circle once determined, becomes an origin, or zero point, from which the polar distances of all objects, referred to other points on the same limb, reckon. It matters not whether the actual commencement 0° of the graduations stand there, or not; since it is only by the differences of the readings that the arcs on the limb are determined; and hence a great advantage is obtained in the power of commencing anew a fresh series of observations, in which a different part of the circumference of the circle shall be employed, and different graduations brought into use, by which inequalities of division may be detected and neutralized. This is accomplished practically by detaching the telescope from its old bearings on the circle, and fixing it afresh, by screws or clamps, on a different part of the circumference.

(173.) A point on the limb of the mural circle, not less important than the polar point, is the horizontal point, which, being once known, becomes in like manner an origin, or zero point, from which altitudes are reckoned. The principle of its determination is ultimately nearly the same with that of the polar point. As no star exists in the celestial horizon, the observer must seek to determine two points on the limb, the one of which shall be precisely as far below the horizontal point as the other is above it. For this purpose, a star is observed at its culmination on one night, by pointing the telescope directly to it, and the next, by pointing to the image of the same star reflected in the still, unruffled surface of a fluid at perfect rest. Mercury, as the most reflective fluid known, is generally chosen for that use. As the surface of a fluid at rest is necessarily horizontal, and as the angle of reflection, by the laws of optics, is equal to that of incidence, this image will be just as much depressed below the horizon as the star itself is above it (allowing for the difference of refraction at the moments of observation). The arc intercepted on the limb of the circle between the star and its reflected image thus consecutively observed, when corrected for refraction, is the double altitude of the star, and its point of bisection the horizontal point. The reflecting surface of a

fluid so used for the determination of the altitudes of objects is called an artificial horizon.*

(174.) The mural circle is, in fact, at the same time, a transit instrument; and, if furnished with a proper system of vertical wires in the focus of its telescope, may be used as such. As the axis, however, is only supported at one end, it has not the strength and permanence necessary for the more delicate purposes of a transit; nor can it be verified, as a transit may, by the reversal of the two ends of its axis, east for west. Nothing, however, prevents a divided circle being permanently fastened on the axis of a transit instrument, either near to one of its extremities, or close to the telescope, so as to revolve with it, the reading off being performed by one or more microscopes fixed on one of its piers. Such an instrument is called a TRANSIT CIRCLE, or a MERIDIAN CIRCLE, and serves for the simultaneous determination of the right ascensions and polar distances of objects observed with it; the time of transit being noted by the clock, and the circle being read off by the lateral microscopes. There is much advantage, when extensive catalogues of small stars have to be formed, in this simultaneous determination of both their celestial co-ordinates: to which may be added the facility of applying to the meridian circle a telescope of any length and optical power. The construction of the mural circle renders this highly inconvenient, and indeed impracticable beyond very moderate limits.

(175.) The determination of the horizontal point on the limb of an instrument is of such essential importance in astronomy, that the student should be made acquainted with every means employed for this purpose. These are, the artificial horizon, the plumb-line, the level, and the collimator. The artificial horizon has been already explained. The plumb

By a peculiar and delicate manipulation and management of the setting, bisection, and reading off of the circle, aided by the use of a moveable horizontal micrometic wire in the focus of the object-glass, it is found practicable to observe a slow moving star (as the pole star) on one and the same night, both by reflection and direct vision, sufficiently near to either culmination to give the horizontal point, without risking the change of refraction in twenty-four hours; so that this source of error is thus completely eliminated.

line is a fine thread or wire, to which is suspended a weight, whose oscillations are impeded and quickly reduced to rest by plunging it in water. The direction ultimately assumed by such a line, admitting its perfect flexibility, is that of gravity, or perpendicular to the surface of still water. Its application to the purposes of astronomy is, however, so delicate, and difficult, and liable to error, unless extraordinary precautions are taken in its use, that it is at present almost universally abandoned, for the more convenient, and equally exact instrument the level.

(176.) The level is a glass tube nearly filled with a liquid, (spirit of wine, or sulphuric ether, being those now generally

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used, on account of their extreme mobility, and not being liable to freeze,) the bubble in which, when the tube is placed horizontally, would rest indifferently in any part if the tube could be mathematically straight. But that being impossible to execute, and every tube having some slight curvature; if the convex side be placed upwards the bubble will occupy the higher part, as in the figure (where the curvature is purposely exaggerated). Suppose such a tube, as A B, firmly fastened on a straight bar, CD, and marked at a b, 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. In such levels accident is not trusted to to give the requisite curvature. They are ground and polished internally by peculiar mechanical processes of great delicacy.

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(177.) 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, DE F, and moveable in one with it on a horizontal axis C, which must be like that of a transit, susceptible of reversal (see art. 161.), 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, LE F, furnished with a micro

scope, or vernier at F, and, if we please, another 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 L C F 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 turning 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 L E F 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. difference, then, will be the double zenith distance of S, and its half will be 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.

This

(178.) 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, an invention of Captain Kater, but of which the optical principle was first employed by Rittenhouse, in 1785, for the purpose of fixing a definite direction in space by the emergence of parallel rays from a material