INSTRUMENTS OF REFLECTION—OCTANT OR QUADRANT—REFLECTING CIRCLE—SEXTANT—PRINCIPLE—PARALLAX—CONSTRUCTION—EXAMINATION—ADJUSTMENT—ARTIFICIAL HORIZON—SOUNDING SEXTANT—BOX SEXTANT—SUPPLEMENTARY ARC—IMPROVEMENTS UPON THIS—OPTICAL SQUARE—OPTICAL CROSS—APOMECOMETER.
615.—The Octant or Quadrant measures angles within 90° by an arc of 45°. This instrument is generally termed an octant on the Continent from the space of the divisions; a quadrant by English-speaking races, from the extent of angles it takes. The idea of bringing the reflection of an object from a mirror in line with the direct sight line from another object, to measure the angle at the position of the observer subtended by the two objects, was originally proposed and worked out in a manner by Hooke,[38] and also by Newton.[39] Newton's invention was the more simple and important. This was communicated to Dr. Halley, then Astronomer Royal, but it was left unpublished until after his death, when it was found in Newton's own handwriting among Dr. Halley's papers.
Newton employed two mirrors to obtain the reflection of an object placed at any angle of less than 90° to the axis of the telescope or sight tube, to throw an image directly through the tube. One of these mirrors was placed at an angle of 45° to the axis of the telescope and covered half its field aperture, so that a direct image of an object could be received by the eye from the open uncovered part of the telescope at the same time as the reflected image of another object from the mirror. The second mirror was placed so as to throw its reflection into the mirror on the end of the telescope without giving any obstruction to the open aperture. This side mirror was fixed with the centre of its plane over the axis of a movable arm which read upon an arc the amount of its angular displacement to 90°. The mirrors were so arranged that their faces should be parallel to each other when the movable arm was placed at the zero of the arc. The graduation of the arc was of double the closeness of the ordinary arc reading, so that the angular positions of the two mirrors in relation to each other was indicated according to the following law:—
That the angle between two reflections in the same plane is equal to twice the inclination of the reflecting surfaces to each other.
616.—Hadley's Quadrant.—In Newton's quadrant the arc was brought most inconveniently in front of the face. By Hadley's arrangement the telescope or sight line is brought in a direction about parallel with the chord of the arc, producing the very convenient form of instrument now in use. This instrument was exhibited at the Royal Society, 13th May, 1731.[40] It was tried experimentally by the Astronomer Royal, August, 1732, in a yacht excursion, when readings were taken satisfactorily within a minute of arc.[41] It afterwards came into general use.
The quadrant was at first held to be sufficient for measuring the sun's altitude for obtaining latitude, but Hadley, as early as 1731, saw the advantage of extending the arc so as to be able to observe the opposite horizon if the direct one was obscured. It was also found that measuring the moon's angular distance from a star beyond 90° was serviceable in determining longitude. He therefore proposed by a duplicate system of reflections to extend the arc by what is termed a back sight to 220°. The means he suggested, which were commonly carried out in instruments of the period, were found to be too complicated for practice.[42] In the meantime the construction of these instruments, originally framed of a combination of wood, ivory, and metal, was much improved by making the frame entirely of metal. There were also great improvements made in the optical parts, by which the arc of 90° was extended. In 1757 Captain Campbell had an instrument constructed of metal of 60° of arc which therefore read to 120°. This instrument, with details of improvement, principally by Ramsden,[43] became the modern sextant.
617.—Reflecting Circle.—As soon as the success of the sextant was assured there appeared to be a general desire to complete the circle by reflections, many inventors thinking this would possess great advantages over the arc of 120°, and we find therefore no lack of inventions to this end, even by eminent men. Reflecting circles, as they are termed, that were of sufficient merit to come into limited use, were designed by Mayer, 1770; Borda, 1787; Mendoza, 1801; Hassler, 1824; Fayrer, 1830. Troughton's circle of about this period was no doubt the best instrument of the class.[44] We have also meritorious reflecting circles by Pistor and Martins, and by Amici.[45] Although these instruments were used at sea to a limited extent, particularly on foreign ships, they were also used on land, where indeed they were more manageable. As no further reference to these reflecting circles will be given, anyone interested in the matter may refer to the books mentioned in the notes, where very full particulars of their structure are given. It was felt necessary to mention the subject here, as the same ideas are constantly cropping up as assumed advantages where previous experience is forgotten. Reflecting instruments at sea are tedious to use when the angle to be taken exceeds that taken in by the eye without movement of the whole body. On land, when the angle exceeds 120°, a theodolite is better; but supplementary angles may be taken with the sextant conveniently on land, where the portability of the instrument is of great consideration. This will be again brought forward in discussing box sextants with supplementary arc.
618.—The Sextant, of the invention of which some particulars have just been given, is only used as a surveying instrument for the exploration of new countries, for which employment—it may be used with or without a tripod or stand—it is found to be a most convenient, light, and portable instrument for the traveller for ascertaining longitude, latitude, and time with the aid only of an artificial horizon. Triangulation may also be taken with it of terrestrial objects, even for the complete circle, by repetitions from station to station in angles within 120°. The same principles which are followed in the construction of the nautical sextant are followed also in the manufacture of two modified forms of this sextant which are used for surveying only, the sounding sextant and the box sextant. As the nautical sextant is most open to observation of its parts it will be more convenient to discuss the construction and general arrangements of this instrument first.
619.—Optical Arrangements of the Sextant.—Newton in the description of his instrument placed the mirrors parallel to each other, that is, to zero of the arc, in his illustration for the demonstration of the principle. In this position he showed that the direction of the reflected ray is coincident with the direct ray entering the eye from the same object or star. This scheme the author has generally found the clearest for illustrating the principle to persons not well acquainted with optics, there being some difficulty in explaining the law just given, art. 615, from a more complicated scheme.
Fig. 283.—Reflection in direct line from two plain mirrors.
620.—If two mirrors be placed with their faces parallel to each other in such a manner that a ray of light may continue after two reflections from them, the ray will continue its path parallel in its direction to its incidence upon the first mirror.
Let MM′, Fig. 283, be two mirrors placed with their faces opposite and parallel to each other. Let the incident ray IM fall on the mirror M whose normal is a. Then, as the angles of incidence and reflection are equal, art. 54, it will be reflected at equal and opposite angle to the normal to M′. Let the normal of M′ be a′. Then again, the incident line MM′ will be reflected at equal angles to the normal to D′, that is, as shown by the diagram, it will continue parallel with the incident ray and in such a position that an object at P would appear to the eye, placed at D′, as though it were at P′ in the direct line of sight.
621.—Parallax.—It will be seen by the figure that the point P does not appear to the eye at D′ in its true position but at P′ therefore with the mirrors MM′ quite parallel, the points P and P′ appear coincident, and would read as one point with the index of the sextant set at zero, that is, at the position when the mirrors are parallel to each other; whereas the points P and P′ really subtend a small angle if direct lines be drawn from them to D′. It is therefore clear that the angle read by coincident reflection and direct or, as it is sometimes called, visual image is less than the true angle at about the position shown. This difference is called the error of parallax. When the object is distant this error is immeasurably small. The parallax error varies proportionately to the distance of the mirrors apart and with their angular position. If the mirrors are in such an angular position that the rays proceeding from an object impinging upon the centre of the first mirror would, if continued, reach the eye, there would be no error of parallax. This occurs in the nautical sextant at about 60°, and the parallax error increases on either side of this point.
622.—In the practice of surveying this small error is neglected. When the box sextant is used the mirrors are placed at a very small distance apart, and the parallax error therefore is extremely small even for near objects. Where two objects are to be triangulated, the one near and the other distant, the parallax error is much decreased or eliminated by taking the near object by direct vision, and the distant object by reflection. In this case, if the near object be towards the right hand, the sextant must be used in an inverted position. If the two objects be both near, a distant object may be sighted in the direction of one of them for the reflected image.
623.—It is readily seen that if the parallelism of the glasses shown in the figure be disturbed, say by a change in the relative angular position of M′ so that the planes M and M′ continued to subtend an angle to each other, then the normal of M′ must also be changed in direction equal to this; but the ray MM′ remaining constant, as there is no movement of M, this ray will therefore be displaced in its reflection from M′ an amount equal to the angle of incidence on M′ from its normal, plus the angle of reflection from the opposite side of the normal, that is, to double the amount of angular change of the position of the mirror or of its normal, which is the same thing. The sextant therefore reads, by change of position of one of its mirrors, half the angle of reflection upon its arc; and to make it read to the angular value of its reflection the divisions on the arc are made twice as close, that is, half degrees are made to read as degrees. This will be better explained by the following scheme.—
Fig. 284.—Principles of reflection of the sextant.
624.—The above scheme, Fig. 284, is taken from Captain Magnaghi's admirable work before mentioned, which gives a very clear geometrical demonstration of the value of angular positions in compound reflection. A ray of light SR directed to a plane mirror R is reflected therefrom to a plane mirror R′, following a plane of reflection perpendicular to the intersection of the two mirrors. The direction R′T of the ray reflected by the second mirror falls into the same plane of reflection, and makes with the direction SA of the incident ray an angle double that which is comprised between the two mirrors.
The two planes of reflection SAB and ABT unite in one because they both contain the line AB and the normal BP to the mirror R′.
In prolonging the normals of the mirrors to their point of intersection P we find that—
BTS = BAS - ABT;
but as ½ BAS - ½ ABT = BPA = BDA,
therefore BTS = 2 BDA.
625.—The mirrors being placed in the position shown in the figure, if we look through a telescope whose visual axis is placed in the line ET, with its objective to the mirror R′, we see in the centre of the field of view the image of the object S reflected consecutively by the mirrors R and R′. We also see in the telescope whether the mirror R′ is only a certain height above the plane of reflection, so as to permit half of the object-glass to receive the rays coming from the point E situated in the prolongation of the line TB, also the image of E which is necessarily coincident with that of S, because the rays by which each image is formed enter the telescope in the same direction BT. Therefore when the images of the two objects E and S appear superimposed or coincident in the middle of the field of view, we have an index given that the mirrors form an angle with each other which is half that which is made at the point T from the same objects, and when one is known the other is easily deduced.
626.—Nautical Sextant.—The ordinary construction of this instrument, Fig. 285, consists of a cast gun-metal frame, forming approximately in outline a segment of a circular disc AA″ including within its extreme radii about 155°.
Fig. 285.—Nautical or astronomical sextant.
627.—The Limb G, which is made only about 1/12 inch in thickness, has generally a face of about ¾ inch in width, which is inlaid with silver or platinum, as Fig. 127, p. 186, to take the graduation to about 140°. The limb is stiffened by a deep, thin rib about ½ inch wide, supported by a corner hollow. The exterior radial arms and interspace framing, Fig. 285 MM, which vary very much in design according to the taste of the maker, is made generally of about 1/14 of an inch in width upon the face of the bars, with a depth of 3/8 inch. This arrangement of the bars placed edgewise gives great stiffness to the surface of the arc with little weight. A handle L, made generally of ebony, is supported on two standards or brace-pieces N, which are carried off to about 2 inches from the back of the frame to hold the handle parallel with the face. The handle has sometimes a hole bushed through it with metal, to support the sextant upon a corresponding pin forming part of a stand or tripod when the instrument is used for taking observations on land. Three feet are placed at the corners of the frame of the sextant, one shown at Q, to support it conveniently on a table to take the reading of an observation just made.
628.—At the centre of the arc a female axis of about 1½ inches in depth E is attached by three screws to the frame perpendicular to the plane of graduation. This carries the male axis, which centres the vernier on the vernier arm M. The axis is covered by a protecting tube which forms one of the three feet upon which the instrument rests when laid down. The vernier arm is made of gun-metal of about 1/16 inch in thickness and from 1 inch diminishing to ¾ inch in width. This is stiffened by a light rib on its upper side.
629.—The Vernier V reads upon an 8-inch sextant, that is, one of eight inches radius, to 10″, the graduations being to 20′ and the vernier taking 120 divisions. A description of the vernier reading was given, art. 318. The vernier falls upon the arc on the plan shown Fig. 127, p. 186. It is clamped near to position by the milled-headed screw H, and is adjusted by the tangent I. A magnifier J is placed on a jointed sling-piece K which traverses the vernier. This is sometimes provided with a ground glass shade to dull the silver for reading. The sling-piece moves the magnifier opposite to any division of the vernier.
630.—Over the axis of the vernier arm a large, oblong mirror, termed the index glass, A, is fixed with its face in a plane cutting the centre of the axis. The index glass is placed with its longest sides approximately in line with the vernier arm. This mirror is placed in a metal tray and is sometimes made adjustable by three screws; but it is better fixed by the maker by screwing the flange-piece, which forms one end of the tray, hard down. The index glass moves with the index arm and gives the first reflection of sun, moon, or star which falls thence upon the horizon glass B.
631.—The Horizon Glass B is placed upon a spur-piece formed in the same casting as the frame. This glass, which is worked perfectly parallel, has the lower half of its surface next the frame silvered. The silver is cut to a sharp line against the plain part. The horizon glass placed in its metal tray has adjustments given to it by means of capstan-headed screws in a manner that will be presently described.
632.—The Telescope screws into a ring fitted at R, which stands upon a bar erect from near the edge of the frame. The female screw by which the telescope is held is formed of two rings which adjust for the amount and direction of separation, so that the telescope may be directed coincident with the horizon glass. The bar or standard supports the ring fitting and is made of either square or triangular section, fitted accurately in a deep socket fitting, in which it slides to raise or lower the ring by means of a milled-headed screw placed on the end of the bar. This permits adjustment only sufficient to bring the axis of the telescope opposite the line of division between the plain and silvered parts of the horizon glass.
633.—Four Circular Shades, carried in square frames fitted with dark bluish-grey glasses, are jointed to the frame at C. These have nib-pieces at the upper corners, so that one or more of the shades may be turned up at a time by the finger-nail to intercept any surplus amount of light from a luminous body reflected from the index-glass; or the whole of the shades may be turned up when observation is made of the mid-day sun. Three other similar shades, but placed in circular frames are fixed at D, which hinge over and back, to be thrown in or out of interception, and are used to subdue the light from the horizon if required.
634.—The Telescopes used as a part of the sextant are generally two in number. One for direct vision is a short tube of about 3 inches in length, focussing at about 4 inches. The optical arrangement is the same as that of an opera glass, consisting of an achromatic object-glass of about 4 inches focus and a concave eye-glass of about 2 inches negative focus, Fig. 14. The second telescope is about 7 inches to 8 inches in length. This has two Huygenian eye-pieces, which have each a wired diaphragm at the mutual focus of the eye-piece and the object-glass. One of these has two fine wires placed parallel for use in adjusting the telescope, and the other has two pairs of crossed wires to indicate the centre of the field of view. There is also a plain pin-hole sight provided for open vision.
635.—The Case in which the instrument is packed is generally made of well-seasoned mahogany, dovetailed together at its corners. The fittings are made to put the instrument back in its case as it was last used within a wide range. A tommy-pin for adjustments and a hand magnifier are supplied with the instrument. The case is generally French polished inside as well as out to prevent absorption of moisture from sea air.
636.—Manufacture and Examination of the Nautical Sextant.—Besides the general good work that this instrument demands, the important points to be observed are, that the glasses should be of hard crown glass worked perfectly parallel from face to face; they should also be well polished. These observations apply to both the reflecting glasses and the shades. The silvering of the mirror should be protected with a good coating of copal varnish. The mirrors should be held by three points only, and be quite free from strain. The upper of the three points should detach, so as to be able to remove the glass at any time for resilvering. The axis should be fitted with all the care necessary for a theodolite, and be placed truly central to the arc. The extremity of the vernier arm when free of its clamp should traverse the arc at equal distance from its face and move with very light friction. The extreme lines of the vernier should cut equal divisions all along the arc 0° to 140°, observations being taken particularly at both ends and in the centre of the arc. The vernier should lie flat on the limb from end to end of the arc. The standard or stem-piece for elevating the telescope should move upwards and downwards stiffly but equally by the motion of its milled-headed screw. The division lines of the limb and vernier should be cut fine but very deep: they should be cut on the dividing engine from the axis of the sextant to ensure true centring of the arc, and not as in the usual plan of having the axis adjusted to the divisions.
Fig. 286.—Section of axis and index glass of sextant.
Fig. 287.—Section of limb and clamp and tangent.
637.—Axis.—This is the most important part of the instrument, and requires the greatest care in construction. Fig. 286 represents this to a scale half size. a the axis, made of hard gun-metal, has a collar by which it is attached to the index arm. The axis is ground and burnished carefully into S the socket-piece, which is fitted into the frame and held down by three screws. At the end of the socket there is a collar-piece B attached upon an angular or tight conical fitting by the screw D, which prevents the axis rising out of its socket. The axis is covered by a cap L which protects it from injury, and this at the same time forms a leg to the instrument as before mentioned. The index glass I is mounted in a tray T shown in section. There are two points of contact at the lower part of the back of this glass, formed by pins, and one point of adjustment pressing against the clip G by a spring C in front, acting contra to a screw at the back E, which adjusts only a small distance to bring the index glass to perpendicularity. The flange-piece F is adjusted in the manufacture so as to leave very small separate adjusting to the index glass necessary.
638.—Section of the Limb and Clamp and Tangent.—The general arrangement is shown in Fig. 287. M arms of the frame; J section of the limb; C clamp attached to the tangent N for clamp and tangent motion, described art. 346; O milled head to clamp; N milled head to tangent. The vernier is shown at V, reading through an opening on the face of the index arm P. The rib to stiffen this arm is shown at R.
639.—The Adjustment Arrangement of the Horizon Glass.—This most important adjustment is constructed in various ways. The plan now generally thought to be the best is for the maker to fix the horizon glass frame firmly in its true position perfectly perpendicular to the surface of the frame, and to allow a small amount of adjustment to the glass only. A convenient plan of doing this is shown in the vertical section full size in Fig. 288. The frame FF is made in one casting, which has its base collar firmly fixed to the frame of the sextant. Fig. 289 is a cross section A to B. H the horizon glass is held upon its face by three points, one of which is shown at L, which is placed in the centre of the top. The lower front points are the exterior corners of a plate which is cut away between. This plate is held by the screw G. The screw G forms a kind of hinge which, together with the elasticity of the plate, gives a slight pressure directing the glass hard upon the points of the screws J and Q. The screw J resists this pressure lightly and permits adjustment of the horizon glass H to angular position in relation to the plane of the index glass to a small extent, by means of a pin placed in the capstan head J. The perpendicular position of the horizon glass, H, is secured by slight adjustment of the capstan head K, which moves against a spring L in the vertical centre of the top of H. This piece, with screw and spring, is attached to the horizon glass frame FF′ by the screw M, so that it may be easily removed to replace or resilver the glass. The silver on the glass is cut to a sharp line at about the point H with a razor.
640.—Testing the Parallelism of the Surfaces of the Glasses.—The best method is to firmly fix a telescope provided with webbed or pointed index diaphragm so that the webs or points cut a distant, sharply defined object, or its edge only, quite clearly. If the glass to be tested be now placed in four directions agreeing with its four sides in front of the object-glass of the telescope, and it is worked perfectly parallel, and is free from striæ, the distant object will not appear to be displaced by its presence in the slightest degree at any position. If the glass be not mounted and is quite square, should there be any very small error, the thickest or thinnest edge should be placed towards the frame; but in this case only a very small error is permissible. The coloured glasses require the same test as the white ones. Where the parallel glass to be tested is small, the object-glass of the telescope may be covered by a paper cap, with a small hole only left through its centre, sufficient to take the glass.
641.—The glasses, when fixed in the sextant, may be examined for parallelism approximately by setting them end up singly to the sun, with the sextant set at an angle that the direct and reflected images of the sun's limb appear just to touch, the eye-piece of the telescope being constantly covered by the sun-glass. If there be a want of parallelism, the image will be disturbed. One reason that the telescopic plan first proposed is better to be followed in the construction of the instrument, is that the telescope is fixed and that there is no indistinctness from unavoidable motion of the body, such as occurs when the sextant is held in the hand.
642.—The Quality of the Surfaces of the Glasses may be examined, both for flatness and brightness and for equality of density, by holding them so that the reflected image of a straight body, as for instance a stretched thin string placed at a distance, may be observed by reflection in glancing over the surfaces with the eye nearly parallel with its plane. If the glass be imperfect the image that reaches the eye will appear to be wavy. If the reflection appear misty, this is generally due to want of parallelism of the glass; but this mode of observation is altogether somewhat technical and difficult to attain without skill.
643.—To Silver the Index or Horizon Glass with Mercury.—Clean the glass thoroughly by boiling it in water containing an alkali (potash or soda), and then polish it off with whiting and water, using a clean piece of old linen or perfectly clean wash-leather. Do not touch the surface with the fingers. Take a piece of clean tin-foil freshly opened from the roll and cut out a piece slightly larger than the glass to be silvered. Lay this upon a smooth pad—an old leather book-cover answers. Place a single drop of clean mercury about the size of an ordinary shot upon the tin-foil and rub this gently over the surface until it is entirely silvered. Now pour very gently sufficient mercury upon the foil till the surface appears to be flooded. Take a sharply cut straight-edge formed of stiff writing-paper, and draw this over the surface of the mercury to clear it. Take a slip of clean smooth writing-paper very little wider than the foil and of about one and a half times its length: spring the paper to a slight curve and place one part of it over the silvered foil so that when it springs open it will cover it and exclude the air from the surface. Now give the glass a final polish and lay it upon the paper over the foil. Hold the glass down with slight pressure with the left hand, and slowly and steadily draw out the slip of paper in the linear direction of the surface of the glass with the right hand. This will take out the air between the foil and the glass, so as to bring the mercury in contact and leave a perfect mirror. It must now be set aside with the glass turned face downwards in an inclined position, so that the surplus mercury may drain off from the foil. Small slips of foil should be put at its lower edge, which, by their attraction for the mercury, will accelerate the draining. The mirror should not be touched after setting it up to drain for twelve hours at least, after which the surplus foil may be trimmed off. After another thirty hours or more it may have any varnish or other protection applied to the back of the silver.
644.—Where instruments are taken abroad mercury silvering may become spotted, so that a small store of mercury and tin-foil should be taken out with the sextant for resilvering. But it should be particularly observed that the mercury should never be placed in the same case with the instrument, as the smallest particle, if it touch the frame, will eat into the brass and destroy its strength. Sealing-wax dissolved in spirit answers for a varnish at the back of the foil fairly well after resilvering if proper varnish be not at hand. It is advisable before attempting to silver a sextant mirror to practise on a few slips of ordinary glass in order to get into the way of doing it. In modern practice base silver is deposited, and no mercury is used, but the process requires special skill.
645.—Adjustment of the Index Glass.—Hold the sextant clamped to about 60° in a horizontal position with the index glass near the eye. Look nearly along the plane of the glass in such a manner as to be able to see one part of the plane of the arc by direct vision, and another part by reflection of it at the same time. If the direct view and the reflected join in one line, and the arc appears as the continuity of a single plane, the index glass is perpendicular to the plane of the sextant. If this be not the case it can be adjusted by turning the set screw placed at the back of its upper centre, Fig. 286 E, very gently.
646.—Adjustment of the Horizon Glass to Perpendicularity.—Place the vernier at zero. Hold the plane of the sextant parallel to the horizon and observe if the image of the horizon seen by reflection at the edge of the silver line coincides exactly with the image received directly through the plain part of the glass. If it does so the horizon glass is perpendicular to the plane of the instrument, that is, assuming the index glass is also perpendicular. In this adjustment it is well to rock the plane of the instrument say 20°, to see that the horizon is cut as a clear line about its horizontal position for this amount of angle. If the mirror be not perpendicular adjust gently by the single screw at the top of the horizon glass frame. If the horizon be not water, the sharp outline of any distinct distant object will answer, or a piece of fine string placed at a distance and stretched straight.
647.—Adjustment for Index.—This is the adjustment for parallelism of the two mirrors at the zero of the arc. The sextant is clamped at zero as before: the arc of the instrument is turned in a vertical position and the horizon again observed. If this appears to cut a clear line through the plain glass and the mirror there is no index error, and the planes of the glasses are truly parallel to each other in this position. If the line is not continuous adjust gently by the lower screw, Fig. 288, at G.
648.—Adjustment of the Horizon Glass by the Sun.—This is a better adjustment than that given above, except that it introduces any error that may be due to the imperfection of the shades; and it is more difficult particularly for the first approximate adjustment. Arrange the telescope and shades so that a clear outline of the sun's limb may be observed without distressing the eye. Place the vernier at zero. Observe the sun, which will be most conveniently sighted at about 40° elevation, first with the plane of the frame vertical, and then horizontally perpendicular to this. If the sun presents a round disc in both these positions the sextant is in adjustment. If in the vertical position there appears to be a small notch at top and bottom of the sun's limb, the glass is not perpendicular to the plane of the instrument, and this requires adjustment by the screw at Fig. 288 K. If notches appear at the sides of the limb when it is held horizontally there is an index error, which may be adjusted at G if it be small.
649.—Index Error after Adjustment Allowance.—The limb of the sextant is graduated 5° beyond the zero position when the glasses are parallel to each other. This is called the arc of excess. The vernier is also divided three lines beyond its zero position, which is marked by an arrow. These extra divisions are placed on the instrument for correcting the index error by measurement of the angle subtended by the diameter of the sun's disc alternately on one side and the other of the zero line, in which observations, if the two readings agree, the sextant must be in perfect adjustment; when they do not agree half the error may be adjusted by the horizon glass. The same observations may also be made with a bright star by setting the index alternately on one and the other side of zero. When the sun is used the reflected and direct images are brought together, so that the two suns that appear in the instrument just touch limb to limb, first upon direct reading and then upon the arc of excess. When the division is adjusted very nearly, any small error, plus or minus, may be allowed as a constant for all readings. In observations of the sun care should be taken that the eye is protected, both by the sun-glass cover to the telescope and by sufficient use of the shades.
650.—Adjustment of the Telescope to Set its Axis Parallel to the Plane of the Sextant.—In fixing up the instrument after manufacture, the ring standard which carries the telescope is set at a measured distance from the plane of the frame, so that the centre of the ring coincides with the height of the silver line cut on the horizon glass. This is necessarily a primary adjustment. For final adjustment the long, inverting telescope is screwed home in the ring, and the eye-piece which has two parallel wires across its diaphragm placed in it. The telescope is brought to focus on any distant object, the eye-piece being turned at the same time to bring the wires parallel with the face of the instrument. Two objects are taken subtending an angle of 90° or over,—as the sun and moon, or the moon and a bright star,—and the index is moved so as to bring the objects, say the limbs of sun and moon, in contact with the wire nearest to the sextant, and fixed there. Then by changing the position of the instrument a little, the images are made to appear upon the wire furthest from the sextant. If the limbs of the sun and moon still remain in exact contact as they appeared before, the axis of the telescope is truly adjusted. If the limbs of the two objects appear to separate at the wire furthest from the sextant, the ring-adjusting screw furthest must be loosened a very little and the screw nearest the sextant tightened the same amount. If the reverse, and the images appear to overlap, adjust in the reverse direction. By repeating this operation a few times the contact will appear to be the same at both wires, and the axis of the telescope will be in collimation, that is parallel with the plane of the instrument. After the telescope is truly adjusted it may be raised or lowered a little to make the reflected and direct images appear equally clear.
651.—Final Examination of the Sextant.—It will be readily seen that an instrument, although correct in theory but depending upon perfection of workmanship in centring, division, surface and parallelism of glasses, and also in its adjustments, can scarcely be brought to perfection. The errors generally increase from the zero point, where adjustments are possible, and are greatest at 140°. In the ordinary commercial sextant of the dealers the errors of centring alone are commonly 3 minutes to 5 minutes, with like errors in other parts. It is therefore better, where the sextant has to be absolutely relied upon, to subject it to actual trial. The zero point can be readily fixed by rules already given; besides this the meridian altitude of several bright stars subtending angles of about 30°, 60°, 90°, and 120° should be measured either from a clear horizon or from a mercury artificial horizon, to be described presently, for angles under 60°, and the errors plus or minus tabulated. The data for the meridian altitudes of certain stars upon any night may be taken from the Nautical Almanac, which will require correction for the latitude and longitude of the observer. This subject is too complicated to be entered upon in detail here. At the present time the National Physical Laboratory undertakes the examination of sextants for a moderate fee. This is effected by means of fixed collimators, art. 229. For angles distributed over the arc the parallax error is eliminated by placing the collimators in pairs. The N.P.L. certificate may now be had with good instruments when purchased. It may be noted that an originally well-made instrument retains its qualities for all time, the wear of such instruments being inappreciable.
652.—To Use the Sextant the right foot should be placed nearly 2 feet in advance of the left and directed at right angles to it. In this position the body is firm. The instrument is supported by the right hand, the elbow being brought down firmly upon the body. The clamp screw first and then the tangent screw are moved by the thumb and finger of the left hand. Some practice is required to make a steady observation. To bring two objects into apparent juxtaposition, methods of observation for terrestrial objects will be reconsidered in discussing the box sextant further on. As regards celestial observations reference should be made to works on practical astronomy, as the subject would take too much space to be entered upon here. The whole subject, with many refinements of correction of parallax, etc., which fall beyond the limits of practical surveying with the sextant, is ably discussed in Chauvenet's Spherical and Practical Astronomy.
653.—Artificial Horizon.—For ascertaining the latitude of a place from the observation of a celestial body by means of a sextant, it is necessary to have some means of estimating the position of the horizon. A method of doing this, originally proposed by the elder George Adams, optician, 1748,[46] was to float a parallel disc of glass upon a basin of mercury, and to receive the reflected image of a star from the mercury by the sextant simultaneously with its direct image. The angle then given by the reading of the arc is double the angle at which the true horizon is placed relatively at the same time. This idea, carried out in a practical form in an instrument henceforth called the artificial horizon[47] is due to Wm. Jones, a well-known optician at the end of the 18th and beginning of the last centuries, who arranged convenient means of making the instrument portable, and to keep the mercury from disturbance of the air by covering it with a glass roof. The form of artificial horizon that he invented has been in common use ever since. He also invented another simpler form, which was that of taking the reflection from a piece of silvered, or of black, glass. The performance of the artificial horizon depends in any case entirely upon means of obtaining a reflection from a perfectly horizontal surface.
Fig. 290.—Diagram of artificial horizon.
654.—Theory of the Artificial Horizon.—A ray M′ Fig. 290, from a luminous body, at infinite distance will have its image reflected from a level reflecting surface SS′ at an angle equal and opposite to the incident ray, the angles M′AS and EAS′ being equal. Let E be the place of the eye or the sextant: this will receive a ray from the same distant body in direction ME, which is sensibly parallel with M′A. The angle MEA being double the angle of incidence M′AS, the half of this angle will therefore produce the horizontal line EH at the height of the observer's eye if the plane of reflection SS′ be level. Therefore if we take half this angle MEA as it appears in the sextant, it will give an angular position of the object in relation to the horizon at the height of the eye, or be tangential to the surface of the earth. If M′AS be 30°, the angle AEM will be 60°, showing the elevation of object half this or 30°. The sextant takes 120° with certainty; therefore 60° will be the limit of meridian altitude the artificial horizon will measure.