will be the error of collimation in altitude, and this error being added to, or subtracted from, the observed angles, according as the sum of the readings is less or greater than 90', will give the true zenith distance and altitude. The error of collimation in altitude may then be corrected by adjusting the microscopes to read the true zenith distance and altitude, thus found, while the object is bisected by the cross wires of the telescope. The error of collimation of this and other astronomical instruments may also be found, or corrected, by the collimator. Use of the Altitude and Azimuth Instrument.-In using the altitude and azimuth instrument, for astronomical purposes, double observations should always be made, with the face first to the east, and then to the west, or vice versa, or several observations may be made with the face to the east, and as many with the face to the west, and the mean of the results, reduced to the meridian, taken as the true results. The place for a meridian mark may be determined by the methods already explained when describing the transit instrument, or by observing the readings of the azimuthal circle, or noting the times, when any celestial object has equal altitudes. Since the diaphragm of the telescope is furnished not only with the central horizontal wire, but with other horizontal wires at equal distances above and below it, so that there may be altogether either three or five, or seven horizontal wires, the azimuths and times may be observed, when the object observed is bisected by each of these wires. If a fixed star be the object observed, the mean of the times will give the time of the star's passing the meridian, and the mean of the azimuths will give the reading of the azimuth circle when the star was on the meridian, or the correction to be applied to the readings of the azimuth circle to give the true azimuths. If the sun be the body observed, a correction is necessary on account of the change of his declination, during the intervals between the observations. The correction for the time, as deduced from a pair of equal altitudes of the sun, is given by the formula, Correction: = X t 14-4 (tan. D X cos. 15°·1⁄2—tan. L.) 720 sin. 15° in which represents the variation in the sun's declination from the noon of the day preceding the observations to the noon of the day succeeding; t represents the interval between the observations expressed in hours and decimals of an hour; D represents the sun's declination at noon on the day on which the observations are made; L represents the latitude of the place. ♪ is to be reckoned positive when the sun's declination is increasing, and negative when it is decreasing. The correction for azimuth is given by the formula, Correction (D'— D) sec. lat. cosec. 15 (T_T). 2 in which D'D represents the change of the sun's declination, and T-T represents the interval in time. between the observations. When the sun is advancing towards the North Pole, this correction will carry the middle point towards the west of the approximate south point; but when he is approaching the South Pole, it will carry the same point towards the east, and must be applied accordingly. The altitude and azimuth instrument being adapted to observe the heavenly bodies in any part of the visible expanse of the heavens, its powers may be applied at any time to determine the data from which the time, the latitude of the place of observation, or the declination of the body observed, may be at once determined. We subjoin some of the formula, adapted to logarithmic computation, connecting the parts of what may be called the astronomical triangle, of which the angular points are, the pole, P, the zenith, z, and the apparent place of the body observed, s. Let P z, the colatitude of the place, be represented by λ. Ps, the polar distance of the body observed...... T. h. ......... a. Then we have the following formulæ for determining the time, the latitude, and the declination of the body observed. THE READING MICROSCOPE. The first of the annexed figures represents a longitudinal section of this instrument, and the second represents the field of view, showing the magnified divisions of the limb of the instrument to which the microscope is applied, and the diaphragm, d d, of the microscope, with its comb, c c, and cross wires, w w. The diaphragm is contained in the box, t t, and consists of two parts moving one over the other, the comb, c c, which is moved by the screw, i, at the bottom of the box, for the purpose of adjustment, and the cross wires, w w, and index, i, which are moved over the comb and the magnified image of the limb, by turning the milled head, h. The micrometer head, m, is attached by friction to the screw turned by the milled head, so that, by holding fast the milled head, the micrometer head can be turned round for adjustment. e is the eye-piece, which slides with friction into the cell, c, so as to produce distinct vision of the spider's lines of the micrometer. The object-glass, o, is held by a conical piece, d d, which screws further into, or out of, the body of the instrument, so as to produce distinct vision of the divided limb to be read by the microscope, and, when adjusted, is held firmly in its place by the nut, bb. The microscope screws into a collar, so as to be capable of adjustment with respect to its distance from the divided limb, and, when so adjusted, is held firmly in its place by the nuts, nn, n' n'. Adjustments of the Reading Microscope. Screw the object glass home. Insert the body of the microscope into the collar destined to receive it, and screw home the nuts, n n and n'n'. Make the diaphragm and spider's lines visible distinctly, by putting the eye-piece, e, the proper depth into the cell, c. Then make the graduated limb also distinctly visible without parallax by turning the nuts, nn, and n'n', unscrewing one and screwing up the other till the desired object is attained. Now bring the point of intersection of the spider's lines upon a stroke of the limb, and turn the micrometer head, m, to zero; then, turning the screw through five revolutions, if the point of intersection of the spider's lines has not moved over the whole of one of the divided spaces on the limb, the object lens must be screwed up to diminish the power by turning the cone, d d; and if it has moved over more than one of the divided spaces, it must be unscrewed to increase the power, and then altering the position of the microscope, by turning the nuts, n n and n'n', till distinct vision of the limb is again obtained, the measure of the space, moved over by five revolutions of the screw, must be repeated, as before. When, after repeated trials, the result is satisfactory, the three nuts, nn, n' n', and b b, must be screwed tight home, to render the adjustment permanent. When the microscope has been thus adjusted for distance, the zero of the division on the limb must be brought to the point of intersection of the spider's lines, and the divided head, m, turned, till its zero is pointed to by its index, and, then, if the zero on the comb, c c, be not covered exactly by the index, i, the comb must be moved by turning the screw, i, which enters the bottom of the micrometer box, till its zero is covered by the index pin. The adjustment of the reading microscope will now be perfect; and the graduated limb to be read by it, being divided at every five minutes, the degree and nearest five minutes of an observed angle will be shown by the pointer or index to this graduated limb; while the number of complete revolutions, and the parts of a revolution, of the screw, in the order of the numbers upon the micrometer head, m, required to bring the point of intersection of the spider's lines upon a division of the graduated limb, will be the number of minutes and seconds, respectively, to be added to the degrees and minutes shown by the index of the circle. The complete revolutions, or minutes, to be added, |