meridian of the place of observation. The extremities of the axis are formed into cylindrical pivots of exactly equal diameters, which rest in notches formed in metallic supports, bedded (in the case of large instruments) on strong pieces of stone, and susceptible of nice adjustment by screws, both in a vertical and horizontal direction. By the former adjustment, the axis can be rendered precisely horizontal, by level

ling it with a level made to rest on the pivots. By the latter adjustment the axis is brought precisely into the east and west direction, the criterion of which is furnished by the observations themselves made with the instrument, in a manner presently to be explained, or by a well-defined object, called a meridian mark, originally determined by such observations, and then, for convenience of ready reference, permanently established, at a great distance, exactly in a meridian line passing through the central point of the whole instrument. It is evident, from this description, that, if the axis, or line of collimation of the telescope be once well adjusted at right angles to the axis of the transit, it will never quit the plane of the meridian, when the instrument is turned round on its axis of rotation.

(160.) In the focus of the eye-piece, and at right angles to the length of the telescope, is placed, not a single cross, as in our general explanation in art. 157., but a system of one horizontal and several equidistant vertical threads or wires, (five or seven are more usually employed,) as represented in the annexed figure, which always appear in the field of view, when properly illuminated, by day by the light of the sky, by night by that of a lamp introduced by a contrivance not necessary here to explain. The place of this system of wires may altered by adjusting screws, giving it a lateral (horizontal) motion; and it is by this means brought to such a position, that the middle one of the vertical wires shall intersect the line of collimation of the telescope, where it is arrested and

be

permanently fastened.* In this situation it is evident that the middle thread will be a visible representation of that portion of the celestial meridian to which the telescope is pointed; and when a star is seen to cross this wire in the telescope, it is in the act of culminating, or passing the celestial meridian. The instant of this event is noted by the clock or chronometer, which forms an indispensable accompaniment of the transit instrument. For greater precision, the moments of its crossing all the vertical threads is noted, and a mean taken, which (since the threads are equidistant) would give exactly the same result, were all the observations perfect, and will, of course, tend to subdivide and destroy their errors in an average of the whole in the contrary case.

(161.) For the mode of executing the adjustments, and allowing for the errors unavoidable in the use of this simple and clegant instrument, the reader must consult works especially devoted to this department of practical astronomy.† We shall here only mention one important verification of its correctness, which consists in reversing the ends of the axis, or turning it east for west. If this be done, and it continue to give the same results, and intersect the same point on the meridian mark, we may be sure that the line of collimation of the telescope is truly at right angles to the axis, and describes strictly a plane, i. e. marks out in the heavens a great circle. In good transit observations, an error of one or two tenths of a second of time in the moment of a star's culmination is the utmost which need be apprehended, exclusive of the error of the clock in other words, a clock may be compared with the earth's diurnal motion by a single observation, without risk of greater error. By multiplying observations, of course, a yet greater degree of precision may be obtained.

(162.) The plane described by the line of collimation of

* There is no way of bringing the true optic axis of the object glass to coincide exactly with the line of collimation, but, so long as the object glass does not shift or shake in its cell, any line holding an invariable position with respect to that aris, may be taken for the conventional or astronomical axis with equal effect. Also Bianchi Sopra

† See Dr. Pearson's Treatise on Practical Astronomy. lo Stromento de' Passagi. Ephem. di Milano, 1824.

a transit ought to be that of the meridian of the place of observation. To ascertain whether it is so or not, celestial observation must be resorted to. Now, as the meridian is a great circle passing through the pole, it necessarily bisects the diurnal circles described by all the stars, all which describe the two semicircles so arising in equal intervals of 12 sidereal hours each. Hence, if we choose a star whose whole diurnal circle is above the horizon, or which never sets, and observe the moments of its upper and lower transits across the middle wire of the telescope, if we find the two semidiurnal portions east and west of the plane described by the telescope to be described in precisely equal times, we may be sure that plane is the meridian.

(163.) The angular intervals measured by means of the transit instrument and clock are arcs of the equinoctial, intercepted between circles of declination passing through the objects observed; and their measurement, in this case, is performed by no artificial graduation of circles, but by the help of the earth's diurnal motion, which carries equal arcs of the equinoctial across the meridian, in equal times, at the rate of 15° per sidereal hour. In all other cases, when we would measure angular intervals, it is necessary to have recourse to circles, or portions of circles, constructed of metal or other firm and durable material, and mechanically subdivided into equal parts, such as degrees, minutes, &c. The simplest and most obvious mode in which the measurement of the angular interval between two directions in space can be performed is as follows. Let A B C D be a circle, divided into 360 degrees, (numbered in order from any point 0° in the circumference, round to the same point again,) and connected with its centre by spokes or rays, x, y, z, firmly united to its circumference or limb. At the centre let a circular hole be pierced, in which shall move a pivot exactly fitting it, carrying a tube, whose axis, a b, is exactly parallel to the plane of the circle, or perpendicular to the pivot; and also two arms, m, n, at right angles to it, and forming one piece with the tube and the axis; so that the motion of the axis on the centre shall carry the tube and arms smoothly round the circle, to be

m

B

S

arrested and fixed at any point we please, by a contrivance called a clamp. Suppose, now, we would measure the angular interval between two fixed objects, S, T. The plane of the circle must first be adjusted so as to pass through them both, and immoveably fixed and maintained in that position. This done, let the axis a b of the tube be directed to one of them, S, and clamped. Then will a mark on the arm m point

T

either exactly to some one of the divisions on the limb, or between two of them adjacent. In the former case, the division must be noted as the reading of the arm m. In the latter, the fractional part of one whole interval between the consecutive divisions by which the mark on m surpasses the last inferior division must be estimated or measured by some mechanical or optical means. (See art. 165.) The division and fractional part thus noted, and reduced into degrees, minutes, and seconds, is to be set down as the reading of the limb corresponding to that position of the tube ab, where it points to the object S. The same must then be done for the object T; the tube pointed to it, and the limb "read off" the position of the circle remaining meanwhile unaltered. It is manifest, then, that, if the lesser of these readings be subtracted from the greater, their difference will be the angular interval between S and T, as seen from the centre of the circle, at whatever point of the limb the commencement of the graduations or the point 0° be situated.

(164.) The very same result will be obtained, if, instead of making the tube moveable upon the circle, we connect it invariably with the latter, and make both revolve together on an axis concentric with the circle, and forming one piece with it, working in a hollow formed to receive and fit it in some fixed support. Such a combination is represented in section in the annexed sketch. T is the tube or sight, fastened, at p p, on the circle A B, whose axis. D, works in

H

the solid metallic centring E, from which originates an arm, F, carrying at its extremity an index, or other proper mark.

to point out and read off the exact division of the circle at B, the point close to it. It is evident that, as the telescope and circle revolve through any angle, the part of the limb of the latter, which by such revolution is carried past the index F, will measure the angle described. This is the most usual mode of applying divided circles in astronomy.

(165.) The index F may either be a simple pointer, like a clock hand (fig. a); or a vernier (fig. b); or, lastly, a com

pound microscope (fig. c), represented in section in fig. d, and furnished with a cross in the common focus of its object and eye-glass, moveable by a fine-threaded screw, by which the intersection of the cross may be brought to exact coincidence with the image of the nearest of the divisions of the circle formed in the focus of the object lens upon the very same principle with that explained, art. 157. for the pointing of the telescope, only that here the fiducial cross is made moveable; and by the turns and parts of a turn of the screw