differences of right ascensions of the stars, we may be sure that the telescope describes a true meridian, and that, therefore, the declination axis is truly perpendicular to the polar one; - if not, the deviation of the intervals from this law will indicate the direction and amount of the deviation of the axis in question, and enable us to correct it.*

(186.) A very great improvement has, within a few years from the present time, been introduced into the construction of the equatorial instrument. It consists in applying a clockwork movement to turn the whole instrument round upon its polar axis, and so to follow the diurnal motion of any celestial object, without the necessity of the observer's manual intervention. The driving power is the descent of a weight which communicates motion to a train of wheelwork, and thus, ultimately, to the polar axis, while, at the same time, its too swift descent is controlled and regulated to the exact and uniform rate required to give that axis one turn in 24 hours, by connecting it with a regulating clock, or (which is found preferable in practice) by exhausting all the superfluous energy of the driving power, by causing it to overcome a regulated friction. Artists have thus succeeded in obtaining a perfectly smooth, uniform, and regulable motion, which, when so applied, serves to retain any object on which the telescope may be set, commodiously, in the centre of the field of view for whole hours in succession, leaving the attention of the observer undistracted by having a mechanical movement to direct, and with both his hands at liberty.

(187.) The other position in which such a compound apparatus as we have described in art. 182. 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

See Littrow on the Adjustment of the Equatorial (Mem. Ast. Soc. vol. ii. p. 45.), where formulæ are given for ascertaining the amount and direction of all the misadjustments simultaneously. But the practical observer, who wishes to avoid bewildering himself by doing two things at once, had better proceed as recommended in the text.

of azimuth, and those of 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. 162.), and noting, in this position, the reading off of the lower circle; or by the following process.

(188.) Let a bright star be observed at a considerable. distance to the east of the meridian, by bringing 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 descending 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 motion 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 determined, and will therefore become known.

I

(189.) This method of determining the north and south points of a horizontal circle 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 versâ, 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.

(190.) Thus also a meridian line may be drawn and a meridian mark erected. For the readings of the north and south points on the limb of the horizontal circle being known, the vertical circle may be brought exactly into the plane of the meridian, by setting it to that precise reading. This done, let the telescope be depressed to the north horizon, and let the point intersected there by its cross-wires be noted, and a mark erected there, and let the same be done for the south horizon. The line joining these points is a meridian line, passing through the centre of the horizontal circle. The marks may be made secure and permanent if required.

(191.) 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 deviation 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.

(192.) The zenith sector and the theodolite are peculiar

modifications of the altitude and azimuth instrument. The former is adapted for the very exact observation 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 divisions of its arc, is obtained. The latter is especially devoted to the measures 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 perpendi cularity of the plane of the telescope's motion, by resting its horizontal axis on two supports like the piers of a transitinstrument, which themselves are firmly bedded on the spokes of the horizontal circle, and turn with it.

(193.) The next instrument we shall describe is one by whose aid the 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 reflection on the surface of mercury. 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.*

(194.) The principle of this instrument is the optical property of reflected rays, thus announced: "The angle be

*Newton communicated it to Dr. Halley, who suppressed it.

The descrip

tion 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.

The

E

D

B

tween the first and last directions of a ray which has suffered two reflections in one plane is equal to twice the inclination of the reflecting surfaces to each other." Let A B be the limb, or graduated arc, of a portion of a circle 60° in extent, but divided into 120 equal parts. On the radius C B let a silvered plane glass D be fixed, at right angles to the plane of the circle, and on the moveable radius CE let another such silvered glass, C, be fixed. glass D is permanently fixed parallel to A C, and only one half of it is silvered, the other half allowing objects to be seen through it. The glass C is wholly silvered, and its plane is parallel to the length of the moveable radius C E, at the extremity E of which a vernier is placed to read off the divisions of the limb. On the radius A C is set a telescope F, through which any object, Q, may be seen by direct rays which pass through the unsilvered portion of the glass D, while another object, P, is seen through the same telescope by rays, which, after reflection at C, have been thrown upon the silvered part of D, and are thence directed by a second reflection into the telescope. The two images so formed will both be seen in the field of view at once, and by moving the radius CE will (if the reflectors be truly perpendicular to the plane of the circle) meet and pass over, without obliterating each other. The motion, however, is arrested when they meet, and at this point the angle included between the direction CP of one object, and FQ of the other, is twice the angle ECA included between the fixed and moveable radii CA, CE. Now, the graduations of the limb being purposely made only half as distant as would correspond to degrees, the arc A E, when read off, as if the graduations were whole degrees, will, in fact, read double its real amount, and therefore the numbers so read off will express not the angle E C A, but its double, the angle subtended by the objects.