zon.

which may be called the celestial horizon. A plumb line hanging freely and at rest, is perpendicular to the plane of the horizon, and a small fluid surface at rest is in the plane of the horiThese two circumstances are of the utmost importance to the practical astronomer. The impossibility of having, except at sea, an uninterrupted view, and other causes, make it difficult for him to use the horizon itself, but the plumb line and fluid surface fully compensate for these inconveniences.

The altitude of a celestial object is its distance from the horizon, measured, on a great circle passing through the object, and at right angles to the horizon. Such a circle is called a secondary to the horizon; a great circle at right angles to another great circle, being called a secondary circle. And the zenith distance of a celestial object is its distance from the upper pole of the horizon, which is called the zenith. By the assistance of a plumb line and quadrant, the altitude or zenith distance may be readily found. Let ACQ (Fig. 1.) be an astronomical quadrant, the arch AQ of which is divided into degrees, &c., the radius AC is adjusted perpendicular to the horizon, by turning the quadrant about the point C, till a plumb line, suspended from C, passes over a point A. The radius CQ is then horizontal. A moveable radius or index CT is placed in the direction CO of the object, by means of plain sights at the extremities of the radius C and T (now rarely used), or by means of a telescope affixed to the radius. The arch TQ will then shew the altitude, for TCQ equals HCO the altitude; and the arch TA will shew the zenith distance, for ACT equals OCZ the zenith distance. The method of observing altitudes will be more accurately described hereafter: it was thought necessary to advert to it here; and also to mention how an angular distance on the concave surface may be measured.

A circle HABG (Fig. 2) divided into degrees, &c., furnished with a fixed radius AC, and a moveable radius BC, be

B

Z

N

per

ing placed in the plane passing through two objects and the eye, the circle may be turned till the fixed radius AC passes through one object, and then the moveable radius BC being made to pass through the other, the arch AB will shew the angular distance. This method is now rarely used. The angular distance of two objects when required, is seldom directly observed, on account of the inconvenience of adjusting the plane of the instrument, and the two radii, to two objects, both of which haps are moving, and with different motions. Therefore, in this way, great accuracy cannot be attained: but the conception of this method, although inaccurate, will be useful in what follows. When an angular distance on the concave surface is required, it is generally obtained by computation from other observations, e. g. from the declinations and right ascensions (to be explained hereafter). In one instance, indeed, in the lunar method of finding the longitude, it is necessary to observe, with great precision, the distance of the moon from the sun or a fixed star. This is done in a manner hereafter described, by an Hadley's sextant, an invaluable instrument for the purpose. By this instrument also the angular distance between any two objects may be measured.

6. To explain the phenomena of the apparent diurnal motions of the celestial bodies, we imagine an hemisphere below our horizon, and in it a point diametrically opposite to the north pole, which we call the south celestial pole; we also imagine that the concave surface turns uniformly on an axis, called the axis of the world, passing through the north and south poles, completing its revolution in the space of 23h 56m nearly, carrying with it the sun, moon, and stars, while the horizon remains at rest.

This hypothesis illustrates and represents the apparent diurnal motion of the several celestial objects in parallel circles, with an equable motion, each completing its circular path in the same

time. That the motion of each star is equable, and that they describe parallel circles on the concave surface, we deduce from observation and the computations of spherical trigonometry. This will be readily understood from what follows.

The great circle, the plane of which is at right angles to the axis of the world, is called the Equator. This circle is bisected by the horizon, and therefore all celestial bodies situated in it are, during equal times, above and below the horizon; consequently when the sun is in this circle, day and night are of equal length, whence it is also called the equinoctial.

This representation of the diurnal motion, by the motion of a sphere about an axis inclined to a plane representing the horizon, on which sphere the celestial bodies are placed at their proper angular distances, must have been among the first steps in astronomy. Yet in the infancy of the science, doubtless, a considerable time elapsed before it was known that the diurnal paths of the stars were parallel circles, described with an equable motion. Without this, little progress indeed could have been made. It is likely that at first it was little more than an hypothesis, in some degree confirmed by the construction of a sphere, to represent by its motion the celestial diurnal motions; for its confirmation, by the application of spherical trigonometry, seems to require a greater knowledge than we can suppose then existed.

This diurnal motion, we now know, is only apparent, and arises from the rotation of the earth about an axis, by which the horizon of the spectator revolves, successively uncovering, as it were, the celestial bodies, while the circles of the sphere are at rest. But the phenomena are the same, whether the horizon is at rest and the imaginary sphere revolves, or the horizon revolves and the imaginary sphere is at rest. By conceiving the sphere to revolve and the horizon to be at rest, the phenomena are more easily represented. Three centuries since, this appa

rent diurnal motion was generally considered to be real; and had we not the knowledge derived from navigation, and the communication of observations made in distant countries, we might still contend for the truth of it. Now we only imagine it, for more readily explaining the phenomena of the sphere and the circles thereof.

7. Circles of the sphere.-Secondaries to the equator are called circles of declination, because the arc of the secondary, intercepted between an object and the equator, is called its declination north or south, according as the object is on the north or south side of the equator.

The great circle passing through the pole and the zenith, is called the meridian. This circle is at right angles, or a secondary, both to the horizon and equator. It is easy to see that it divides the visible concave surface into two parts, eastern and western, in every respect similarly situate as to the pole and parallel circles. The eastern parts of the parallel diurnal circles being equal to the western, and the motions equable, the times of ascent from the horizon to the meridian," are equal to the times of descent from the meridian to the horizon.

In (Fig. 3) the circle HFKOGW represents the horizon, the centre C of which is the place of the spectator. The part

"A common celestial globe, or even a reference to the concave surface itself, will much better assist the conception of the circles of the sphere, than figures drawn on a plane surface, which are rather apt to mislead a beginner. The horizon of the globe must be considered as continued to pass through the centre, where the eye is supposed situate viewing the hemisphere above the horizon, and the axis of the globe is to be placed at the same elevation, as the axis of the concave surface of the spectator. In this way all the circles of the celestial sphere will be easily understood. Any consideration of the form of the earth is entirely foreign to a knowledge of the circles of the sphere. They were originally invented without any reference to or knowledge of it.

b Vide Appendix, Prop. I.

of the figure above this circle represents the visible concave surface; and the part below, the invisible. Z is the zenith; P the visible, and R the invisible pole. PZEHRNQO is the meridian, EGQV the equator. AB a small circle parallel to the equator, FLW the visible portion of another parallel to the equator. A star, situate in AB, is continually above the horizon. A star in the equator is only visible while in the part GEV equal to VQG. A star in FLW is only visible in the portion FLW above the horizon; it rises at W, and sets at F. ZSK is a portion of a secondary to the horizon. tude of the point S, and SZ its zenith distance. PSD is a secondary to the equator, or a circle of declination, and DS the declination of the point S.

SK is the alti

A telescope being directed to any star, and the time noted by a clock, if the telescope remain fixed, the same star will again pass through it after an interval of 23h 56m nearly. And the time of passing over the aperture of the telescope being the same to whatever part of the star's diurnal path the telescope is directed, proves the equable motion in that diurnal path. A telescope particularly fitted up, and placed so as to be conveniently moved in the plane of the meridian, is of as much use in the practice of astronomy as the quadrant: it is called a transit instrument; its uses will be afterwards explained, as well as the method of finding the direction of the meridian.

The time of describing a diurnal circle by a star may be nearly ascertained, without a telescope, by suspending two plumb lines at two or three feet from each other, then observing when the star appears in the plane of the strings, noting the time by a clock well regulated: the same star will pass the plane again after 23h 56m. An upright wall will serve for the same purpose. Vice versâ, this method will serve to ascertain the rate of going of a clock. It may also be applied to ascertain the time of passage over the meridian, by adjusting the plumb lines in the plane of the meridian.