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 elegant 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.

† See Dr. Pearson's Treatise on Practical Astronomy. Also Bianchi Sopra 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 bo

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 T directed to one of them, S, and clamped. Then will a mark on the arm m point

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

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

a

b

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

required for this purpose the distance of that division from the original or zero point of the microscope may be estimated. This simple but delicate contrivance gives to the reading off of a circle a degree of accuracy only limited by the power of the microscope, and the perfection with which a screw can be executed, and places the subdivision of angles on the same footing of optical certainty which is introduced into their measurement by the use of the telescope.

(166.) The exactness of the result thus obtained must depend, 1st, on the precision with which the tube a b can be pointed to the objects; 2dly, on the accuracy of graduation of the limb; 3dly, on the accuracy with which the subdivision of the intervals between any two consecutive graduations can be performed. The mode of accomplishing the latter object with any required exactness has been explained in the last article. With regard to the graduation of the limb, being merely of a mechanical nature, we shall pass it without remark, further than this, that, in the present state of instrument-making, the amount of error from this source of inaccuracy is reduced within very narrow limits indeed.* With regard to the first, it must be obvious that, if the sights a b be nothing more than simple crosses, or pin-holes at the ends of a hollow tube, or an eye-hole at one end, and a cross at the other, no greater nicety in pointing can be expected than what simple vision with the naked eye can command. if, in place of these simple but coarse contrivances, the tube itself be converted into a telescope, having an object-glass at b, an eye-piece at a, and a fiducial cross in their common focus, as explained in art. 157.; and if the motion of the tube on the limb of the circle be arrested when the object is brought just into coincidence with the intersectional point of that cross, it is evident that a greater degree of exactness. may be attained in the pointing of the tube than by the unassisted eye, in proportion to the magnifying power and distinctness of the telescope used.

But

* In the great Ertel circle at Pulkova, the probable amount of the accidental error of division is stated by M. Struve not to exceed 0"-264. Desc. de l'Obs. centrale de Pulkova, p. 147.