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purposely exaggerated). Suppose such a tube az A B firmly fastened on a straight bar, CD, and marked at ab, two points distant by the length of the bubble ; then, if the instrument be so placed that the bubble shall occupy this interval, it is clear that C D can have no other than one definite inclination to the horizon; because, were it ever so little moved one way or other, the bubble would shift its place, and run towards the elevated side. Suppose, now, that we would ascertain whether any given line P Q be horizontal ; let the base of the level C D be set upon it, and note the points a b, between which the bubble is exactly contained ; then turn the level end for end, so that C shall rest on Q, and D on P. If then the bubble continue to occupy the same place between a and b, it is evident that P Q can be no otherwise than horizontal. If not, the side towards which the bubble runs is highest, and must be lowered. Astronomical levels are furnished with a divided scale, by which the places of the ends of the bubble can be nicely marked ; and it is said that they can be executed with such delicacy, as to indicate a single second of angular deviation from exact horizontality.

(143.) The mode in which a level may be applied to find the horizontal point on the limb of a vertical divided circle may be thus explained : Let A B be a telescope firmly fixed to such a circle, DEF, and move

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able in one with it on a horizontal axis C, which must be like that of a transit, susceptible of reversal (see art. 127.), and with which the circle is inseparably connected. Direct the telescope on some distant well. defined object S, and bisect it by its horizontal wire, and in this position clamp it fast. Let L be a level fastened at right angles to an arm, LEF, furnished with a microscope, or vernier at F, and, if we please, an. other at E. Let this arm be fitted by grinding on the axis C, but capable of moving smoothly on it without carrying it round, and also of being clamped fast on it, so as to prevent it from moving until required. While the telescope is kept fixed on the object S, let the level be set so as to bring its bubble to the marks a b, and clamp it there. Then will the arm LCF have some certain determinate inclination (no matter what to the horizon. In this position let the circle be read off at F, and then let the whole apparatus be reversed by turn. ing its horizontal axis end for end, without unclamping the level arm from the axis. This done, by the motion of the whole instrument (level and all) on its axis, restore the level to its horizontal position with the bubble at a b. Then we are sure that the telescope has now the same inclination to the horizon the other way, that it had when pointed to S, and the reading off at F will not have been changed. Now unclamp the level, and, keeping it nearly horizontal, turn round the circle on the axis, so as to carry back the telescope through the zenith to S, and in that position clamp the circle and telescope fast. Then it is evident that an angle equal to twice the zenith distance of S has been moved over by the axis of the telescope from its last position. Lastly, without unclamping the telescope and circle, let the level be once more rectified. Then will the arm LEF once more assume the same definite position with respect to the horizon; and, consequently, if the circle be again read off, the difference between this and the previous reading must measure the arc of its circumference which has passed under the point F, 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. Cir. cuitous 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 convenient 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 im

mediately 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 mo. tion 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 com. plete, 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 pre. dicament, 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 strength. ened 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 rcad off by

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