traversing across the arc. The magnifier should have about 1 inch or less focus, and should stand square to the plane of the sextant when in focus. The graduation should be deep and fine, and the vernier should read 30 = 29 at the two ends and the centre of the arc. If there be a small excess or defect of vernier to arc, this should be noted and allowed for, either at the time of reading or as an index error. The sliding fittings of the pin-hole sight, shades, and under shutter should move firmly but not stiffly. The telescope should fit without shake. The covering box should fit well in both positions of cover or hand-hold.

673.--_Adjustment._--The box sextant is best adjusted by the sun upon the plan described art. 648. The adjusting screws, as already stated, are moved by the key, which unscrews from the face of the sextant, Fig. 297 _K_. The adjustment is made permanently by the maker, except only that of the horizon glass, which is at the command of the user. The adjustment to perpendicularity of face is made by the two screws upon the face near _b_; adjustment to zero of arc by the screw at the side _a_. In defect of appearance of the sun, the sextant may be adjusted to any clear, sharp line, as that of a stretched piece of twine, for perpendicularity of plane, and to any object of clear outline sufficiently distant, say at half a mile, to avoid error of parallax for index zero, art. 621.

674.--_Use of the Box Sextant._--The sextant has its under shutter opened by pressing the stud attached over in its slot. The nibs of the shade levers, Fig. 297 _S_, are then raised and the shades depressed. The cover is then screwed, or slid on if it fixes with bayonet notches, upon the under side of the sextant to form the hand-hold. The pin-hole sight is pressed over for use if not already in its position, unless it be intended to use the telescope. The box sextant is held in the left hand, with the right-hand thumb and forefinger constantly holding the milled head, and turning this so as to bring the two objects, of which it is desired to obtain the angular position, from the observer, exactly in apparent juxtaposition, the one over the other. In turning the milled head it is better to let all the other fingers of the right hand clutch and steady the instrument. To take angles objects should be observed that cut sharp, erect outlines, as buildings, posts, trees, etc., if possible. In open country it is necessary to use pickets, to be described further on. With pickets the reflected image of the upper half of one picket should form a continuous outline with the direct image of the lower half of the other picket in the eye, so that the pair of pickets appear as one. Where an angle greater than 120° is required an intermediate picket is set up, and angles taken to the right and left of this are added together.

675.--It must always be remembered that the sextant takes angular positions _actually_, whereas plans are made in _azimuthal_ angles. There are some not very satisfactory means of approximate correction for this, for which books on surveying may be consulted; but altogether the sextant is not very useful for taking angles for plans on other than fairly level ground, wherein it has proved a most valuable and sufficiently exact instrument. Where ground is undulatory fairly good work may be done with it by taking stations for exterior triangles at equal heights on the hillsides, as ascertained by a hand level or clinometer to be described, or sometimes from hilltop to hilltop where these are of fairly equal heights. For sketch plans of very hilly or mountainous districts the prismatic compass, art. 148, is better, as this gives, although with less precision than the sextant, its angles in azimuth.

676.--=Box Sextant with Supplementary Arc.=--This sextant is preferred by many because of its more extended use. It is complete as an ordinary sextant for angles up to 120°; but if it be thought desirable to extend the angles to 220°--by a single observation this may be done. The ordinary arrangement of the box sextant just described is left intact and forms the upper part of the instrument. This arrangement, as in the box sextant, is attached entirely to the face or arc plate, the only difference being that the index glass is made of less depth. For the supplementary arc arrangement a mirror is fixed upon the lower or _sole plate_ exactly under the position of the index glass. This mirror is termed the _supplementary index glass_. The position of the face of the index glass is at right angles to the face of the ordinary index glass when the index is at zero. The arrangement of glasses is shown Fig. 301: _MM′_ index glasses. The supplementary angle is read through a separate pin-hole sight which is placed at about 90° from the pin-hole sight of the proper sextant and a little lower down on the rim. The arc of this sextant reads in the ordinary manner, left to right, to an inner circle of figures for angles from 0° to 130°. The supplementary arc reads by the same vernier, and is figured in the same manner at the tens; but it reads into an outer circle of figures which progress in the _reverse direction_, that is, right to left. The readings of the supplementary arc are from 90° to 220°, so that for a certain range, that is, for angles from 90° to 130°, these may be taken either by direct arc or by supplementary arc. The supplementary angle is taken by means of the coincident images of _two reflections_, one from the index glass and one from the supplementary index glass, and not by one direct and one reflected image as in the sextant proper.

677.--_Theory of Supplementary Angles to the Sextant._--For the measurement of these angles we have to consider direct reflections only of two reflecting planes placed one above the other nearly in contact, so that the images projected from both planes may reach the eye superimposed. Let Fig. 302 _II′_ be the surface of a mirror (_index glass_) which is movable to any angle in relation to the face of the mirror _SS′_ (_supplementary index_). For demonstration of the principle these mirrors are shown in this diagram at 90° to each other; therefore coincident reflections will be at 90° + 90° = 180°. Let the lines _FC_ and _BC_ form a right line (180°); _F_ fore sight and _B_ back sight. An object at _F_ would be reflected from the mirror _II′_ to the eye at _E_, the angles _FCI_ and _ECI′_ being equal. Another object at _B_ reflected from the face of the mirror _SS′_ would also reach the eye at _E_, the angles _BCS′_ and _ECS′_ being equal. And as the angles _FCI_ and _BCI′_ are equal in crossing a right line, the line _FCB_ must be also a right line (180°) which is indicated by the angle of coincidence of the two reflections to _E_. The positions of the reflections are shown as angular measurements upon the graduated arc.

678.--In Fig. 303 let _SS′_ remain as before, angle _BCE_ will remain as shown in both figures. Move the index glass from the position _II′_ of Fig. 302 to the position _JJ′_ of Fig. 303, so that after this movement the eye at _E_ would receive the image of an object at a new position _F′_ as reflected from the mirror _JJ′_, _F′CJ_ and _ECJ′_ being equal. In this process, as the reflector _JJ′_ in the angle _ICJ_ would have moved half the angle _JCF_, the record of this movement upon the index, which moves with _JJ′_, is at the same time double the true angular difference, as with the sextant proper fully described, the graduations being in both cases the same _pro ratâ_. The increase of angle is taken supplementary to the angle given by the first reflection, by addition to this angle in a direction right to left from the right line of the former sight _EC_; consequently this increase is read backward on the sextant, that is, right to left, and is indicated by the outer line of numerals.

679.--_Manufacture._--The general structure of this instrument is nearly the same as the ordinary box sextant, except the parts just referred to. The supplementary index glass is an ordinary mirror similar to the index glass but of only ¼ inch in depth: it is mounted in the same way. Its adjustments are similar to the horizon glass in kind, but there are no exterior screws, this glass being permanently fixed by the maker. Opposite the supplementary index glass a wide window is cut through the rim of the case near the sole plate to take sight of the object at angles exceeding 120°, so that in this sextant two large windows are cut out opposite to each other. The diameter of this sextant is 3 inches; the exterior depth about 1-5/8 inches, that is, 1/8 inch deeper than the ordinary box sextant. It weighs about 20 oz. It is carried in a solid leather case with strap to pass over the shoulder.

680.--_Examination and Adjustment._--Examination will be nearly the same as for the common box sextant. The most important point is that the readings taken within both arcs should be alike, assuming, which is necessary, that the part comprising the sextant proper is perfectly adjusted. Thus there is a 90° on both direct and reverse arcs. The 90° may be measured by any pair of objects on the direct arc, and afterwards compared by shifting the index to the 90°, on the supplementary arc. If no object be found at 90°, then 95° 30′ or any other quantity may be compared. It is also well to compare readings at or about 120° on both arcs. The 90° and 120° fall in the same position in the reading, and this checks any error in either. If the adjustment be not fairly perfect, the instrument should be returned to the maker. Indeed, this sextant would be better without any external means of adjustment, leaving these to be made by the optician in such a permanent form that they will not be liable to change. It is, as the plain box sextant, exceptionally protected from accident.

681.--_In using this instrument_ the arc up to 120° is taken exactly as with the plain box sextant. Beyond 120° the sextant is shifted to take sight through the supplementary pin-hole, being particular to observe that the pinion is now turned the _reverse way to increase the angle_, and that the vernier reads for the supplementary arc right to left. It is in this reversing, if not carefully performed, that a little difficulty is experienced in using this instrument.

682.--=Box Sextant, with Continuous Arc to 240°.=--This instrument is an improvement by the author upon one originally designed by Mr. W. Franklin. The reading is taken continuously from the same sight-hole and by the same arc, and in a direct manner without any reversal for part of the arc. This sextant reads with certainty to 240°.

683.--In the construction of this sextant there are two horizon glasses superimposed one above the other and crossing each other, with faces which are adjustable for perpendicularity at an angle of 120°. The horizon glass is divided top from bottom by a clear band cut through it, as in the old form of back-sight nautical sextants. One of the wide glasses reflects into the upper, and the other into the lower mirror of the horizon glass. The pin-hole sight or the telescope is placed in the same position as in the plain box sextant described. The horizon glass is fixed and both the index mirrors adjust to angular positions, or one index glass only and the horizon glass is adjusted, this arrangement being optional. The arc is graduated as the plain box sextant, but it reads with two rows of figures from 0° to 120°, and from 120° to 240°, the 0° of the under line being under 120° of the upper. When the arc is set to zero the index glasses are in such a position that the direct vision and the reflection as seen in the upper mirror of the horizon glass are coincident for direct images, as at the zero of the plain sextant, but at this point the lower mirror of the horizon glass reflects to the eye an object at 120°. When the index is moved forward the angles continue onward, reflected from both glasses, so that the upper reads on 10°, 20°, 30°, etc., whereas the lower read 130°, 140°, 150°, etc.; so that if the objects desired to be triangulated are under 120° the coincidence is seen in the upper mirror, and if over this in the lower, the great distance of 120° apart of the angles preventing the risk of accidentally taking the one for the other. In the compact form of a box sextant this instrument embraces the uses of the ordinary reflecting circle of double the diameter, due to the entire circle graduation; and the range is sufficient, as beyond 240° the head materially interferes with observation. The size and weight of the instrument are generally but little over that of the plain box sextant. The adjustments are made permanently by the maker. The use of this instrument is fully inferred from the description given. The construction is shown in Fig. 304, _E_ place of the eye with direct ray through the horizon glass _H_ to _O_. The index glass _I_ is that of the ordinary sextant, shown by dotted lines, throwing the image of an object at _P_ to the upper horizon glass and thence to the eye at _E_. _B_ is the fixed supplementary glass with its surface at 60° to the lower horizon glass at _A_. The sight lines from an object at _Q_ are reflected from _B_ to _A_ and thence to _E_. A spring arrangement shown _SS_ with a milled head underneath permits the lower glass _A_ to be drawn down to convert the instrument into a simple box sextant.

684.--_Details of Spring Arrangement_ to the supplementary horizon glass are shown in Fig. 305 full size in section. The springs _SS_ in Fig. 304 and _S_ Fig. 305 form two points of support to the horizon glass, the silvered face of which is shown at _A_. A third point of contact is near _D_, placed in the centre of the end of the supporting plate for the horizon glass. When the screw _R_, which is placed in a loose fitting, is released, the springs bring the supporting plate tight up to _D_ and hold the horizon glass firmly in an elevated position. When the screw _R_ is tightened it brings this glass down. The horizon glass is adjusted over a rocking centre by the screws _CC′_. A screw and collar b prevent the loss of the screw _R_. By this arrangement the horizon glass is brought in or out of the field of view, in order to use the supplementary arc or for leaving it as a plain sextant.

685.--=Open Surveying Sextants=, similar to nautical sextants but generally smaller and of stronger construction, preceded the box sextant, and are still used to a limited extent upon the Continent, particularly with some form of supplementary arc, or arrangement to produce a large part of the reflecting circle. These forms are also occasionally revived by the opticians of our own country. The reason of this is easily seen. To the optician who lives in a town, moves on a level surface, and has comfortably warm hands, even in the winter, to hold and move the separate parts of an instrument, the open sextant appears the most perfect, as he can get at every part of it easily to clean and adjust. The surveyor takes another view of the subject. He is exposed in the open country to all weathers and all difficulties of movement over the land; therefore that form of instrument which is best protected and least liable to injury by a fall will be sure to be popular with him. It is upon these conditions the box sextant of some form is generally preferred.

A handy form of portable surveying sextant has been devised by the author and is shown at Fig. 306.

The arc is of 4 inches radius and is divided on silver to read 20″, is complete with shades and telescope and packs into a case 7 × 6 × 2½ inches.

686.--=Optical Square.=--This extremely handy little instrument is invaluable for taking offsets in chaining for any irregularity or obliquity to the right line in the boundaries of fields, hedgerows, fences, streams, etc., giving as it does instantly at sight a right angle to any object that may be sighted on either hand. The instrument is optically constructed exactly as a box sextant; but the glasses are fixed with their faces permanently at the angle of 45° to each other, by which means the reflection of 90° is truly given on principles fully discussed at the commencement of this chapter. This instrument being made very small, that is, 2 inches or less in diameter, it is found most convenient for manipulation to place the adjustments to the larger glass, that is, the index glass. The horizon glass, Fig. 307, _h_ is therefore fixed firmly, like the index glass of the box sextant, by two screws to the sole plate. The index glass _i_ is held and adjusted in exactly the same manner as the horizon glass of the box sextant, as shown in detail, Figs. 299, 300, the only difference being that the frame which holds the glass is made of the entire height. The rim of the case of the optical square is formed of a short length, 3/8 inch to 5/8 inch, of a pair of telescope tubes which slide easily together. One of these is attached to the sole plate and the other to the cover, so that at first they close together as a box and lid. All the openings required for sight, as Fig. 307 at _Q_ for horizon sight, _o_ for index sight, and _e_ for pin-hole or eye sight, are cut through the two tubes.

687.--The inner case is cut in the plane of some part of the circumference of the instrument from a pin-hole into a bayonet notch, made with a horizontal slot for the two cases to revolve upon each other upon a pin, sufficiently to close and open the sight holes. This plan secures the instrument from any intrusion of dust when it is closed and out of use. An adjusting key is placed in the case, held by a tube or stud at the position _k_. The weight of the entire instrument is about 4 oz. if of ordinary make; but smaller ones are made in German-silver or silver, 1¼ inches diameter, 3/8 inch thick, weighing under 2 oz. These latter are very convenient for the waistcoat pocket, and are equally as exact as the larger instruments. Fig. 309 shows the general outward appearance of the optical square.

688.--_Examination and Adjustment of the Optical Square._--Place two pickets in an open space at a distance apart, the further the better. Range an intermediate short picket in right line with these or the top of a stake the height of the eye, or what is better still, if at hand, the top of a tripod stand. Place the optical square over the intermediate station or tripod. Place another picket, which we will distinguish as the 90° _picket_, at a distance, and make this appear in the optical square coincident by reflection with the direct sight of one of the pickets in the right line from our station. Turn the optical square right over on its place, and looking in the opposite direction take a sight at the other right line picket and observe the 90° picket. If this still appears coincident with the direct line in reflection the optical square is in perfect adjustment. If it does not appear so, half the difference must be adjusted by means of the key taken from the interior of the case and placed on the square at _k_, Fig. 307, and this observation repeated until the 90° is correct.

689.--_In Using the Optical Square_ it is customary to walk along the chain line at about the desired position for taking an offset, looking by direct vision through the plain part of the horizon glass _h_ at a fore sight object until the required object is sighted by reflection at right angles to this, where it appears by coincidence of image with the fore sight. The heel of the forward foot in stepping indicates fairly the vertical position of the optical square; but some surveyors prefer the use of a drop arrow to fix the point. The offset is then chained in the line.

690.--=Double Optical Square.=--This instrument is exactly what its title indicates, that is two optical squares, the one placed exactly over the other, the one reflecting to the right hand and the other to the left. A simpler name, however, would be an _optical cross_. This arrangement of reflectors greatly extends it use. First, as regards the 90°, this need not depend in any way upon the position of the observer, as two objects may be observed, one to the right and one to the left, to appear to cut the direct forward line of sight, and therefore to cut the base line at the exact position of the instrument at right angles to it. Secondly, an intermediate station can be found in direct line between any two points, as the 90° + 90° forms this line.

691.--The arrangement of the optical part of the instrument is shown Fig. 308. The two index glasses _CD_ are fixed at equal angles to the direct line of sight _EO_. The two horizon glasses _AB_ are superimposed with the interval of a small space, 1/16 inch, between them. The horizon glasses are each separately adjusted so that their reflecting planes are respectively 45° to the index glass from which they receive the reflections. The diameter of the instrument as usually made is about 2¼ inches; its depth 7/8 inch. The weight is about 9 oz. It is generally carried in a light, solid leather, sling case. Total weight with instrument, 12 oz.

692.--_Examination and Adjustment of the Double Optical Square._--1. Place the instrument, as already described for the optical square, at a station intermediate between two pickets. Examine the right angles, first looking towards one picket and then towards the other from the same position, as with the optical square, turning it over for this examination. 2. Turn the instrument half round and examine it this way also by turning it over again in like manner. Adjust either horizon glass if required. 3. Now take the position for the eye of the former 90° and see whether the extreme pickets appear in true position by the exact coincidence of their images at 180°. 4. Do this again, facing the opposite way and turning the instrument half round. If the extreme pickets still range in line from the central station the adjustment is perfect. If they do not do so half the error must be corrected by returning to the first and second adjustments to find out between which pair of mirrors it lies. For this adjustment the instrument is much better to be placed upon the top of a tripod, as the position of the axis should remain fixed after turning it over or changing the direction of the instrument. It is only from severe accident that the maker's adjustment will be disturbed.

693.--=Apomecometer.=--This little instrument, the invention of Mr. R. C. Millar, is intended to measure the height of buildings, trees, etc., by measuring the distance from the vertical upon the surface of the ground. It performs one of the functions of the box sextant in the same manner as the optical square, that is, to measure a single angle by reflection. The angle measured is 45°, consequently by measuring a space upon level ground up to a vertical, the vertical will be known, this being equal to the horizontal. Of course this will always be approximate, as the ground will seldom be truly level; but by taking a position, even on an incline, as nearly as possible level with the object, a very fair estimate may be made. Horizontal distances may be measured in the same manner from a perpendicular to any line.

694.--The instrument is constructed in exactly the same manner as the optical square just described as regards its mirrors and its adjustments, but the faces of the mirrors are fixed at the angle of 22° 30′, so as to give a reflection of 45°, upon principles fully discussed. In Fig. 310, _A_ is the index glass, _B_ the horizon glass, _E_ the pin-hole sight. There is a window opposite the index glass, and one behind the horizon glass, each sufficient to take in a wide field of view at about 45° and in the direct line _E_ to _H_. These windows close by rotation of the casing of the box, which is made as the optical square. When closed the instrument is dust-tight and may be carried in the waistcoat pocket loose, or in a light snap leather case. Its size is 1¼ inches diameter, 3/8 inch in thickness, weight 2 oz. in German silver.

695.--_The Use of the Apomecometer._--To measure the altitude of a building the open side nearest level is selected, and a station for observation is taken which is at a distance thought to be approximate to the height. The instrument is held edgewise with the pin-hole sight to the eye, and the reflection of a point of the building about level with the eye is observed by direct vision through the instrument. At the same time there will appear a reflection of the summit of the building. If we now walk backwards or forwards, as the case demands, keeping sight of a level object, as for instance in Fig. 311 the plinth of a building, then at a certain point the summit of the building will appear by coincident reflection. The height of the object will be the same as the distance plus the height of the observer's eye. This distance may be measured on the ground, or if a rough estimate is sufficient it may be stepped, the principle of which is shown by Fig. 310 in the line _OH_, being equal to _FH_. If a part of an object is required to be measured such part may be taken on the horizontal plane, as for instance the height of the figure in Fig. 311, by _ab_ being = _ed_, as the base _ab_ can easily be measured. An approximate may be found by dropping a small pebble at _a_ and at _b_ and then measuring the distance apart of these pebbles.

696.--The distance of an inaccessible object may be measured, as for instance a buoy at sea, by measuring in any straight line double the distance and taking equal angles thereto by the apomecometer on any direct line. An approximate idea may be formed by walking over measuring points. As for instance, _b_ being a buoy at sea, Fig. 312, walk from _e_, at which a walking-stick may be set up, towards an object _o_. At _E_ the buoy and object _o_ will appear to be coincident. Then drop a stone or make a mark directly under the instrument. Walk on till beyond _E′_ and turn to face _e_. Now in returning, the buoy and the object e will appear coincident at _E′_. The distance _EE′_ is double that of the intermediate _a_ to _b_.

FOOTNOTES:

[38] _Posthumous Works_, p. 502; also _Animadversions to the_ Machina Cælestis _of Helvetius_, p. 49.

[39] _Phil. Trans._, vol. xlii. p. 155.

[40] _Phil. Trans._, vol. xxxvii. p. 147.

[41] _Ibid._ p. 340.

[42] See Nicholson's _Navigator's Assistant_.

[43] Pearson's Practical Astronomy, p. 537.

[44] _Ibid._ p. 577.

[45] _Gli Strumenti a Reflessione per Mesurare Angoli_, by G. B. Magnaghi, 1875.

[46] _Description of a New Quadrant_, by George Adams, 1748.

[47] Adams' _Geometrical Essays_, edited by William Jones, 1803.

[48] Prov. Patent No. 2624; Christopher George, 1868.

[49] See British patents--Winter, 1760, No. 752; Ould, 1791, No. 1842; Nugent, 1794, No. 1980; Wright, 1796, No. 2081; Cook, 1796, No. 2087; Roxby, 1822, No. 4695; Glover, 1839, No. 8256; Lane, 1857, No. 1669; Rahill, 1860, No. 1845, etc.

[50] Adams' _Geometrical Essays_, p. 264, 1803.