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it sometimes contains a space of 7 degrees, or 21 subdivisions of the limb, and is divided into 20 equal parts; hence each division on the Nonius will be one-twentieth part greater, that is, one minute longer than the divisions on the Arch; consequently, if the first division of the Nonius marked 0, be set precisely opposite to any degree, the relative position of the Nonius and the arch must be altered one minute, before the next division on the Nonius will coincide with the next division on the Arch, the second division will require a change of 2 minutes, the third of 3 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 No

nius.

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 right hand 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 O 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 de

grees, then 25 degrees will be the measure of the angles observed; if it coincides with the next division on the left hand, 25 degress 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 Nonius; 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 degress 2 minutes, and so on to 20 minutes, when the 0 on the Nonius 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 O 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 balf, 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 degress 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 adjus

ter 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.

1. To set the Piane of the Index Glass perpendicular to that of the Instrument.

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

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