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with the next division on the arch, the second division will require a change of two minutes, the third of three minutes, and, so on, till the 20th stroke on the nonius arrives at the next 20 minutes on the arch ; the 0 on the nonius will then have moved exactly 20 minutes from the division whence it set out, and the intermediate divisions of each minute have been regularly pointed out by the divisions of the nonius. The divisions of the nonius scale are in the above case reckoned from the middle towards the right, and from the left towards the middle; therefore the first 10 minutes are contained on the right of the 0, and the other 10 on the left. But this method of reckoning the divisions being found inconvenient, they are more generally counted beginning from the righthand towards the left; and then 20 divisions on the nonius are equal to 19 on the limb, consequently one division on the arch will exceed one on the nonius by one-twentieth part, that. is, one minute. The 0 on the nonius points out the entire degrees and odd twenty minutes subtended by the objects observed; and if it coincides with a division on the arch, points out the required angle: thus, suppose the 0 on the nonius stands at 25 degrees, then 25 degrees will be the measure of the angles observed; if it coincides with the next division on the left-hand, 25 degrees 20 minutes is the angle; if with the second division beyond 25 degrees, then the angle will be 25 degrees 40 minutes; and so on in every instance where the 0 on the nonius coincides with a division on the arch; but if it does not coincide, then look for a division on the nonius that stands directly opposite to one on the arch, and that division on the nonius gives the odd minutes to be added to that on the arch nearest the right-hand of the 0 on the monius; for example, suppose the index division does not coincide with 25 degrees, but that the next division to it on the nonius is the first coincident division, then is the required angle 25 degrees 1 minute; if it had been the second division the angle would have been 25 degrees 2 minutes, and so on to 20 minutes, when the 0 on the monius would coincide with the first 20 minutes on the arch from 25 degrees. Again, let us suppose the 0 on the nonius to stand between 50 degrees and 50 degrees 20 minutes, and that the 15th division on the nonius coincides with a division on the arch, then is the angle 50 degrees 15 minutes. Further, let the 0 on the nonius stand between 45 degrees 20 minutes and 45 degrees 40 minutes, and at the same time the 14th division on the nonius stands directly opposite to a division on the arch, then will the angle be 45 degrees 34 minutes. The index glass F is a plane speculum, or mirror of glass quicksilvered, 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. This mirror being fixed to the index moves along with it, and has its direction changed by the motion thereof. This glass is designed to reflect the image of the sun, or any other object, upon either of the two horizon glasses, from whence it is reflected to the eye of the observer. The brass frame, with the glass, is fixed to the index by the screw M: the other screw N serves to place it in a perpendicular position, if by any accident it has been put out of order. The horizon glasses G and H are two small speculums on the radius of the octant; the surface of the upper one is parallel to the index glass when the 0 on the nonius is at 0 on the arch; these mirrors receive the rays of the object reflected from the index glass, and transmit them to the observer. The fore horizon glass G is only silvered on its lower half, the upper half being transparent, in order that the direct object may be seen through it. The back horizon glass H is silvered at both ends; in the middle there is a transparent slit, through which the horizon may be seen. Each of these glasses is set in a brass frame, to which there is an axis; this axis passes through the wood-work, and is fitted to a lever on the under side of the quadrant, by which the glass may be turned a few degrees on its axis, in order to set it parallel to the index glass. To set the glasses perpendicular to the plane of the quadrant there are two sunk screws, one before and one behind each glass: these screws pass through the plate on which the frame is fixed into another plate, so that by loosening one and tightening the other of these screws, the direction of the frame, with its mirror, may be altered, and thus be set perpendicular to the plane of the instrument. The dark glasses, or shades, I, are used to prevent the bright rays of the sun, or the glare of the moon, from hurting the eye at the time of observation; there are generally three of them, two red, and one green. They are each set in a brass frame which turns on a centre, so that they may be used separately or together, as the brightness of the object may require. The green glass may be used also alone, if the sun be very faint; it is likewise used in taking observations of the moon; when these glasses are used for the fore observation, they are set immediately before the fore horizon glass, as in fig. 1, but in front of the other horizon glass at O when a back observation is made.

The sight vanes K and L are pieces of brass, standing perpendicular to the plane of the instrument: the vane K is called the fore sight vane, and L the back sight vane. There are two holes in the fore sight vane, the lower of which and the upper edge of the silvered part of the fore horizon glass are equidistant from the plane of the instrument, and the other is opposite to the middle of the transparent part of that glass; the back sight vane has only one hole, which is exactly opposite to the middle of the transparent slit in the horizon glass to which it belongs: but as the back observations are liable to many inconveniences and errors, we shall not give any directions for their practice.

The adjusting lever (fig. 3), which is fixed on the back of the quadrant, serves to adjust the horizon glass, by placing it parallel to the index glass ; when this lever is to be used, the screw B must be first loosened, and when by the adjuster A, the horizon glass is sufficiently moved, the screw B must be fastened again, by which means the horizon glass will be kept from changing its position.

ADJUSTMENTS.

The several parts of the quadrant being liable to be out of order from a variety of accidental circumstances, it is necessary to examine and adjust them, so that the instrument may be put into a proper state previous to taking observations.

An instrument properly adjusted must have the index glass and horizon glasses perpendicular to the plane of the quadrant; the plane of the fore horizon glass parallel, and that of the back horizon glass perpendicular, to the plane of the index glass, when the 0 on the nonius is at 0 on the arch ; hence, the quadrant requires five adjustments, the first three of which, being once made, are not so liable as the last two to be out of order; however, they should all be occasionally examined, in , case of an accident.

I. To set the plane of the index glass perpendicular to that of the instrument. o Place the index near to the middle of the arch, and holding the quadrant in a horizontal position, with the index glass close to the eye, look obliquely down the glass, in such a manner that you may see the arch of the quadrant by direct view and by reflection at the same time; if they join in one direct line,

and the arch seen by reflection forms an exact plane, or straight line, with the arch seen by direct view, or if the image of any point of the arch near B appear of the same height as the corresponding part of the arch near C, seen direct, the glass is perpendicular to the plane of the quadrant; if not, it must be restored to its right position by loosening the screw M, and tightening the screw N, or vice versa, by a contrary operation. II. To set the fore horizon glass parallel to the index glass, the inder being at 0. Set the 0 on the nonius exactly against 0 on the arch, and fix it there by the screw at the under side. Then holding the quadrant vertically, with the arch lowermost, look through the sight vane, at the edge of the sea, or any other well-defined and distant object. Now, if the horizon in the silvered part exactly meets, and forms one continued line with that seen through the unsilvered part, the horizon glass is parallel to the index glass. But if the horizons do not coincide, then loosen the button-screw in the middle of the lever, on the under side of the quadrant, and move the horizon glass on its axis, by turning the nut at the end of the adjusting lever, till you have made them perfectly coincide; then fix the lever firmly in this situation by tightening the button-screw. This adjustment ought to be repeated before and after every observation. Some observers adopt the following method, which is called finding the inder error. Let the horizon glass remain fixed, and move the index till the image and object coincide; then observe whether 0 on the nonius agrees with 0 on the arch, if it does not, the number of minutes by which they differ is to be added to the observed altitude or angle, if the 0 on the nonius be to the right of the 0 on the arch, but if to the left of the 0 on the limb, it is to be subtracted. It has already been observed, that that part of the arch beyond 0 towards the right-hand is called the arch of excess: the nonius, when the 0 on it is at that part, must be read the contrary way, or, which is the same thing, you may read off the minutes in the usual way, and then their complement to 20 minutes will be the real number to be added to the degrees and minutes pointed out by the 0 on the nonius.

III. To set the fore horizon glass perpendicular to the plane of the quadrant.

Having previously made the above adjustment, incline the quadrant on one side as much as possible, provided the horizon continues to be seen in both parts of the glass; if, when the instrument is thus, inclined, the edge of the sea seen through the lower hole of the sight vane continues to form one unbroken line, the horizon glass is perfectly adjusted; but if the reflected horizon be separated from that seen by direct vision, the speculum is not perpendicular to the plane of the quadrant: then if the limb of the quadrant is inclined towards the horizon, with the face of the instrument upwards, and the reflected sea appears higher than the real sea, you must slacken the screw before the horizon glass, and tighten that which is behind it; but if the reflected sea appears lower, the contrary must be performed. Care must be always taken in this adjustment to loosen one screw before the other is screwed up, and to leave the adjusting screws tight, so as to draw with a moderate force against each other. This adjustment may be also made by the sun, moon, or a star: in this case the quadrant is to be held in a vertical position; if the image seen by reflection appears to the right or left of the object seen directly, then the glass must be adjusted as before by the two screws. It will be necessary, after having made this adjustment, to examine if the horizon glass still continues to be parallel to the index glass, as sometimes by turning the sunk screws the plane of the horizon glass will have its position altered.

USE OF HADLEY'S QUADRANT.

The use of the quadrant is to ascertain the angle subtended by two distant objects at the eye of the observer; but princicipally to observe the altitude of a celestial object above the horizon. This is pointed out by the index when one of the objects seen by reflection is made to coincide with the other, seen through the transparent part of the horizon glass.

To take an altitude of the sun, moon, or a star, by a fore observation.

Having previously adjusted the instrument, place the 0 on the nonius opposite to 0 on the arch, and turn down one or , more of the screens, according to the brightness of the sun; then apply the eye to the upper hole in the fore sight vane, if the sun's image be very bright, otherwise to the lower, and holding the quadrant vertically, look directly towards the sun, so as to let it be behind the silvered part of the horizon glass, then the coloured sun's image will appear on the speculum; move the index forward till the sun's image, which will appear to descend, just touches the horizon with its lower or upper limb; if the upper hole be looked through, the sun's image must be made to appear in the middle of the trans arent part

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