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verniers, or microscopes; the one attached to the fixed support which carries the principal axis, the other to an arm projecting from that axis. Both circles also are susceptible of being clamped, the clamps being attached to the same ultimate bearing with which the apparatus for reading off is connected.

(148.) It is manifest that such a combination, however its principal axis be pointed (provided that its direction be invariable), will enable us to ascertain

the situation of any object with respect to the observer's station, by angles reckoned upon two great circles in the visible hemisphere, one of which has for its poles the prolongations of the principal axis or the vanishing points of a system of lines parallel to it, and the other passes always through these poles : for the former great circle is the vanishing line of all planes pa

rallel to the circle AB, while the latter, in any position of the instrument, is the vanishing line of all the planes parallel to the circle G H; and these two planes being, by the construction of the instrument, at right angles, the great circles, which are their vanishing lines, must be so too. Now, if two great circles of a sphere be at right angles to each other, the one will always pass through the other's poles.

(149.) There are, however, but two positions in which such an apparatus can be mounted so as to be of any practical utility in astronomy. The first is, when the principal axis C D is parallel to the earth's axis, and therefore points to the poles of the heavens which are the vanishing points of all lines in this system of pa. rallels; and when, of course, the plane of the circle A B is parallel to the earth's equator, and therefore has the equinoctial for its vanishing circle, and measures, by its arcs read off, hour angles, or differences of right ascension. In this case, the great circles in the heavens, corresponding to the various positions, which the circle G H can be made to assume, by the rotation of the instrument round its axis C D, are all hour-circles; and the arcs read off on this circle will be declinations, or polar distances, or their differences.

(150.) In this position the apparatus assumes the name of an equatorial, or, as it was formerly called, a parallactic instrument. It is one of the most convenient instruments for all such observations as require an object to be kept long in view, because, being once set upon the object, it can be followed as long as we please by a single motion, i.e. by merely turning the whole apparatus round on its polar axis. For since, when the telescope is set on a star, the angle between its direction and that of the polar axis is equal to the polar distance of the star, it follows, that when turned about its axis, without altering the position of the telescope on the circle GH, the point to which it is directed will always lie in the small circle of the heavens coincident with the star's diurnal path. In many observations this is an inestimable advantage, and one which belongs to no other instrument. The equatorial is also used for determin. ing the place of an unknown by comparison with that of a known object, in a manner to be described in the fourth chapter. The adjustments of the equatorial are somewhat complicated and difficult. They are best performed by following the pole-star round the entire diurnal circle, and by observing, at proper intervals, other considerable stars whose places are well ascer. tained.*

(151.) The other position in which such a com

* See Littrow on the Adjustment of the Equatorial. – Mem. Astron. Soc. vol. ii, n. 45.

pound apparatus as we have described in art. 147. may be advantageously mounted, is that in which the principal axis occupies a vertical position, and the one circle, A B, consequently corresponds to the celestial horizon, and the other, G H, to a vertical circle of the heavens. The angles measured on the former are therefore azimuths, or differences of azimuth, and those on the latter zenith distances, or altitudes, according as the graduation commences from the upper point of its limb, or from one 90° distant from it. It is therefore known by the name of an azimuth and altitude instrument. The vertical position of its principal axis is secured either by a plumb-line suspended from the upper end, which, however it be turned round, should continue always to intersect one and the same fiducial mark near its lower extremity, or by a level fixed directly across it, whose bubble ought not to shift its place, on moving the instrument in azimuth. The north or south point on the horizontal circle is ascertained by bringing the vertical circle to coincide with the plane of the meridian, by the same criterion by which the azimuthal adjustment of the transit is performed (art. 137.), and noting, in this position, the reading off of the lower circle, or by the following process.

(152.) Let a bright star be observed at a considerable distance to the east of the meridian, by bring'ing it on the cross wires of the telescope. In this position let the horizontal circle be read off, and the telescope securely clamped on the vertical one. When the star has passed the meridian, and is in the descend. ing point of its daily course, let it be followed by moving the whole instrument round to the west, without, however, unclamping the telescope, until it comes into the field of view ; and until, by continuing the horizontal motion, the star and the cross of the wires come once more to coincide. In this position it is evident the star must have the same precise altitude above the western horizon, that it had at the moment of the first observation above the eastern. At this point let the mo

tion be arrested, and the horizontal circle be again read off. The difference of the readings will be the azimuthal arc described in the interval. Now, it is evident that when the altitudes of any star are equal on either side of the meridian, its azimuths, whether reckoned both from the north or both from the south point of the horizon, must also be equal,- consequently the north or south point of the horizon must bisect the azimuthal arc thus deter. mined, and will therefore become known.

(153.) This method of determining the north and south points of a horizontal circle (by which, when known, we may draw a meridian line) is called the “ method of equal altitudes,” and is of great and constant use in practical astronomy. If we note, at the moments of the two observations, the time, by a clock or chronometer, the instant halfway between them will be the moment of the star's meridian passage, which may thus be determined without a transit; and, vice versa, the error of a clock or chronometer may by this process be discovered. For this last purpose, it is not necessary that our instrument should be provided with a horizontal circle at all. Any means by which altitudes can be measured will enable us to determine the moments when the same star arrives at equal altitudes in the eastern and western halves of its diurnal course; and, these once known, the instant of meridian passage and the error of the clock become also known.

(154.) One of the chief purposes to which the altitude and azimuth circle is applicable is the investigation of the amount and laws of refraction. For, by following with it a circumpolar star which passes the zenith, and another which grazes the horizon, through their whole diurnal course, the exact apparent form of their diurnal orbits, or the ovals into which their circles are distorted by refraction, can be traced; and their devi. ation from circles, being at every moment given by the nature of the observation in the direction in which the refraction itself takes place (i. e. in altitude), is made a matter of direct observation.

(155.) The zenith sector and the theodolite are peculiar modifications of the altitude and azimuth instrument. The former is adapted for the very exact observ. ation of stars in or near the zenith, by giving a great length to the vertical axis, and suppressing all the circumference of the vertical circle, except a few degrees of its lower part, by which a great length of radius, and a consequent proportional enlargement of the divi. sions of its arc, is obtained. The latter is especially devoted to the measure of horizontal angles between terrestrial objects, in which the telescope never requires to be elevated more than a few degrees, and in which, therefore, the vertical circle is either dispensed with, or executed on a smaller scale, and with less delicacy; while, on the other hand, great care is bestowed on securing the exact perpendicularity of the plane of the telescope's motion, by resting its horizontal axis on two supports like the piers of a transit-instrument, while themselves are firmly bedded on the spokes of the hori. zontal circle, and turn with it.

(156.) The last instrument we shall describe is one by whose aid the direct angular distance of any two objects may be measured, or the altitude of a single one determined, either by measuring its distance from the visible horizon (such as the sea-offing, allowing for its dip), or from its own reflexion on the surface of mer. cury. It is the sextant, or quadrant, commonly called Hadley's, from its reputed inventor, though the priority of invention belongs undoubtedly to Newton, whose claims to the gratitude of the navigator are thus doubled, by his having furnished at once the only theory by. which his vessel can be securely guided, and the only instrument which has ever been found to avail, in applying that theory to its nautical uses. *

* Newton communicated it to Dr. Halley, who suppressed it. The de. scription of the instrument was found, after the death of Halley, among his papers, in Newton's own handwriting, by his executor, who communicated the papers to the Royal Society, twenty-five years after Newton's death, and eleven after the publication of Hadley's invention, which might be and probably was, independent of any knowledge of Newton's, though Hutton insinuates the contrary.

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