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the diaphragm containing the wires by means of the screws at the side of the tube, till the intersection of the wires is brought half way back to cover the distant point; bring the cross wire on the same or some other point again, by means of the screw in the Y, which gives a horizontal motion to the whole instrument, and repeat the process already described; after a few trials the point will be found to be exactly covered by the intersection of the wires in both positions of the telescope. This indicates that the line of collimation, or line determined by the intersection of the cross wires, and the distant point, is exactly perpendicular to the axis on which the instrument turns as the object end of the telescope is elevated or depressed.

2. To render the supporting axis horizontal.-This is done by means of a spirit level, of which there are two kinds for the purpose, the hanging level, and the riding or striding level.

The former is suspended by hooks from the pivots of the supporting axis, so as to hang parallel to it underneath. The latter is sustained above the supporting axis by two long feet with notches at their bottoms, by means of which it stands upon the pivots of the axis.

First, to adjust the spirit level itself, place it on the pivots, and by means of the screw in the y at that extremity of the axis which gives it a vertical motion, bring the long air bubble of the level to reach exactly the same distance on either side of the centre marked with a zero on the level scale above the tube; for which purpose the divisions of this scale are numbered in precisely the same manner on the right and left of the zero. Then reverse the level on the pivots, turning it end for end, and if the bubble still reaches the same distance on both sides of the zero, the level requires no adjustment. If not, make half the correction by filing away the notch in one of the feet, or by means of a screw sometimes added for shortening the foot, and the other half by the screw in the y. Repeat this process till the adjustment is complete. When the level itself is once

This may be exhibited with the error of collimation exaggerated in the annexed diagram, in which a b represents the supporting axis, c d the true line of collimation, co the erroneous position of the line of collimation in the first position of the instrument in the direction co of the object, and c e the position of the line of collimation in the reversed position.

adjusted, the supporting axis is made horizontal by placing the level upon it, and turning the screw in the y till the centre of the air bubble is opposite the zero of the scale.

3. To adjust the instrument to the meridian.-Observe the instant that some circumpolar* star (the pole star is the best, from the slowness of its motion) crosses the vertical wire of the transit instrument both at its superior and inferior transit, that is above and below the pole. If the interval of time between the superior and inferior transit be the same with that between the latter and the next superior transit of the same star again, the instrument is in the meridian. If not, it is on that side of the meridian on which the arc described by the star between the two transits is shortest, and must be moved a little by means of the screw in the y, which gives horizontal motion, and the same observations repeated. When the instrument is once fixed in the meridian, a meridian mark about half a mile distant may be made upon some object, set up if necessary, upon which the vertical wire is to be brought whenever afterwards an observation is to be made.

Method of observing the meridian transit of a star.-Before describing this we shall observe that for diminishing the error of observation there are inserted on each side of the vertical middle wire, one, two, or three others, making three, five, or seven in all. There is also attached to the supporting axis near one of the pivots a graduated circle, the plane of which is perpendicular to that axis, and consequently vertical. This circle is graduated so that the index points to zero when the telescope points to the zenith, or else when the telescope is horizontal, so that when the telescope is directed to a star, the index will mark the zenith distance of the star in the former case, and its altitude in the latter. The star's declination being known from the Nautical Almanac, or from a catalogue, and the latitude of the place of observation being also known, the instrument may be easily set so that when the star makes its meridian transit it will pass through the middle of the field of view of the telescope. For it is only necessary to bear in mind that the declination is the distance of the star from the equator and the latitude is the distance of the zenith from the equator, so that by simple addition or subtraction of these quanti

* A circumpolar star is one which never sets, but describes daily a circle round the pole of the heavens, the whole of which is visible above the horizon.

† A method of determining the exact deviation from the meridian, and the consequent error in the time of meridian transit, will be presently given.

These measures are all made on the same great circle of the heavens, viz. the meridian of the place of observation, upon which the star is supposed to be at the instant of transit.

ties the distance of the star from the zenith is obtained. Thus, if the star be south of the zenith and north of the equator its declination must be subtracted from the latitude to obtain the zenith distance. If the star be south of the equator, or its dec. be S., the dec. must be added to the lat. If the star be N. of the zenith, i. e. if its N. dec. exceed the N. lat. of the place, then the lat. must be subtracted from the dec. to obtain the zenith distance. The above definitions for dec. and lat will always be the best guide. If the instrument be graduated for altitudes instead of zenith distances it is only necessary to recollect that the altitude is the complement of the zenith distance. If an inferior transit, or transit sub polo of a circumpolar star is to be taken, it may be convenient to remember that the altitude of the pole is equal to the latitude of the place.*

The instrument being set to the proper altitude, so that when the star crosses the meridian it will be sure to be seen in the field of view of the telescope, it remains now only to know when to look for its arrival at the meridian, and its consequent appearance in the field. This is shown by the astronomical clock, which is supported upon a stone pier in the same room with the transit instrument. This clock, when correctly set, should indicate the zero of time, or 0 0 0' at the exact instant that the vernal equinox is on the meridian; then at the instant any star is on the meridian, the clock would show the distance of that star in time from the vernal equinox or the right ascension of the star.

(

A minute or two therefore before the clock shows a time equal to the right ascension of the star, (for whose zenith distance or altitude the instrument is set,) as given by the Nautical Almanac or by catalogue, place the eye at the telescope, and the star will be seen entering the field of view, and moving in a direction contrary to its real motion, i. e. from west to east instead of from east to west, because an astronomical telescope inverts. Bring it near the horizontal wire, by means of a clamp and tangent screw attached to the vertical circle, and before the star reaches the first vertical wire in its motion across the field, look at the clock and take up the count of the seconds, which keep by the ear, applying the eye again to the telescope, and note the instant the star crosses or is bisected by the first vertical wire; record the second in a blank book, then look

* For the zenith being 90° from the horizon, and the pole 90° from the equator, the pole will be just as far from the horizon as the zenith is from the equator. + Unless it be making its transit sub polo.

Or between the two horizontal wires if there are two near together, as is sometimes the case.

at the clock, and record the minute; the hour may be left till the observation is finished. Take up the count of the second again, and apply the eye to the instrument; by this time the star will be seen approaching the second vertical wire. Observe and record the instant of its transit over that wire in the same way, and so on for all the vertical wires. The sum of the minutes and seconds divided by the number of wires will give the minutes and seconds of the time of passing the middle wire, with a probable error of or (according to the number of wires) of the error if the observation had been made upon the middle wire alone.*

* The star will often be seen bisected by a wire between two beats of seconds. The eye then notes how far from the wire the star was at the beat before the bisection and how far at the beat after, and estimates the fraction of a second at which the bisection took place. By the aid of electro-magnetism the exact instant, to a very small fraction of a second, may be not only observed, but recorded without the trouble of keeping count. The arrangement for the purpose is as follows: A wire is made to communicate from one pole of a voltaic battery to the brass work of the clock; the electricity perviates all the brass work, and passes down the pendulum rod; underneath the pendulum a globule of mercury is supported in a little metallic cup from which a wire passes to a magnet, round which it coils, and then passes on to the other pole of the battery. Every time the pendulum vibrates on reaching the lowest point of its arc, it dips into the globule of mercury for an instant, and thus a communication is made between the two poles of the battery, and the magnet acts, drawing back a little hammer which is armed with a sharp point that pricks a narrow strip of paper made to pass along under it, at a uniform rate, by clockwork. The intervals between the points on the paper will correspond to seconds. Two wires communicate also from the opposite poles of a battery (one of them coiling round a magnet close beside the magnet already mentioned) to a wooden block held in the hand of the observer at the instrument, by touching a button in which he connects the wires communicating with it, and the magnet then acts, causing a small hammer to prick with its sharp point the narrow strip of paper a little on one side of the line of points which mark the seconds. The precise position in the interval between two even seconds, of the instant of bisection of the star by the wire, is thus indicated with great precision, and by applying a scale with a vernier, the fraction of a second may be obtained to thousandths, the space on the strip of paper corresponding to a second being usually from half an inch to an inch. The observer at the end of the observation notes on the clock the minute with which the observation closes, and writes it with the hour on the strip of paper in pencil.

The even minutes in the line of dots which marks the seconds on the strip of paper are indicated by the omission of a dot, which is effected as follows. To the axis which carries the second hand of the clock is attached a fork of two prongs, projecting perpendicularly from the axis; when the second hand has made a complete revolution of the clock dial, the two prongs of the fork dip into two globules of mercury communicating by it with the two poles of the battery, one of which wires is the same that communicates the electricity to the brass work of the clock from which

The interval between the wires ought to be exactly the same. As this is scarcely attainable in practice, the mean of the times of transit over all the wires obtained as above will be the time of transit over an imaginary wire situated very near the middle wire. If, by sudden cloudiness or any other accident the transits over some or all the wires but one should be lost, the time of transit over the imaginary middle wire may be obtained as follows:

Having made a complete observation of the times of transit of some star over all the wires, take the difference between the mean of all and the time of transit over each wire. Multiply the intervals thus obtained by the cosine of the star's declination (see Spher. Geom., Prop. 2, Cor. 6, and see Navigation, Art. 99*), and the products will be the equatorial interval between that wire and the imaginary middle wire, or the time that would be occupied by a star situated on the equator in traversing the same interval.t The equatorial intervals being once obtained, to know the time of any star's passing the imaginary middle wire from the time of its passing any other wire, divide the equatorial interval between this wire and the middle wire by the cosine of the star's declination.

it goes down the pendulum as before described. When the connexion is made by the fork dipping into the two globules of mercury the electricity goes back to the battery by the shortest path instead of taking the course down the pendulum, and that beat is lost on the magnet.

A number of rapid strokes of the button, which impress a corresponding number of points on the paper, serve to indicate the commencement of the observation.

The principle alluded to here, which is of frequent use in astronomy, may be stated thus; the arc on a great circle comprehended between two of its secondaries, is to the arc of a small circle parallel to the primary comprehended between the same secondaries, as unity is to the cosine of the distance of the parallel small circle from the primary, this distance being measured on one of the secondaries.

The fourth term of the proportion, instead of the cosine of the distance from the primary, may be the sine of the distance from the pole of the primary or the point in which the two secondaries meet.

+ For as the length of arc passed over between two hour circles in the same time on the equator, and on a parallel of declination, is as the cosine of the declination to 1, so the times of passing over the same length of arc (as for instance that included between the wires) on the equator and on a parallel of declination will be in the same ratio.

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