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time is determined by a pointer, which gives the arc on the azimuth circle to five minutes, and two opposite reading microscopes, one of which is seen at F, which give the additional minutes and seconds.

The two connected vertical circles, K, K, are firmly attached to the telescope and horizontal axis, and, therefore, turn with the telescope as it is directed to different altitudes. That to the left is graduated, and the altitude or zenith distance of the body to which the telescope is directed is read off by the reading microscopes R, R. The spirit level, Q, Q, is used in making the vertical axis of the instrument truly vertical. The screws, whose heads are seen at P and P, serve to elevate or depress the Y's in which the pivots of the horizontal axis rest. By means of these and a striding level, such as is used with the transit instrument, the axis is made horizontal and placed at such a height that the zeros of the reading microscopes, R, R, shall be at opposite points of the graduated vertical circle. The plate T is a stand for a lantern to illuminate the spiders-lines, of which there are five horizontal as well as five vertical ones. When the ring to which these are attached is properly adjusted, by means of the screws which connect it with the tube, the intersection of the middle lines of the two sets is exactly in the optical axis of the telescope.

When the instrument is properly adjusted and placed so that, as the telescope revolves, its optical axis moves in the plane of the meridian, it may be used either as a transit instrument or transit circle

47. The Equatorial is an instrument consisting of the same essential parts as the altitude and azimuth instrument. It is so mounted that one of the axes is at right angles to the plane of the equator and the other parallel to it. The circles connected with these axes are called, respectively, the Hour and Declination Circles. The former is usually graduated into hours, and parts of an hour; and is so adapted to the axis that, when the telescope points toward a star on the meridian, the vernier will read 0 hrs., 0 min., 0 sec. If, then, the telescope be turned slowly westward, about the axis, at a rate corresponding with the diurnal motion of the heavens, it will be constantly directed towards the star, and the vernier will indicate, upon the hour circle, the star's hour-angle at

any moment. The declination circle is so adjusted that, when the optical axis of the telescope is in the plane of the equator, the vernier reads 0°; and hence, if the telescope be directed to any star, this vernier will indicate the star's declination.

The larger instruments of this class are generally provided with clock work, which communicates to the telescope a slow motion from east to west, causing it to follow a star for any length of time.

48. A Sextant is an instrument used for measuring the angular distance between two heavenly bodies or other objects. In Fig. 14, which represents a sextant, A, A, is a double frame connected by small pillars a, a, &c. The arc BO is usually graduated to 10′ and subdivided by a vernier E, to 10, The degrees are numbered from 0° near B to about 130° near C; the construction of the instrument being such that half degrees on the arc correspond to whole degrees of the angle measured, they are for convenience regarded and numbered as whole degrees. The microscope H may be moved over the vernier, and aids in distinguishing the division line of the vernier that coincides, or is the nearest to coincidence with a division line on the arc. A glass reflector F, called the index glass, is attached perpendicularly to the index IE, which is moveable about the centre of the circular part I; this centre being also the centre of the graduated arc BC. Another glass G, called the horizon glass, is attached at right angles to the frame of the instrument, being parallel to the index glass when the index is at zero of the arc. The lower half of this glass is silvered so as to make it a reflector; the upper half is clear. A small telescope is placed in a ring L, and may be so adjusted by a screw M, that its optical axis shall be directed towards the division between the silvered and unsilvered parts of the horizon glass, or a little higher or lower, as may be desired. At K and N are sets of dark glasses of different colours, one or more of which may be interposed between the index and horizon glasses, or horizon glass and telescope, or both, to moderate the light and heat of the sun when that body is observed. The instrument, when in use, is held in the hand by a handle at O; or it is sometimes attached to a stand, called a centre of gravity stand, which admits its being placed at any inclination to the horizon.

In observing the angle contained between two bodies, the sextant is placed so that the telescope is directed to one of them, which is seen through the clear part of the horizon glass, and being then turned till its plane corresponds with the directions of both bodies, the index is moved till the second body appears to be in contact with the first; its light having been reflected from the index glass to the silvered part of the horizon glass, and thence through the telescope. The arc indicated by the vernier index, is then the measure of the angle contained between the nearest limbs of the two bodies.

The sextant, with the aid of an instrument called an artificial horizon, consisting of a small trough containing mercury, covered by a glass roof to protect the surface from agitation by the wind, serves to observe, with considerable accuracy, the altitude of a heavenly body. In doing this, the image of the body seen by reflection from the index and horizon glasses, is brought into contact with the image reflected from the surface of the mercury, and seen. through the clear part of the horizon glass; the arc indicated by the index being then double the altitude of the lower limb of the body.

49. The Reflecting Circle is an instrument constructed on the same principle, and used for the same purposes as the sextant. In it, the arc BC extends to the whole circumference, and there are three vernier indices. It is regarded, on several accounts, as being a rather more accurate instrument than the sextant.

50. A Micrometer is an instrument or appendage, which, when attached to a telescope, serves to measure with great accuracy small angles, such as the apparent diameters of the sun, moon, or planets, or the angular distance between two bodies very near to each other.

This instrument is constructed in various ways. In Troughton's spiders-line micrometer, which may be substituted for the usual eye-piece of a telescope, there are two small frames placed side by side, at right angles to the optical axis, and moveable by screws. with graduated heads. Across each frame a spiders-line is fixed at right angles to the direction in which it moves. The heads of the screws may be so adjusted, that they shall be at zero when the frames have such a position, that one of the lines is directly behind

the other, the two appearing as one line. When thus adjusted, if the screws be turned till one of the lines appears to touch one edge or limb of a heavenly body, and the other to touch the opposite limb, the contained angle, or apparent diameter of the body, becomes known from the number of whole turns and parts of a turn of the screws, required to put them in those positions.

A Heliometer is a telescope fitted up with a peculiar kind of micrometer, for the especial purpose of measuring the apparent diameters of the heavenly bodies, or other small angular spaces.

A Position Micrometer is an instrument, which serves not only to measure the angular distance between two contiguous bodies, but also the angle contained between the arc of a great circle joining them, and a declination circle passing through one of them.*



51. To place an altitude and azimuth instrument in the plane of the meridian. Let ENWS, Fig. 2, be the horizon of a place A; Z the zenith, P the north pole, NZS the meridian, and S' and S" two positions of the same star when at equal altitudes B'S' and B"S", on opposite sides of the meridian. Then, since a star, in its

* From the preceding brief notices, the student may obtain a general view of the constructions and uses of the instruments mentioned, sufficient to enable him to comprehend the astronomical observations to which reference will be made in subsequent parts of the work. For full descriptions of these and various other astronomical instruments, with the methods of adjusting and using them, he may be referred to the second volume of Dr. Pearson's Treatise on Practical Astronomy. Those who have not access to the large work of Dr. Pearson, may obtain considerable information from a small work on the principal mathematical instruments used in Surveying, Levelling, and Astronomy, by Simms. An American edition, edited by J. W. Alexander, has been published in Baltimore.

apparent diurnal motion, describes a circle about the pole P (15), we have in the two spherical triangles ZPS' and ZPS", the side. PS' equal to PS"; and we have also ZS' and ZS" equal, being the complements of the equal altitudes B'S' and B'S'', and PZ common. The angles PZS' and PZS" are therefore equal, and consequently their measures, the azimuths NB' and NB", are also equal.

Hence, the instrument being placed on a firm support, and properly adjusted and levelled, let the altitude of a star, when at a position S' to the east of the meridian, be observed, and let the azimuth arc be also read off. Let the star be again observed, when, after having passed the meridian, it has arrived at a position S", in which its altitude is the same as before, and let the azimuth are be again read off. From these azimuth arcs, the azimuth arc B'B' becomes known. Then, if the instrument be turned eastwardly through an arc equal to B"N, the half of B'B', and be clamped in that position, the telescope, when turned about its horizontal axis, will, if the observations have been accurately made, move in the plane of the meridian NZS.

To ascertain whether the instrument is truly placed in the plane of the meridian, let several culminations of a circumpolar star, both above and below the pole, be observed, and the time, as shown by a good clock or chronometer, be noted. Then, as the diurnal motion of a star is uniform (15), and as the star must therefore be as long to the east of the meridian as to the west, it follows that if the interval during which the star appears to be to the east, is equal to that during which it appears to be to the west, the instrument is truly placed. If the intervals are unequal, the instrument deviates towards the side of the less interval, and should be slightly moved in a contrary direction. The observations and movement of the instrument should be repeated, till the intervals are found to be equal.

When the instrument is thus truly placed in the meridian, it may be used for observing the culminations and meridian altitudes of the heavenly bodies.

52. To place a transit instrument in the meridian. A transit instrument, or transit circle, may be placed in the plane of the meridian by first putting it by estimation nearly in that position,

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