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I. To set the Index-Glass perpendicular to the Plane of the Instrument

Place the index-bar near the middle of the arc, and holding the instrument in a horizontal position, with its plane upwards, the index-glass close to the eye, and the arc away from you, look obliquely into the glass in such a manner that you may see the arc by direct view, and by reflection, at the same time ; if the arc seen by reflection forms an exact plane with the arc seen by direct view, the glass is perpendicular to the plane of the instrument, and it is in adjustment; but if the reflected part of the arc appears lower than the true arc, tighten the adjusting (outer) screw at the back of the frame ; if higher, slacken it.

II. To set the Horizon-Glass perpendicular to the Plane of the Instrument

Screw the plain tube, or the common telescope, into the collar ; set o on the vernier to o on the arc; and, holding the instrument horizontally, | look through the telescope and the horizon glass at the sea-horizon, and observe if the reflected and true horizons appear in one line ; if they are, the horizon-glass is perpendicular to the plane of the instrument, and in adjustment; otherwise, turn the uppermost screw at the back of the instrument till they perfectly coincide.

This adjustment may also be made by directing the view through the telescope to the sun, o on the vernier coinciding with o on the arc; hold the instrument perpendicularly and direct the telescope to the object; move the index-bar so that the reflected image shall pass over the direct object ; if the reflected image be to the right or left of the direct object, turn the screw (as before) till they coincide with each other, when the glass will be perpendicular to the plane of the instrument. If the adjustment be made by a star, move the index backwards and forwards slowly, and observe if the reflected image, in passing the star, coincides with it.

When this or the following adjustment is made by observing the sun, the inverting telescope is always to be used, and one or more of the shades, both before and behind the horizon-glass, are to be turned up, in order to screen the eye from the bright solar rays proceeding from the direct and reflected suns, which are to be made, by means of the shades, to appear as nearly as possible of the same degree of brightness.

III. To set the Horizon-Glass parallel to the Index-Glass, when the Index

Division is at o on the Arc Make the index division of o on the vernier to coincide exactly with o on the arc; and, in order to make the coincidence as perfect as possible, examine them through the magnifying glass, or microscope, and fix the index by the clamp under it; screw on the telescope. Having done this, hold the sextant perpendicularly, and direct the sight through the telescope to the horizon ; then, if the true horizon seen through the clear part of the horizon-glass appears in a line with the reflected horizon on the silvered part, the horizon-glass and index-glass are parallel. But if the reflected and truc horizons do not coincide, turn the lower screw at the back of the horizon-glass till they are made to appear in the same straight line, then vill the planes of the horizon-glass and index-glass be parallel.

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IV. To set the Axis of the Telescope, when screwed into the collar, parallel to the

Plane of the Instrument (Error of Collimation) In measuring angular distances, the line of sight, or axis of the telescope, should be parallel to the plane of the instrument, as a deviation in that respect may occasion a considerable error in the observation, and this is most sensible in large angles; to determine the error use the telescope in which are placed two wires parallel to each other, and equidistant from the centre, to which are generally added two others at right angles to these, and parallel to each other. By means of these wires the adjustment may be made thus : screw on the telescope, and turn the tube containing the eyeglass till two of the wires are parallel to the plane of the instrument; then take two objects, as the sun and moon, or the moon and a star, or two stars, whose angular distance must not be less than go to 100 degrees, because the error is more easily discovered when the distance is great: bring them exactly into contact at the wire which is nearest to the plane of the sextant, and fix the index; then by altering a little the position of the instrument, make the objects appear on the other wire. If the contact still remains perfect, the axis of the telescope is in its right situation ; but if the limbs of the two objects appear to separate at the wire that is farthest from the plane of the instrument, it shews that the object-end of the telescope inclines towards the plane of the instrument, which must be rectified by tightening the screw of that part of the collar nearest to the sextant, having previously slackened the screw farthest away. If the images overlap each other at the wire farthest from the sextant, the object end of the telescope is inclined from the plane of the instrument, and therefore adjust in a contrary manner. By repeating this observation a few times, the contact will be precisely the same at both wires, and consequently the axis of the telescope will be parallel to the plane of the instrument, or the line of collimation will be correct.

The inverting telescope is a lunar instrument. It is now of no particular use except for taking altitudes in connection with the artificial horizon. It is of little use for altitudes at sea, since we are never sure of the horizon to half a minute owing to abnormal refraction.

To find the Index Error The index error is the number of minutes and seconds pointed out by the vernier, when the direct object and its reflected image coincide with each other, and may be found (1) by the sea-horizon, or (2) with greater accuracy by the sun.

By the horizon.-Set o on the vernier to o on the arc, hold the sextant vertically, and look at the horizon through the horizon-glass : if the horizon and its image are not in one line, move the tangent screw till they are so : the reading is the error.

The reading may be on the arc proper, or on the arc of excess : it is on The latter when o on the vernier is to the right of o on the arc, and the reading is then said to be off the arc; when o on the vernier is to the left of o on the arc, the reading is said to be on the arc. The error is really the difference between the position of o on the arc and o on the vernier.

If o on the vernier falls to the right of o on the arc, i.e., off the arc proper but on the arc of excess, every measurement will be too small, therefore index error is additive : if o on the vernier falls to the left of o on the arc, i.e., on the arc proper, every measurement will be too great, therefore the index error is subtractive.

This method of finding the index error is not one of great precision.

By the sun.—Having screwed the inverting telescope into its place, adjusted the eye-tube to distinct vision, and turned up the proper shades, place o on the vernier about 30' to the right of o on the arc, and tighten the clamp under the index of the sextant; then, holding the instrument perpendicularly, bring the direct and reflected suns in exact contact by the tangent screw, and read off the minutes and seconds pointed out by the vernier on the arc of excess, which note down, and call it off ; next place o of the vernier about 30' to the left of o on the arc, and make the contact of the two suns correct, as before; read the minutes and seconds indicated by the vernier on the arc proper, which call on, and set them under the first reading ; then half the difference between the two readings will be the index error, which is additive to all angles taken with the sextant, when the greater reading is on the arc of excess, and subtractive when the greater reading is on the arc proper. The direct and reflected suns will appear through the inverting telescope thus Appearance on the arc of excess.

Appearance on the arc proper.

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If the following observations had been taken to determine the index error, mark off with a positive sign, and on with a negative sign.

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Index error 37" subtractive, be- Index error 25" additive, because the arc to the left, or on, cause the arc to the right, or off, is greater than the arc to the is greater than the arc to the right, or off.

left, or on. To prove that the contacts were made correctly, add the arcs together and divide their sum by 4; the quotient should then be equal to the sun's semi-diameter, as given in page II. of the given month in the Nautical Almanac. Thus, suppose the observations in Example I. were made on February 26th, 1888: here the sum of the arcs is 64' 45", the fourth part of which is 16' 11", agreeing nearly with the sun's semi-diameter (16' 11":I) as

given on that day in the Nautical Almanac; it may therefore be presumed that the contacts were correctly made.

NOTE.—If the altitude of the sun should be less than about 20° at the time of taking the above observations, the sun's horizontal, instead of the perpendicular, diameter should be measured ; for as refraction affects the lower limb more than the upper, it occasions the perpendicular diameter to be less than the horizontal, which is that given in the Nautical Almanac: in this case the sextant is to be held horizontally, with the face upwards, and the reflected sun brought into contact alternately with the right and left limbs of the direct (or real) sun, as before explained; the contacts will then appear thusReflected

Direct
Direct

Reflected sun.

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By a star.-Set the sextant exactly at 0. Select a moderately bright star, look at it through the telescope and horizon-glass in the usual way, holding the sextant vertically. If the reflected and real stars coincide there is no index error and the sextant is in adjustment.

If the horizon-glass is not perpendicular to the plane of the sextant the reflected star will appear to one side thus

If the horizon-glass and the index-glass are not parallel to one another the reflected star will appear thus

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While still holding the sextant vertically slip the small lever found in the box into one of the holes in the adjusting screws and turn the screws, first one and then the other, until the reflected and the real stars coincide.

USE OF THE SEXTANT

To observe Altitudes at Sea, by the Sea-Horizon The altitude of any object is measured by the position of o on the vernier, when, by reflection, the object appears to be on the sea horizon: the face of the observer is directed towards that part of the horizon immediately under the object, and the instrument must be held perpendicular to the horizon so that its plane produced would pass through the object.

TO TAKE THE SUN's ALTITUDE.-Set the index at o ; fix what shades you require ; direct the eye through the sight vane and horizon-glass to that part of the horizon exactly under the sun; move the index from you, along the arc, and the image of the sun will appear to descend towards the horizon; when the sun's lower limb touches the horizon with accuracy in the centre of the field, stop, and read off the altitude on the arc of the instrument.

Or having proceeded as just described, and having taken a rough or ap proximate altitude, you can clamp the index, screw in the telescope, and use the tangent screw to get a more perfect observation when the sun's lower limb just touches the horizon.

FOR AN ALTITUDE OF A STAR.—In order to be sure that you have the right star : when the index is at o, direct the sight to it, and bring it down gradually to the horizon by moving the index from you.

Both for Sun and Star it may be better to give the instrument a slight vibratory motion to right and left, to be sure that you have measured a part of a vertical circle.

The meridian altitude will have to be watched for some minutes, and the use of the tangent screw is indispensable; the altitude rises until the object is on the meridian, then seems to be stationary for the moment, and subsequently descends (dips).

For the moon's altitude observe the enlightened limb; it may be the upper or lower limb according to her position.

The Artificial Horizon When altitudes are to be taken on shore with a sextant, where the observer has not the advantage of the sea-horizon, he is obliged to have recourse to an artificial horizon, which is a horizontal plane with a smooth or polished surface, on which the rays of the sun or other object falling are reflected back to an eye placed in a proper position to receive them ; theangle between the real and reflected objects being then measured with a sextant, will be double the altitude above the horizontal plane.

Such a horizontal plane may be obtained by pouring a quantity of oil, tar, treacle, or other fluid and viscous substance, into a shallow vessel ; and to prevent the wind giving a tremulous motion to its surface, a piece of thin gauze, muslin, or plate-glass, whose surface is perfectly plane and parallel, may be placed over it when used for observation.

An artificial horizon sometimes consists of a plane mirror, fixed in a brass frame, standing upon three adjusting screws, by which its surface may be made horizontal with the assistance of a spirit-level placed on its surface in various positions ; observing that the screws be turned until the air-bubble always rests in the middle of the tube. The under surface of the plate of glass is sometimes unpolished and blackened, so that the image of the sun can only be reflected from the upper surface, which would be carefully polished, and be a perfect plane; by this means the errors that might arise from a defect of parallelism in the two surfaces are avoided.

But the best and most approved kind of artificial horizon is that produced by quicksilver, which being poured into a small shallow trough will always preserve an exact horizontal plane at its surface : over this is placed a roof to protect the quicksilver from the action of the wind; in the roof are fixed two plates of glass, the two sides of each being ground perfectly plane and parallel. These are usually packed in a mahogany box, with a vessel containing a quantity of quicksilver, ready for use when wanted.

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