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H is the horizon-glass, one-half of which is a reflector or mirror, and the other half plain glass to admit of objects being seen through it; it is fixed perpendicularly to the plane of the instrument, and parallel with the index-glass when o° on the vernier stands at o° on the arc.
At S are the index shades, of coloured glass, to be turned down between the index-glass and horizon-glass, as the eyesight requires, in order to moderate the brightness of an object-as the sun or moon.
At S'are the horizon shades, of coloured glass, to be turned up (as required) beyond the transparent part of the horizon-glass.
T is the telescope, to be screwed in the collar C, which is a double ring. When the telescope is absent, the collar is the place of the sight vane.
M is the microscope (movable) for reading accurately the divisions of the arc and vernier.
B is a tangent screw for giving a small motion to the index after it has been partially fixed by a clamping screw, which is at the back of the lower end of the index-bar and under the vernier (V).
The handle of the sextant, by which it can be held in any position between the vertical and horizontal, is partly shown beneath the index-bar.
The arc (or limb).-The limb is the circular part of the frame of the sextant, into which is let the arc (A A') consisting of a thin piece of platinum, or silver.
The INDEX-GLASS (I) is a plane reflector or mirror of quick-silvered glass, set in a brass frame, and so placed that the face of it is perpendicular to the plane of the instrument, and immediately over the centre of motion of the index-bar. This mirror, being fixed to the index-bar, moves with it, and changes its direction as the direction of the index-bar is changed.
This glass is designed to reflect the image of the sun, or any other object, upon the horizon-glass, whence it is reflected to the eye of the observer. The brass frame of the index-glass is fixed to the index-bar by two screws directly at the back; and a third (outer) screw serves to adjust it in a position perpendicular to the plane of the instrument.
NOTE. The graduation of the arc may be perfect in itself, but if the index-glass and indexbar are not properly centered, to correspond to the arc of the instrument to which they are attached, then you have the centre of another arc, and consequently the vernier in passing along the arc of the instrument will give inconsistent readings as it is moved to different parts of the limb.
The HORIZON-GLASS (H) is parallel to the index-glass when o on the vernier stands at o on the arc; this mirror receives the rays of the object reflected from the index-glass, and transmits them to the observer. The horizon-glass is only silvered on its lower half, the upper half being transparent (or plain), in order that any object may be seen directly through itas, for instance, the horizon or any object towards which the line of sight is directed. The glass is set in a brass frame, standing perpendicularly to the plane of the instrument, and fixed there; on the back of the frame are two screws-one towards the top, and the other near the bottom (or base), of the glass, towards one side, to effect any required adjustments of the horizon-glass.
The COLOURED GLASSES or SHADES (S S') are used to prevent the rays of the sun, or glare of the moon, from affecting the eye when taking observations. Each glass is set in a brass frame which turns on a centre. Four shades are placed between the index-glass and horizon-glass, to screen the
eye from the brightness of the reflected solar image, or the glare of the moon, and may be used separately, or together, as occasion requires. Three more such glasses are placed behind the horizon-glass to weaken the rays of the sun or moon when they are viewed directly through the horizonglass. The pale glass is sometimes used in observing altitudes at sea, to take off the strong glare of the horizon.
These glasses, when examined singly, should exhibit no streakiness or flaws, and each glass should show a uniform shade of colour over its whole area; also each glass should work easily and parallel to its fellows on either side.
The TANGENT SCREW (B) and Clamping Screw.-In order to observe with accuracy, and make the images of the observed objects come precisely in contact, an adjusting, or tangent screw (B), is attached to the index, by which it may be moved with greater regularity than can be done by hand; but it must be observed this screw does not act until the index-bar is fixed by the clamp or finger screw, placed at the back of the lower part of the indexbar. Care should be taken not to force the tangent screw when it arrives at either extremity of its arc. When the index is to be moved any considerable quantity, the clamping screw must be loosened; but when the index is brought nearly to the division required, this back screw should be slightly tightened, and then the index be moved gradually by the tangent screw.
The vernier will require a special description presently.
Accuracy of the instrument.-When the joints of the framework are close and tight, and the various screws fit closely and act well-when the centering of the instrument is perfect-when the graduation of the limb and the vernier is accurate in every part-when each of the reflectors or mirrors has its two faces parallel, and the glass perfectly clear-and when the shades have clear glasses, the two faces of each glass parallel, and the set work with all their faces parallel-the instrument may be considered perfect, as regards the optical and mechanical principles of its construction, and without any sensible error but what the adjusting screws can rectify.
Inside the box which holds the sextant, when not in use, are various telescopes and glasses.
TELESCOPES.-The sextant is generally furnished with a plain tube without any glasses-which is merely a sight vane. Also to render objects still more distinct, it has likewise two telescopes; one to represent objects erect, or in their natural position; the other, a longer one, which shows the objects inverted; but the latter has a larger field of view, and a greater magnifying power, with other advantages: use and experience will soon accustom the observer to the inverted position, and the instrument can then be as readily managed by it as with the plain tube alone. By a telescope the contact of the images is more perfectly distinguished; and by the place of the images in the field of the telescope it is easy to perceive whether the sextant is held in the proper plane for observation. By sliding the tube that contains the eye-glasses in the inside of the other tube, the object is suited to different eye-sights, and objects made to appear perfectly distinct and well defined.
The telescope is to be screwed into a circular ring or collar (C): this ring rests on two points, against an exterior ring, and is held thereto by
two screws; by turning one and tightening the other, the axis of the telescope may be set parallel to the plane of the sextant. The exterior ring is fixed on a brass stem that slides into a socket; and by means of the screw at the back of the sextant, it may be raised or lowered so as to move the centre of the telescope to point to that part of the horizon-glass which shall be judged the most fit for observation.
A circular eye-piece, with coloured glasses, accompanies the sextant and is to be screwed on the eye-end of the tube, or on that of either telescope.
To these appendages are added a small screw-driver, to adjust the screws; a magnifying glass, to read off the observation with greater accuracy; and a microscope, for the same purpose, made to fit into a tube fixed at the lower end of the index-bar.
PRINCIPLE OF THE SEXTANT
The principle on which the sextant or quadrant and other reflecting instruments depend is connected with certain principles of optics, and the laws relating thereto
(1) The angle of incidence and angle o, reflection are equal; that is, if a ray of light is incident (or falls) upon a plane reflecting surface, and is thence received by the eye, or passes into space, the incident ray makes, with the perpendicular to the reflecting surface, an angle equal to the angle made with the same perpendicular and the reflected ray. Again
(2) If a ray of light suffers two successive reflections in the same plane by two plane mirrors, the angle between the first and last directions of the ray is equal to twice the inclination of, or angle between, the reflecting surfaces of the mirrors
In the annexed fig. which represents the outline of the sextant, the two mirrors are: I the index-glass, and H the horizon-glass; when the index-bar I V lies in one with I A' the two mirrors are parallel. Move the index-bar I V to the middle of the arc: let a ray of light coming from the sun S fall on the index-glass I, at a certain angle, and thence be reflected at the same angle to the half-silvered part of the horizon-glass H, whence it is again reflected along the line HE to the telescope, or observer's eye at E. The telescope, or eye-piece, is always so placed that the lines EH and I H make equal angles with the direction of the mirror H; then, by the law of reflection, a ray falling on the mirror H, in the direction I H, is always reflected in the direction H E. The observer looking along the line E H will see, through the transparent part of the horizon-glass, the sea-horizon, and also at the same time the image of the sun in the silvered part of the horizon-glass.
The angle SE H is the angular height of the sun, which is its altitude; and this angle is twice the angle of the mirrors, that is twice IB H or twice A'I V. The arc A' V which measures this angle is then the measure of one-half the altitude, or angular distance of S from the sea-horizon. The vernier at V indicates the exact value of the arc; but in crder to avoid
the necessity of doubling this value after reading, a half degree of the arc is numbered as a whole degree: thus an arc of 60° (as on the sextant) is divided into 120 equal parts, each of which is reckoned as a degree.
PROOF OF THE PRINCIPLE OF THE SEXTANT
Let I A' be the position of the index bar when the mirrors are parallel to each other, and I V the position when moved to V. It is required to prove that the angle SE S' is double the angle V I A' or BIE.
Draw P I perpendicular to the index glass I, bisecting the SIH, and draw BH parallel to A'I. Now / SIa = HIB because they are each the complement of the equal angles SIP and PI H, also SI a = /BIE (Euc. I. 15), therefore HIE = twice the BIE or twice the angle of the inclination of the mirrors.
Now the S'HI = /HIE + HEI (Euc. I. 32); produce B H to D, bisecting the S' HI. Now DHS' HE I, and the remaining /DHI= <HI E, therefore the HIE = / H E I, and as HIE = 2 BIE, it is proved that S E S', the altitude, is equal to twice the inclination of the mirrors to each other.
TO READ THE SEXTANT
The VERNIER (see Plate VIII. Figs. 1 and 2) is a small scale attached to the lower part of the index-bar of the instrument; it is slightly inclined to the face of the limb, and moves, with the index-bar, in close contact with the graduated arc A A': by means of the vernier we are enabled to read off aliquot parts of the smallest spaces into which the arc of the instrument is divided.
To read off the sextant by means of the vernier; look at an instrument while you read the description: first, note that the starting-point of the vernier, on the right, is sometimes o, and sometimes an arrow head or other device. The limb (arc) of the instrument is divided (graduated) to degrees, and parts of a degree; the degrees are indicated at intervals by numerals, the intermediate long strokes are also degrees, and the shortest divisional strokes are parts (i.e., a certain number of minutes) of a degree. You will also see long and short strokes on the vernier-the long ones are minutes of a degree, and the shorter ones a certain number of seconds of a minute. Both are read from right towards left.
If the degrees on the arc are divided into three equal parts then each stroke equals 20', and each stroke on the vernier equals 20"; when the degrees on the arc are divided into four equal parts, each stroke equals 15' and each stroke on the vernier equals 15", and when the degrees on the arc are divided into six equal parts each stroke equals 10' and each stroke on the vernier equals 10”.
The principle on which the vernier is graduated is as follows: Suppose a vernier is desired for a foot rule; eleven inches would be the length of the vernier, which would then be divided into twelve parts, so with the sextant, 60 divisions on the vernier correspond to 59 on the arc. Thus―
60 v =
o that is, one division on the vernier is of 10'
Read the arc or limb to minutes of a degree, and when you understand
IO" shorter than one on the
this you will soon be able to read to seconds. First, examine well the sequence of degrees and minutes.
Take a sextant divided to 10'; then, on any part of the arc, the first short stroke is 10', the second 20', the third 30', the fourth 40', and the fifth 50'; if the o of the vernier exactly coincides with a long stroke of the arc, the reading is degrees, and no minutes; it may be 10, 14, 20, etc.-any number. Now put o of the vernier to coincide exactly with the fifth short stroke to the left of 20° on the arc, and the reading will be 20° 50′, since each short stroke of the five beyond 20° represents 10'. Lastly, fix your eye on the space between 42° and 43°; now put o of the vernier to stand somewhere between the third and fourth short strokes to the left of 42°; in the first place the reading will be 42° 30', but it must be something more because the vernier indicates minutes between 30′ and 40′; now look along the line of the vernier and see which minute stroke on it coincides with any stroke on the arc of the sextant; let us say that it is the seventh minute stroke; then the reading will be 42° 37'. In Plate VIII. Fig. 2, the o on the vernier is somewhat more than three divisions, or 30', to the left of 56°; and the division on the vernier, coinciding with one on the arc, is 5′ 20′′, therefore the angle pointed out by the index division is 56° 35′ 20′′.
The arc of excess. Thus far we have been reading on the arc; next learn to read off the arc, that is, on the arc of excess to the right of o on the arc: the subdivisions are the same as on the arc, but now you read from left to right; the vernier is also read in the same way; and on the sextant divided to Io' the 10 of the vernier reads as o, then 9 will be 1, and 8 will be 2, &c. ; say the o of the vernier stands between the third and fourth strokes to the right of o on the arc, and the fourth minute stroke of the vernier coincides with a stroke on the arc, then the reading on the arc of excess, that is off, will be 36′, since the fourth stroke is 6 when reckoned from the left of the vernier.
ADJUSTMENTS OF THE SEXTANT
The theory of the sextant as a reflecting instrument requires the following conditions, viz.—
(a) The two surfaces of each mirror and the shade glasses must be parallel planes ;
(b) The graduated arc, or limb, should be a plane, and with its vernier accurately divided;
(c) The axis should be at the centre of the limb, and perpendicular to its plane;
(d) The index-glass and horizon-glass should be perpendicular, and the line of sight parallel, to the plane of the limb.
(a), (b), and (c) are carefully attended to by the maker; they admit of being tested and any deviation found, but only by well-devised observations. The complete theory provides formulæ for ascertaining their defects and the corrections of such errors; (d) indicates the principal adjustments to be made by the observer.
To adjust a sextant is to set the index-glass and horizon-glass perpendicular to the plane of the instrument, and their planes parallel to each other when the index-division is at o on the arc; also, to set the axis of the telescope parallel to the plane of the instrument; each of these particulars must be examined before an observation is taken, and the adjustments, if requisite, made according to the following directions.