The fixed stars, as will be explained more fully hereafter, appear in the telescope, no matter how high its magnifying power be, as mere lucid points, having no sensible magnitude. By the diurnal motion of the firmament, the star passes successively over all the wires, a short interval being interposed between its passages. The observer, just after the star approaching the meridian enters the field of view, proceeds to count the seconds of the clock by his ear. He observes, in the manner already explained, to a fraction of a second, the instant at which the star crosses each of the wires; and taking a mean of all these times, he obtains, with a great degree of precision, the instant at which the star passed the middle wire, which is the time of the transit. The hour and minute indicated by the clock is noted after the observation.

By this expedient the result has the advantage of as many independent observations as there are parallel wires. The errors of observation being distributed, are proportionally diminished.

When the sun, moon, or a planet, or, in general, any object which has a sensible disk, is observed, the time of the transit is the instant at which the centre of the disk is upon the middle wire. This is obtained by observing the clock-time when the western and eastern edges of the disk come in contact respectively with each of the vertical wires. Taking first a mean of all the observed clock-times of the transit of the western edge, the time when it is on the middle wire is found; and in like manner, the mean of all the observed clock-times of the transit of the eastern edge will give the time when that edge is also on the middle wire; the mean of these transits of the two edges, therefore, determines the clocktime of the transit of the centre of the disk over the middle wire, or a mean of all the observed clock-times of the transit of both edges will give the same result.

By day the wires are visible, as fine black lines intersecting and spacing out the field of view. At night they are rendered visible by a lamp, by which the field of view is faintly illuminated.

In many observatories transits are also observed by the chronographic method, and recorded by the aid of galvanism on a revolving cylinder. In this case, the clock is provided with means for sending a galvanic signal to the recording apparatus at every vibration of the pendulum, causing a puncture to be made on the paper with which the cylinder is covered. This series of punctures form one long spiral line, the prickers being attached to a travelling frame, which is carried by an uniform-motion clock, which at the same time causes the cylinder to revolve. The office of the observer is simply to press an ivory key when the star is passing each wire in the field of view; this completes the galvanic circuit and causes a puncture for each wire observed to be made

between the series of clock punctures. It is a matter of very little trouble to extract the exact second and fraction of a second at which the separate observations were made.

The results from this method are considered more trustworthy than those determined by "eye and ear." From a mean of 101 transits observed at Greenwich, it was found that the probable error of one transit by the chronographic method was oo17, while by the "eye and ear" it amounted to oo28. In another determination on a different principle, the excess in the same direction amounted to 0014. Though this amount may seem insignificant to the reader, nevertheless it is of considerable importance in connection with astronomical observations.*

29. Apparent motion of objects in the field of view.— Since the telescope reverses the objects observed, the motion in the field will appear to be from west to east, while that of the firmament is from east to west. An object will therefore enter the field of view on the west side, and, having crossed it, will leave it on the east side. Since the sphere revolves at the rate of 15° per hour, 15' per minute, or 15′′ per second of time, an object will be seen to pass across the field of view with a motion absolutely uniform, the space passed over between two successive beats of the pendulum being invariably 15′′.

Thus, if the moon or sun be in or near the equator, the disk will be observed to pass across the field with a visible motion, the interval between the moments of contact of the western and eastern edges with the middle wire being 2m 8, when the apparent diameter is 32. Thus, the disk appears to move over a space equal to half its own diameter in 1m 4'.

30. Circles of declination, or hour circles.- Circles of the celestial sphere which pass through the poles are at right angles to the celestial equator, and are on the heavens exactly what meridians are upon the terrestrial globe. They divide the celestial equator into arcs which measure the angles which such circles form with each other. Thus, two such circles which are at right angles include an arc of 90° of the celestial equator, and two which form with each other an angle of 1° include between them an arc of 1° of the celestial equator. These CIRCLES OF DECLINATION, OF HOUR CIRCLES as they are called, are carried round by the diurnal motion of the heavens, and are brought in succession to coincide with the celestial meridian, the intervals between the moments of their coincidence with the meridian being always proportional to the angle they form with each other, or, what is the same, to the arc of the celestial equator included between them. Thus, if two circles of

* Astron. Soc. Notices, Vol. xx. p. 86.

declination form with each other an angle of 30°, the interval between the moments of their coincidence with the meridian will be two sidereal hours.

The relative position of the circles of declination with respect to each other, and to the meridian, and the successive positions assumed by any one such circle during a complete revolution of the sphere, will be perceived and understood without difficulty by the aid of a celestial globe, without which it is scarcely possible to obtain any clear or definite notion of the apparent motions of celestial objects.

31. Right ascension.-The arc of the celestial equator between any circle of declination and a certain point on the equator called the FIRST POINT OF ARIES, is called the RIGHT ASCENSION of all objects through which the circle of declination passes. This are is always understood to be measured from the point where the circle of declination meets the celestial equator westward, that is, in the direction of the apparent diurnal motion of the heavens, and it may extend, therefore, over any part whatever of the equator from 0° to 360°. Right ascension is expressed sometimes according to angular magnitude, in degrees, minutes, and seconds; but since, according to what has been explained, these magnitudes are proportional to the time they take to pass over the meridian, right ascension is more frequently expressed immediately by this time. Thus, if the right ascension of an object is 15° 15′ 15′′, it will be expressed also by 1 1 1.

In general, right ascension expressed in degrees, minutes, and seconds may be reduced to time by dividing it by 15; and if it be expressed in time, it may be reduced to angular language by multiplying it by 15.

The difference of right ascensions of any two objects may be ascertained by the transit instrument and clock, by observing the interval which elapses between their transits over the meridian. This interval, whether expressed in time or reduced to degrees, is their difference of right ascension.

Hence, if the right ascension of any one object be known, the right ascension of all others can be found.

32. Sidereal clock indicates right ascension.-If the hands of the sidereal clock be set to oh om os when the first point of Aries is on the meridian, they will at all times (supposing the rate of the clock to be correct) indicate the right ascension of such objects as are on the meridian. For the motion of the hands in that case corresponds exactly with the apparent motion of the meridian on the celestial equator produced by the diurnal motion of the heavens. While 15° of the equator pass the meridian the hands move through 1", and other motions are made in the same proportion.

33. The mural circle.-The transit instrument and sidereal clock supply means of determining with extreme precision the instant at which an object passes the meridian; but the instrument is not provided with any accurate means of indicating the point at which the object is seen on the meridian. A circle is sometimes, it is true, attached to the transit by which the position of this point may be roughly observed; but to ascertain it with a precision proportionate to that with which the transit instrument determines the right ascensions, requires an instrument constructed and mounted for this express object in a manner, and under conditions, altogether different from those by which the transit instrument is regulated. The form of instrument adopted in the most efficiently furnished observatories for this purpose is the MURAL CIRCLE.

This instrument is a graduated circle, similar in form and principle to the instrument described in (13). It is centred upon an axis established in the face of a stone pier or wall (hence the name) erected in the plane of the meridian. The axis, like that of a transit instrument, is truly horizontal, and directed due east and west. Being by the conditions on which it is first constructed and mounted, very nearly in this position, it is rendered exactly so by two adjustments, one of which moves the axis vertically, and the other horizontally, by means of screws, through spaces which, though small, are still large enough to enable the observer to correct the slight errors of position incidental to the workmanship and mounting.

The instrument, as mounted and adjusted, is represented in perspective in fig. 11, where A is the stone wall to which the instrument is attached, D the central axis on which it turns; and F G the telescope, which does not move upon the circle, but is immovably attached to it, so that the entire instrument, including the telescope, turns in the plane of the meridian upon the axis D.

A front view of the circle in the plane of the instrument is given in fig. 12.

The graduation is usually

made on the edge, and not on

E

Fo

0

Fig. 11.

the face limb. The hoop of metal thus engraved forms, therefore,

A trough o, containing mercury, is placed on the floor in a convenient position in the plane of the instrument, on the surface of

Fig. 12.

which are seen, by reflection, the objects as they pass over the meridian. The observer is thus enabled to ascertain the directions, as well of the images of the objects reflected on the mercury, as of the objects themselves, the advantage of which will presently

appear.

Convenient ladders, chairs, and couches, capable of being adjusted by racks and other mechanical arrangements, at any desired inclination, enable the observer, with the utmost ease and comfort, to apply his eye to the telescope, no matter what be its direction.

In the Greenwich observatory, the mural circles formerly in use were six feet in diameter, and consequently about 226 inches in circumference. Each degree upon the circumference measuring, therefore, above six-tenths of an inch, admits of extremely minute subdivision.

The divisions on the graduated edge of the instrument are numbered as usual from 0° to 360° round the entire circle. The position which the direction of the line of collimation of the telescope has with relation to the o° of the limb is indifferent. Nothing is necessary except that this line, in moving round the axis D of the instrument, shall remain constantly in the plane of the meridian. This condition being fulfilled, it is evident that, as the circle revolves, the line of collimation will be successively directed to every point of the meridian when presented upwards, and to every