520. If we require to measure simply the angular distance of one celestial body from another, we employ a sextant; but, generally speaking, what is to be determined is not merely the angular distance between two bodies, but their apparent position either on the sphere of observation or on the celestial sphere itself.

521. In the former case, that is, when we wish to determine positions on the visible portion of the sky,-we employ what is termed an a'titude and azimuth_instrument, or, shortly, an altazimuth; and if we know the sidereal time, or, in other words, if we know the exact part of the celestial sphere then on the meridian, we can by calculation find out the right ascension and declination (Art. 328), referred to the celestial sphere, of the body whose altitude and azimuth on the sphere of observation we had instrumentally determined.

522. An altazimuth is an instrument with a vertical central pillar supporting a horizontal axis. There are two circles, one horizontal, in which is fitted a smaller (ungraduated) circle with attached verniers fixed to the central pillar, and revolving with it; another, vertical, at one end of the horizontal axis, and free to move in all vertical planes. To this latter the telescope is fixed. When the telescope is directed to the south point, the reading of the horizontal circle is o°; and when the telescope is directed to the zenith, the reading of the vertical circle is o°. Consequently, if we direct the telescope to any particular star, one circle gives the zenith distance of the star (or its altitude); the other gives its azimuth. If we fix or clamp the telescope to the vertical circle, we can turn the axis which carries both round, and observe all stars having the same altitude, and the horizontal circle will show their azimuths; if we clamp the axis to the horizontal circle, we can move the telescope so as to make it travel along a vertical circle, and the circle attached to the telescope will give us the zenith distances of the stars (or their altitudes), which, in this case, will lie in

two azimuths 180° apart. A portable altazimuth is represented in Plate XV., the various parts of which will be easily recognised from the foregoing description.

523. To make an observation with the altazimuth, we must first assure ourselves that the instrument itself is in perfect adjustment- that is, that the circles are truly graduated and centred (Art. 518), and that there is no error of collimation in the telescope. This done, it must be perfectly levelled, so that the vertical circle is in all positions truly vertical, and the horizontal circle truly horizontal. Next, we must know the exact readings of the verniers of the azimuth circle when the telescope is in the meridian, and the exact readings of the verniers of the vertical circle when the telescope points to the zenith. This donc, we may point the telescope to the body to be observed, bring it to the cross wires visible in the field of view, and note the exact time. The verniers on the two circles are then read, and from the mean of them the instrumental altitude and azimuth are determined. The observation should then be repeated with the telescope on the opposite side of the central pillar, as by this means some of the instrumental errors are got rid of.

LESSON XLII.-The Transit Circle and its AdjustPrinciples of its Use. Methods of Taking The Chronograph. The Equatorial.

ments. Transits.

524. When we wish to determine directly the position of a celestial body on the celestial sphere itself, a transit circle is almost exclusively used. This instrument consists of a telescope moveable in the plane of the meridian, being supported on two pillars, east and west, by means of a horizontal axis. The ends of the horizontal ais are of exactly equal size, and move in pieces, which, from their shape, are called Ys. When the instrument is in perfect adjustment, the line of collimation of the telescope

is at right angles to the horizontal axis, the axis is exactly horizɔntal, and its ends are due east and west. Under these conditions, the telescope describes a great circle of the heavens passing through the north and south points and the celestial pole ; in other words, the telescope in all positions points to some part of the meridian of the place. On one side of the telescope is fixed a circle, which is read by microscopes fixed to one of the supporting pillars. The cross wires in the eye-piece of the telescope enable us to determine the exact moment of sidereal time at which the meridian is crossed: this time is, in fact, the right ascension of the object. The circle attached shows us its distance from the celestial equator: this is its declination. So by one observation, if the clock be right, the instrument perfectly adjusted, and the circle correctly divided, we get both co-ordinates.

In Plate XVI. is given a perspective view of the great transit circle at Greenwich Observatory, designed by the late Astronomer-Royal, Sir George Airy. It consists of two massive stone pillars, supporting the ends of the horizontal axis of the telescope, which rests on Ys, as shown in the case of one of the pivots in the drawing. Attached to the cube of the telescope (to which the two side-pieces, the eye-piece end and object-glass end, are screwed) are two circles. The one to the right is graduated, and is read by microscopes pierced through the right-hand pillar; the eye-pieces of these microscopes are visible to the right of the drawing. The other circle is used to fix the telescope, or to give it a slow motion, by means of a long handle, which the observer holds in his hand. The eye-piece is armed with a micrometer, with nine equidistant vertical wires and two horizontal ones.

The wheels and counterpoises at the top of the view are to facilitate the raising of the telescope when the collimators, both of which are on a level with the centre of the telescope-one to the north and one to the south —are examined.

525. As we have already seen (Art. 329) a celestial meridian is nothing but the extension of a terrestrial one ; and as the latter passes through the poles of the Earth, the former will pass through the poles of the celestial sphere: consequently, in England the northern celestial pole will lie somewhere in the plane of the meridian. If the position of the pole were exactly marked by the pole· star, that star would remain immoveable in the meridian ; and when a celestial body, the position of which we wished to determine, was also in the meridian, if we adjusted the circle so that it read o° when the telescope pointed to the pole, all we should have to do to determine the north polar distance of the body would be to point the telescope to it, and see the angular distance shown by the circle.

526. But as the pole-star does not exactly mark the position, we have to adopt some other method. We observe the zenith distance (Art. 329) of a circumpolar star when it passes over the meridian above the pole, and also when it passes below it, and it is evident that if the observations are perfectly made, half the sum of these zenith distances will give the zenith distance of the celestial pole itself. When we have found the position of the celestial pole, we can determine the position of the celestial equator, which we know is exactly 90° away from it. As we already know the zenith distance of the celestial pole, the difference between this distance and 90° gives us the zenith distance of the equator. Here, then, we have three points from which with our transit circle we can measure angular distances:

I. From the zenith,

II. From the celestial pole,

III. From the celestial equator,

and we may add,

IV. From the horizon,

as the horizon is 90° from the zenith.

Any of these

distances can be easily turned into any other.