(134.) This is the principle of the mural circle, which is nothing more than such a circle as we have described in art. 129., firmly supported, in the plane of the meridian, on a long and powerful horizontal axis. This axis is let into a massive pier, or wall, of stone (whence the name of the instrument), and so secured by screws as to be capable of adjustment both in a vertical and horizontal direction; so that, like the axis of the transit, it can be maintained in the exact direction of the east and west points of the horizon, the plane of the circle being consequently truly meridional.

(135.) The meridian, being at right angles to all the diurnal circles described by the stars, its arc intercepted between any two of them will measure the least distance between these circles, and will be equal to the difference of the declinations, as also to the difference of the meridian altitudes of the objects—at least when corrected for refraction. These differences, then, are the angular intervals directly measured by the mural circle. But from these, supposing the law of refraction known, it is easy to conclude, not their differences only, but the quantities themselves, as we shall now explain.

(136.) The declination of a heavenly body is the complement of its distance from the pole. The pole, being a point in the meridian, might be directly observed on the limb of the circle, if any star stood exactly therein; and thence the polar distances, and, of course, the declinations of all the rest, might be at once determined. But this not being the case, a bright star as near the pole as can be found is selected, and observed in its upper and lower culminations; that is, when it passes the meridian above and below the pole. Now, as its distance from the pole remains the same, the difference of reading off the circle in the two cases is, of course (when corrected for refraction), equal to twice the polar distance of the star; the arc intercepted on the limb of the circle being, in this case, equal to the angular diameter of the star's diurnal circle. In the annexed diagram, H PO represents the celestial meridian, P the pole,

CHAP. II.

MURAL CIRCLE.

89

BR, AQ, CD the diurnal circles of stars which arat B A and C in their upper,

rive on the meridian

and at RQD in their lower culminations, of which D happens above the horizon HO. P is the pole; and if we suppose h po to be the mural circle, having S for its centre, ba cp d will be the points on its circumference corresponding to BA CPD in the heavens. Now, the arcs ba, bc, bd, and cd are given immediately by observation; and since C P=P D, we have also c p=p d, and each of them cd, consequently the place of the polar point, as it is called, upon the limb of the circle becomes known, and the arcs p b, p a, pc, which represent on the circle the polar distances required, become also known.

(137.) The situation of the pole star, which is a very brilliant one, is eminently favourable for this purpose, being only about a degree and a half from the pole; it is, therefore, the star usually and almost solely chosen for this important purpose; the more especially because, both its culminations taking place at great and not very different altitudes, the refractions by which they are affected are of small amount, and differ but slightly from each other, so that their correction is easily and safely applied. The brightness of the pole star, too, allows it to be easily observed in the daytime. In consequence of these peculiarities, this star is one of con

stant resort with astronomers for the adjustment and verification of instruments of almost every description. In the case of the transit, for example, it furnishes a ready means of ascertaining whether the plane of the telescope's motion is coincident with the meridian. For since this latter plane bisects its diurnal circle, the eastern and the western portion of it require equal times for their description. Let, therefore, the moments of its transit above and below the pole be noted; and if they are found to follow at equal intervals of 12 sidereal hours, we may conclude with certainty that the plane of the telescope's motion is meridional, or the position of its horizontal axis exactly east and west. But if it pass from one to the other apparent culmination in unequal intervals of time, it is equally certain that an extra-meridional error must exist, the deviation lying towards that side on which the least interval is occupied. And the axis must be moved in azimuth accordingly, till the difference in question disappears on repeating the observations.

(138.) The place of the polar point on the limb of the mural circle once determined, becomes an origin, or zero point, from which the polar distances of all objects, referred to other points on the same lines, reckon. It matters not whether the actual commencement 0° of the graduations stand there, or not; since it is only by the difference 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 on a different part of the circumference.

(139.) 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 man

CHAP. II.

POLAR AND HORIZONTAL POINTS.

91

ner 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 elevated 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.

(140.) 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, near to one of its extremities, so as to revolve with it, the reading off being performed by a microscope 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 microscope.

(141.) 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 floating collimator. The artificial horizon has been already explained. The plumb-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.

(142.) The level is nothing more than a glass tube nearly filled with a liquid, (spirit of wine being that

now generally used, on account of its 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