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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, or by a well-defined object, called a meridian mark, originally determined by such obseryations, 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 central line of the telescope (that which joins the centres of its object-glass and eye-glass, and which is called in astronomy its line of collimation) 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.

(126.) In the focus of the eye-piece, and at right angles to the length of the telescope, is placed a system of one horizontal and five equidistant vertical threads or wires, as represented in the annexed figure, which

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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 be 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 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 meri. dian. 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 five 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.

(127.) 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 meri. dian 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 two or three tenths of a second of time in the moment

Also Bianchi

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

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.

(128.) The angular intervals measured by means of the transit instrument and clock are arcs of the equi. noctial, 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. Let ABCD be such a circle, divided into 360 degrees,

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(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, & y %, 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, ab, is exactly parallel to the plane of the circle, or per

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CHAP. II. MEASUREMENT OF ANGLES. pendicular to the pivot; and also the 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 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, ST. The plane of the circle must first be adjusted so as to pass through them both. This done, let the axis ab of the tube be 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 adja. cent. 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 conse. cutive 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. 130.) 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.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 on the point 0° be situated.

(129.) 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 pps 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,

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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.

(130.) The index F may either be a simple pointer, like a clock hand (fig. a); or a vernier (fig. 6); or,

lastly, a compound 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 ; 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

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