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bars, in notches cut in the form of double inclined planes, rest the two extremities of the horizontal axis of the vertical circle RS whose diameter may be the same as that of the former circle. The vertical circle is graduated, and between the two brass pillars on one side of the instrument are fixed, one above the other, at the opposite extremities of a diameter of the circle, two micrometer microscopes F', G', by which the minutes and seconds in the observed altitude or zenith distance are read. This circle carries a telescope TV in the direction of a diameter; and in the focus of the object glass is placed a net-work, consisting of three or five wires in horizontal, and as many in vertical positions; one arm of its horizontal axis is hollow, and a lamp is applied between the pillars on one side of the circle for the purpose, as in the transit instrument, of enlightening the wires when a star is observed by night. A brass ball, suspended in a vessel of water by a fine wire which is attached to the upper part of the instrument, serves to show when the axis of the azimuthal motion is in a vertical position by the suspending wire appearing, during a revolution of the instrument horizontally, to bisect a small dot on a white disk which is fixed below the rim of the vertical circle: this adjustment is effected by successive trials, in part by means of the three screws which, passing through the horizontal frame, rest on the table or pedestal, and in part by a small movement of the disk itself. The axis of the vertical circle is capable of a small movement by means of a capstan-headed screw which raises or depresses the double inclined plane in which one end of the axle rests; and its horizontality is shown by a spirit level which may be made to rest on the cylindrical pivots of the axle.

105. In the telescope, each of the wires which should be parallel to the horizon may have its position in that respect verified by causing a distant and well-defined terrestrial mark to be bisected by it, and observing that it continues to be bisected while it remains in the field of view, on the whole instrument (previously adjusted) being turned in azimuth; or by directing the telescope to an equatorial star when on the meridian, and observing that while the star appears to move across the field of view it is bisected by the wire. Each of the wires, which should be perpendicular to the last, may have its position in this respect verified by observing that a terrestrial mark continues to be bisected by it while the telescope is moved up or down upon the horizontal axis.

106. In this instrument it is of importance that the middle wires, both that which is parallel to the horizon and that which is at right angles to it, should pass through the optical

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axis of the telescope: the position of the latter wire may be verified, as in the transit telescope, by making it bisect some well-defined mark; and then, having reversed the pivots of the vertical circle on their supports, so that the graduated face of the circle which, before, may have been towards the east, shall now be towards the west, observing that the wire is neither to the right nor left of the centre of the mark. Or the error of collimation in azimuth may be found by means of a micrometer, as explained in the description of the transit telescope (arts. 87, 88.). In order to verify the position of the horizontal wire, or find the deviation in altitude of the point of intersection from the optical axis (commonly called the error of collimation in altitude or the index error of the instrument), the apparent zenith distances of a star must be observed when on the meridian, with the graduated face of the vertical circle in contrary positions; and then half the difference between those distances will be the value of the

error.

Let the circle ZDN (fig. to art. 100.) be in the plane of the meridian passing through the optical axis of the telescope, and let ZCN be a vertical line passing through C, the centre of the altitude circle in the instrument; also let A be the true or required place of the intersection of the wires at the focus of the object glass when a star on the meridian is at s in the line AB produced: then if a B' be the observed position of the optical axis, or a be the place of the intersection when the latter appears to coincide with the star s, the arc aN or ZB' will express the apparent distance of the star from the zenith. Next, let the instrument be turned half round in azimuth; then the line CA will be in the position CA', so that NA is equal to NA', and the line ca will be in the position ca'; and if the circle be turned on the horizontal axis passing through c till the star s appears as at first to coincide with the intersection of the wires, CA' will be in the position CA and a will be at b at a distance beyond a equal to A'a' or Aa; the apparent distance of the star from the zenith will then be N or ZB". Hence it follows that half the sum of the apparent zenith distances ZB', ZB" will be equal to ZB, the true zenith distance; or half the difference between the apparent zenith distances will be the index error of the instrument in altitude.

It will be most convenient to obtain the first apparent zenith distance when the star is on the central horizontal wire just before it comes to the intersection of the latter with the meridional wire, and the second apparent zenith distance when the star is on the same horizontal wire just

after it has passed the intersection; for thus the star, particularly if near the pole, will not sensibly change its altitude during the observation. A mean of several observations of this kind, on the same or on different stars, will afford a very nearly correct value of the index error.

107. The Zenith Sector is an instrument by which the angular distance of a star from the zenith of the observer is immediately obtained with great accuracy, the star being on, or very near the plane of the meridian of the station, and being one of those which, in that situation, are within a few degrees, or even minutes, of the zenith. Such distances are taken when it is required to ascertain from observation the effects of nutation, or aberration, or the parallax of the fixed stars; and in geodetical operations they serve to determine astronomically the latitudes of the principal stations.

The instrument consists of a metal plate, or a system of bars, which is placed in a vertical position, and on which, near the lower extremity, is a graduated arc extending to five or ten degrees, or in some cases to five minutes only, on each side of the zero point: this plate is capable of being turned quite round on a vertical axis, the lower extremity resting on a conical pivot, and the upper extremity turning in a collar at the top of the frame by which the instrument is supported. A telescope is attached by several rings to an index bar which turns on a horizontal axis near the top or at the middle it is furnished with wires crossing one another as usual in the field of view, and the lower part of the index bar carries a microscope for the purpose of subdividing the graduations by which the observed angular distance is expressed. The zenith point may be determined for this instrument in the same manner as for the mural circle.

108. With all the zenith sectors hitherto constructed it is necessary to make observations on successive nights having the instrument in reversed positions; but, in order to obviate the inconvenience and delay caused frequently by unsettled weather, the Astronomer Royal has recently caused one to be constructed by which zenith distances may be obtained in one night. The whole stand of the instrument is of castiron, and consists of a base AB with two upright piers which are connected together at top by a horizontal bar CD. Three foot screws pass through the base, and rest upon a plate, or tray, which is bolted or screwed to the top of the pedestal serving to support the whole instrument.

Between the piers is a frame EF of bell-metal about four feet long, which is capable of being placed in direct and reversed positions; and in each of its opposite extremities is

sunk a conical hole which receives a corresponding pivot attached to the base and to the upper horizontal bar, so that whichever of the two extremities is uppermost the frame can be made to revolve about a vertical axis. On one side of this frame is the bar HK, which carries the telescope NP; and both bar and telescope have a move-. ment of small extent on each side of a vertical line, in a plane parallel to the front of the frame and on a horizontal axis which passes through the latter.

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Near each extremity of the revolving frame is a graduated arc with two micrometer microscopes for the subdivisions.

The verticality of the axis of the frame is ascertained by three spirit-levels which are attached horizontally at the back of the frame, and have the power of being reversed when the latter is inverted on the conical pivots. All the corrections due to the want of adjustment in the instrument are to be made by computation, after they have been ascertained by the observed transits of stars with the frame in direct and reversed positions; the reversions being with respect to the east and west sides and to the upper and lower extremities.

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109. In making an observation there must be two observers; the first sets the telescope as nearly as possible to the zenith distance of the star, and reads the four microscopes; the second at the same time reads the scales on the levels. As soon as the star has arrived at a convenient part of the field, and before it comes to the centre, the first observer bisects it by the micrometer wire and reads the micrometers: he then turns the instrument half round in azimuth. second observer now bisects the star by means of the tangent screw, or by the micrometer screw, and then reads the four microscopes; lastly, the first observer reads the levels. This completes the double observation; and the zenith distance may be obtained by the following rule: - Add together the mean readings of the microscopes, their corrections, the mean of the equivalents for the three levels and the equivalent for the micrometer reading: the mean between the two sums for the opposite positions in azimuth will be a quantity corresponding to a zenithal observation. Such a mean may obtained for two or more stars in one night; and the difference between the number of the graduation expressing

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the zenith point and the sum for each star is the true zenith distance of that star.

110. The Equatorial Instrument is occasionally used to obtain by direct observation the right ascensions and polar distances of celestial bodies when not in the plane of the meridian, but it has been of late chiefly employed in determining the differences between the right ascensions and declinations of stars which are visible at the same time in the field of the telescope, and in finding the positions and relative movements of double stars.

It consists of two graduated circles CD and EF, of which one is always parallel to the plane of the equator, being fixed at right angles to the mathematical

axis

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tion circle (to which in general the telescope HK is fixed), turns upon an axis which is always perpendicular to the former; and the circle is consequently in the plane of the meridian when its own axis, whose extremity is seen at G, is parallel to the horizon. But the bar or frame which carries the equatorial circle CD turns upon its axis A B, and carries with it the axis of the declination circle, so that the latter circle is in the plane of a horary circle inclined to the meridian when its axis is inclined to the horizon. The telescope being made to turn with the circle upon this axis, it is evident, when the telescope is directed to a celestial body, that an index fixed to the stand of the instrument may be made to show on the equatorial circle the horary angle of that body, or the angle which the plane of the declination circle makes with the plane of the meridian; and that an index fixed to the polar axis may be made to show on the declination circle the distance of the celestial body from the pole of the equator.

The equatorial circle may be turned round by hand, or by an endless screw working in teeth on the edge of the circle;

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