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ADJUSTMENTS.

Adjustments of the Vertical Axis.-Turn the instrument round till the level, LL, is over two of the foot-screws, and adjust the level, so that its bubble may retain the same position, when the instrument is turned half round, so that the level is again over the same foot-screws, but in the reverse position. The error at each trial is corrected, as nearly as can be judged, half by the foot-screws, and half by the adjusting screw of the level itself.

Next turn the instrument round 90° in azimuth, so that the level, LL, may be at right angles to its former positions, and bring the bubble to the same position as before, by turn ing the third foot-screw. Repeat the whole operation till the result is satisfactory.

Adjustment of the Horizontal Axis.-This adjustment is performed in the same manner, as already described for the transit instrument (p. 147), with the single exception that one end of the axis is to be raised or lowered, if necessary, by the screw acting upon its Y, and not by moving a foot-screw, which would derange the previous adjustment.

Adjustment of the Circle to its Reading Microscopes.--This is performed by raising or lowering both the Ys equally, so as not to derange the previous adjustment, till the microscopes are directed to opposite points in its horizontal diameter.

Adjustment of Collimation in Azimuth.-Instead of taking the axis out of its bearings and turning it end for end, the whole instrument is turned round in azimuth; but in all other respects the method of performing this adjustment is the same as that already described for the transit instrument (p. 148).

Adjustment of Collimation in Altitude.-Point the telescope to a very distant object, or star, and, bisecting it by the cross wires, read off the angle upon the vertical circle denoted by the reading microscopes. Turn the instrument half round in azimuth, and, again bisecting the same object by the cross wires, read off the angle. One of these readings will be an altitude, and the other a zenith distance *, and their sum, therefore, when there is no error of collimation in altitude, will be 90°. If the sum is not 90°, half its difference from 90°

* Both the horizontal and vertical circles are usually divided alike into Jour quadrants, and each quadrant graduated from 0° to 90°, proceeding in the same direction all round the circles.

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 ex plained 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,

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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,

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in which D-D represents the change of the sun's declination, between the and T-T represents the interval in time, 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 formulæ, 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 appa rent place of the body observed, s.

PS,

П

Let Pz, the colatitude of the place, be represented by λ.
the polar distance of the body observed
zs, the zenith distance of the body observed
ZPS, the hour angle from the meridian
P zs, the azimuthal angle

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Z.

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Then we have the following formula for determining the time, the latitude, and the declination of the body observed.

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THE READING MICROSCOPE.

The first of the annexed figures represents a longitudinal section of this instrument, and the second represents the

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field of view, showing the magnified divisions of the limb of the instrument to which the microscope is applied, and the diaphragm, dd, of the microscope, with its comb, c c, and cross wires, w w The diaphragm is contained in the box, tt, 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

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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, dd, 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'.

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