which may be considered as having all the while retained an invariable position. This difference, then, will be the double zenith distance of S, and its half the zenith distance simply, the complement of which is its altitude. Thus the altitude corresponding to a given reading of the limb becomes known, or, in other words, the horizontal point on the limb is ascertained. Circuitous as this process may appear, there is no other mode of employing the level for this purpose which does not in the end come to the same thing. Most commonly, however, the level is used as a mere fiducial reference, to preserve a horizontal point once well determined by other means, which is done by adjusting it so as to stand level when the telescope is truly horizontal, and thus leaving it depending on the permanence of its adjustment.

(144.) The last, but probably not the least exact, as it certainly is, in innumerable cases, the most conve nient means of ascertaining the horizontal point, is that afforded by the floating collimator, a recent invention of captain Kater. This elegant instrument is nothing more than a small telescope furnished with a cross-wire in its focus, and fastened horizontally, or as nearly so as may be, on a flat iron float, which is made to swim on mercury, and which, of course, will, when left to itself, assume always one and the same invariable inclination to the horizon. If the cross-wires of the col

limator be illuminated by a lamp, being in the focus of its object-glass, the rays from them will issue parallel, and will therefore be in a fit state to be brought to a focus by the object-glass of any other telescope, in

which they will form an image as if they came from a celestial object in their direction, i. e. at an altitude equal to their inclination. Thus the intersection of the cross of the collimator may be observed as if it were a star, and that, however near the two telescopes are to each other. By transferring then, the collimator still floating on a vessel of mercury from the one side to the other of a circle, we are furnished with two quasi-celestial objects, at precisely equal altitudes, on opposite sides of the centre; and if these be observed in succession with the telescope of the circle, bringing its cross to bisect the image of the cross of the collimator (for which end the wires of the latter cross are purposely set 45° inclined to the horizon) the difference of the readings on its limb will be twice the zenith distance of either; whence, as in the last article, the horizontal or zenith point is immediately determined.*

*

(145.) The transit and mural circle are essentially meridian instruments, being used only to observe the stars at the moment of their meridian passage. Independent of this being the most favourable moment for seeing them, it is that in which their diurnal motion is parallel to the horizon. It is therefore easier at this time than it could be at any other, to place the telescope exactly in their true direction; since their apparent course in the field of view being parallel to the horizontal thread of the system of wires therein, they may, by giving a fine motion to the telescope, be brought to exact coincidence with it, and time may be allowed to examine and correct this coincidence, if not at first accurately hit, which is the case in no other situation. Generally speaking, all angular magnitudes, which it is of importance to ascertain exactly, should, if possible, be observed at their maxima or minima of increase or

*Another, and, in many respects, preferable form of the floating collimator, in which the telescope is vertical, and whereby the zenith point is directly ascertained, is described in the Phil. Trans. 1828, p. 257, by the same author.

diminution; because at these points they remain not perceptibly changed during a time long enough to complete, and even, in many cases, to repeat and verify, our observations in a careful and leisurely manner. The angle which, in the case before us, is in this predicament, is the altitude of the star, which attains its maximum or minimum on the meridian, and which is measured on the limb of the mural circle.

(146.) The purposes of astronomy, however, require that an observer should possess the means of observing any object not directly on the meridian, but at any point of its diurnal course, or wherever it may present itself in the heavens. Now, a point in the sphere is determined by reference to two great circles at right angles to each other; or of two circles one of which passes through the pole of the other. These, in the language of geometry, are co-ordinates by which its situation is ascertained: for instance,- -on the earth, a place is known if we know its longitude and latitude; - in the starry heavens, if we know its right ascension and declination;-in the visible hemisphere, if we know its azimuth and altitude, &c.

(147.) To observe an object at any point of its diurnal course, we must possess the means of directing a telescope to it; which, therefore, must be capable of motion in two planes at right angles to each other; and the amount of its angular motion in each must be measured on two circles co-ordinate to each other, whose planes must be parallel to those in which the telescope moves. The practical accomplishment of this condition is effected by making the axis of one of the circles penetrate that of the other at right angles. The pierced axis turns on fixed supports, while the other has no connection with any external support, but is sustained entirely by that which it penetrates, which is strengthened and enlarged at the point of penetration to receive it. The annexed figure exhibits the simplest form of such a combination, though by no means the best in point of mechanism. The two circles are read off by

H

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.

K

(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 parallel to the circle A B,

H

B

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 parallels; 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 determining 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 ascertained.*

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

See Littrow on the Adjustment of the Equatorial. Mem. Astron. Soc. vol. ii. p. 45.