CHAP. II. LAWS TRACED BY OBSERVATION.

73

diurnal paths of the stars were attempted to be traced by instruments, even of the coarsest kind, it became evident that the notion of exact circles described about one and the same pole would not represent the phenomena correctly, but that, owing to some cause or other, the apparent diurnal orbit of every star is distorted from a circular into an oval form, its lower segment being flatter than its upper; and the deviation being greater the nearer the star approached the horizon, the effect being the same as if the circle had been squeezed upwards from below, and the lower parts more than the higher. For such an effect, as it was soon found to arise from no casual or instrumental cause, it became necessary to seek a natural one; and refraction readily occurred, to solve the difficulty. In fact, it is a case precisely analogous to what we have already (art. 47.) noticed, of the apparent distortion of the sun near the horizon, only on a larger scale, and traced up to greater altitudes. This new law once established, it became necessary to modify the expression of that anciently received, by inserting in it a salvo for the effect of refraction, or by making a distinction between the apparent diurnal orbits, as affected by refraction, and the true ones cleared of that effect.

(115.) Again: The first impression produced by a view of the diurnal movement of the heavens is, that all the heavenly bodies perform this revolution in one common period, viz. a day, or 24 hours. But no sooner do we come to examine the matter instrumentally, i. e. by noting, by timekeepers, their successive arrivals on the meridian, than we find differences which cannot be accounted for by any error of observation. All the stars, it is true, occupy the same interval of time between their successive appulses to the meridian, or to any vertical circle; but this is a very different one from that occupied by the sun. It is palpably shorter; being, in fact, only 231 56′ 4′09′′, instead of 24 hours, such hours as our common clocks mark. Here, then, we have already two different days, a sidereal

and a solar; and if, instead of the sun, we observe the moon, we find a third, much longer than either, lunar day, whose average duration is 24h 54m of our ordinary time, which last is solar time, being of necessity conformable to the sun's successive re-appearances, on which all the business of life depends.

(116.) Now, all the stars are found to be unanimous in giving the same exact duration of 23h 56′ 4′′-09, for the sidereal day; which, therefore, we cannot hesitate to receive as the period in which the earth makes one revolution on its axis. We are, therefore, compelled to look on the sun and moon as exceptions to the general law; as having a different nature, or at least a different relation to us, from the stars; and as having motions, real or apparent, of their own, independent of the rotation of the earth on its axis. Thus a great and most important distinction is disclosed to us.

(117.) To establish these facts, almost no apparatus is required. An observer need only station himself to the north of some well-defined vertical object, as the angle of a building, and, placing his eye exactly at a certain fixed point (such as a small hole in a plate of metal nailed to some immoveable support), notice the successive disappearances of any star behind the building, by a watch.* When he observes the sun, he must shade his eye with a dark-coloured or smoked glass, and notice the moments when its western and eastern edges successively come up to the wall, from which, by taking half the interval, he will ascertain (what he cannot directly observe) the moment of disappearance of its centre.

(118.) When, in pursuing and establishing this general fact, we are led to attend more nicely to the times of the daily arrival of the sun on the meridian,

*This is an excellent practical method of ascertaining the rate of a clock or watch, being exceedingly accurate if a few precautions are attended to; the chief of which is, to take care that that part of the edge behind which the star (a bright one, not a planet) disappears shall be quite smooth; as otherwise variable refraction may transfer the point of disappearance from a protuberance to a notch and thus vary the moment of observation unduly : this is easily secured, by nailing up a smooth-edged board.

CHAP. II. EMERGENCE OF SUBORDINATE LAWS.

75

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 a fixed instant, common to all the world, and

CHAP. II. OF TIME AND ITS MEASUREMENT.

77

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 dynamical 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 considerable 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