irregularities (so they first seem) begin to be observed. The intervals between two successive arrivals are not the same at all times of the year. They are sometimes greater, sometimes less, than 24 hours, as shown by the clock; that is to say, the solar day is not always of the same length. About the 21st of December, for example, it is half a minute longer, and about the same day of September nearly as much shorter, than its average duration. And thus a distinction is again pressed upon our notice between the actual solar day, which is never two days in succession alike; and the mean solar day of 24 hours, which is an average of all the solar days throughout the year. Here, then, a new source of enquiry opens upon us. The sun's apparent motion is not only not the same with that of the stars, but it is not (as the latter is) uniform. It is subject to fluctuations, whose laws become matter of investigation. But to pursue these laws, we require nicer means of observation than what we have described, and are obliged to call in to our aid an instrument called the transit instrument, especially destined for such observations, and to attend minutely to all the causes of irregularity in the going of clocks and watches which may affect our reckoning of time. Thus we become involved by degrees in more and more delicate instrumental enquiries; and we speedily find that, in proportion as we ascertain the amount and law of one great or leading fluctuation, or inequality, as it is called, of the sun's diurnal motion, we bring into view others continually smaller and smaller, which were before obscured, or mixed up with errors of observation and instrumental imperfections. In short, we may not inaptly compare the mean length of the solar day to the mean or average height of water in a harbour, or the general level of the sea unagitated by tide or waves. The great annual fluctuation above noticed may be compared to the daily variations of level produced by the tides, which are nothing but enormous waves extending over the whole ocean, while the smaller sub

ordinate inequalities may be assimilated to waves ordinarily so called, on which, when large, we perceive lesser undulations to ride, and on these, again, minuter ripplings, to the series of whose subordination we can perceive no end.

(119.) With the causes of these irregularities in the solar motion we have no concern at present; their explanation belongs to a more advanced part of our subject but the distinction between the solar and sidereal days, as it pervades every part of astronomy, requires to be early introduced, and never lost sight of. It is, as already observed, the mean or average length of the solar day, which is used in the civil reckoning of time. It commences at midnight, but astronomers (at least those of this country), even when they use mean solar time, depart from the civil reckoning, commencing their day at noon, and reckoning the hours from 0 round to 24. Thus, 11 o'clock in the forenoon of the second of January, in the civil reckoning of time, corresponds to January 1 day 23 hours in the astronomical reckoning; and one o'clock in the afternoon of the former, to January 2 days 1 hour of the latter reckoning. This usage has its advantages and disadvantages, but the latter seem to preponderate; and it would be well if, in consequence, it could be broken through, and the civil reckoning substituted.

(120.) Both astronomers and civilians, however, who inhabit different points of the earth's surface, differ from each other in their reckoning of time; as it is obvious they must, if we consider that, when it is noon at one place, it is midnight at a place diametrically opposite; sunrise at another; and sunset, again, at a fourth. Hence arises considerable inconvenience, especially as respects places differing very widely in situation, and which may even in some critical cases involve the mistake of a whole day. To obviate this inconvenience, there has lately been introduced a system of reckoning time by mean solar days and parts of a day counted from fixed instant, common to all the world, and

determined by no local circumstance, such as noon or midnight, but by the motion of the sun among the stars. Time, so reckoned, is called equinoctial time; and is numerically the same, at the same instant, in every part of the globe. Its origin will be explained more fully at a more advanced stage of our work.

(121.) Time is an essential element in astronomical observation, in a twofold point of view: — 1st, As the representative of angular motion. The earth's diurnal motion being uniform, every star describes its diurnal circle uniformly; and the time elapsing between the passage of the stars in succession across the meridian of any observer becomes, therefore, a direct measure of their differences of right ascension. 2dly, As the fundamental element (or, independent variable, to use the language of geometers) in all dy-、 namical theories. The great object of astronomy is the determination of the laws of the celestial motions, and their reference to their proximate or remote causes. Now, the statement of the law of any observed motion in a celestial object can be no other than a proposition declaring what has been, is, and will be, the real or apparent situation of that object at any time, past, present, or future. To compare such laws, therefore, with observation, we must possess a register of the observed situations of the object in question, and of the times when they were observed.

(122.) The measurement of time is performed by clocks, chronometers, clepsydras, and hour-glasses: the two former are alone used in modern astronomy. The hour-glass is a coarse and rude contrivance for measuring, or rather counting out, fixed portions of time, and is entirely disused. The clepsydra, which measured time by the gradual emptying of a large vessel of water through a determinate orifice, is susceptible of consider. able exactness, and was the only dependence of astronomers before the invention of clocks and watches. At present it is abandoned, owing to the greater convenience and exactness of the latter instruments. In one case

only has the revival of its use been proposed; viz. for the accurate measurement of very small portions of time, by the flowing out of mercury from a small orifice in the bottom of a vessel, kept constantly full to a fixed height. The stream is intercepted at the moment of noting any event, and directed aside into a receiver, into which it continues to run, till the moment of noting any other event, when the intercepting cause is suddenly removed, the stream flows in its original course, and ceases to run into the receiver. The weight of mercury received, compared with the weight received in an interval of time observed by the clock, gives the interval between the events observed. This ingenious and simple method of resolving, with all possible precision, a problem which has of late been much agitated, is due to captain Kater.

(123.) The pendulum clock, however, and the balance watch, with those improvements and refinements in its structure which constitute it emphatically a chronometer *, are the instruments on which the astronomer depends for his knowledge of the lapse of time. These instruments are now brought to such perfection, that an irregularity in the rate of going, to the extent of a single second in twenty-four hours in two consecutive days, is not tolerated in one of good character; so that any interval of time less than twentyfour hours may be certainly ascertained within a few tenths of a second, by their use. In proportion as intervals are longer, the risk of error, as well as the amount of error risked, becomes greater, because the accidental errors of many days may accumulate; and causes producing a slow progressive change in the rate of going may subsist unperceived. It is not safe, therefore, to trust the determination of time to clocks, or watches, for many days in succession, without checking them, and ascertaining their errors by reference to natural events which we know to happen, day after day, at equal intervals. But if this be done, the erg, to measure.

*

χρονος, time;

longest intervals may be fixed with the same precision as the shortest; since, in fact, it is then only the times intervening between the first and last moments of such long intervals, and such of those periodically recurring events adopted for our points of reckoning, as occur within twenty-four hours respectively of either, that we measure by artificial means. The whole days are counted out for us by nature; the fractional parts only, at either end, are measured by our clocks. Το keep the reckoning of the integer days correct, so that none shall be lost or counted twice, is the object of the calendar. Chronology marks out the order of succession of events, and refers them to their proper years and days; while chronometry, grounding its determinations on the precise observation of such regularly periodical events as can be conveniently and exactly subdivided, enables us to fix the moments in which phenomena occur, with the last degree of precision.

(124.) In the culmination, or transit, (i.e. the passage across the meridian of an observer,) of every star in the heavens, he is furnished with such a regularly periodical natural event as we allude to. Accordingly, it is to the transits of the brightest and most conveniently situated fixed stars that astronomers resort to ascertain their exact time, or, which comes to the same thing, to determine the exact amount of error of their clocks.

(125.) The instrument with which the culminations of celestial objects are observed is called a transit instrument. It consists of a telescope firmly fastened on a horizontal axis directed to the east and west points of the horizon, or at right angles to the plane of the meridian of the place of observation. The extremities of the axis are formed into cylindrical pivots of exactly equal diameters, which rest in notches formed in metallic supports, bedded (in the case of large instruments) on strong piers of stone, and susceptible of nice adjustment by screws, both in a vertical and horizontal direction. By the former adjustment,