deration, however, will suffice to show that such a course of proceeding is perfectly legitimate.

(111.) The steps by which we arrive at the laws of natural phenomena, and especially those which depend for their verification on numerical determinations, are necessarily successive. Gross results and palpable laws are arrived at by rude observation with coarse instruments, or without any instruments at all; and these are corrected and refined upon by nicer scrutiny with more delicate means. In the progress of this, subordinate laws are brought into view, which modify both the verbal statement and numerical results of those which first offered themselves to our notice; and when these are traced out, and reduced to certainty, others, again, subordinate to them, make their appearance, and become subjects of further enquiry. Now, it invariably happens (and the reason is evident) that the first glimpse we catch of such subordinate laws the first form in which they are dimly shadowed out to our minds—is that of errors. We perceive a discordance between what we expect, and what we find. The first occurrence of such a discordance we attribute to accident. It happens again and again; and we begin to suspect our instruments. We then enquire, to what amount of error their determinations can, by possibility, be liable. If their limit of possible error exceed the observed deviation, we at once condemn the instrument, and set about improving its construction or adjustments. Still the same deviations occur, and, so far from being palliated, are more marked and better defined than before. We are now sure that we are on the traces of a law of nature, and we pursue it till we have reduced it to a definite statement, and verified it by repeated observation, under every variety of circumstances.

(112.) Now, in the course of this enquiry, it will not fail to happen that other discordances will strike us. Taught by experience, we suspect the existence of some natural law, before unknown; we tabulate (i. e. draw out in order) the results of our observations; and we per

ceive, in this synoptic statement of them, distinct indications of a regular progression. Again we improve or vary our instruments, and we now lose sight of this supposed new law of nature altogether, or find it replaced by some other, of a totally different character. Thus we are led to suspect an instrumental cause for what we have noticed. We examine, therefore, the theory of our instrument; we suppose defects in its structure, and, by the aid of geometry, we trace their influence in introducing actual errors into its indications. These errors have their laws, which, so long as we have no knowledge of causes to guide us, may be confounded with laws of nature, and are mixed up with them in their effects. They are not fortuitous, like errors of observation, but, as they arise from sources inherent in the instrument, and unchangeable while it and its adjustments remain unchanged, they are reducible to fixed and ascertainable forms; each particular defect, whether of structure or adjustment, producing its own appropriate form of error. When these are thoroughly investigated, we recognize among them one which coincides in its nature and progression with that of our observed discordances. The mystery is at once solved: we have detected, by direct observation, an instrumental defect.

(113.) It is, therefore, a chief requisite for the practical astronomer to make himself completely familiar with the theory of his instruments, so as to be able at once to decide what effect on his observations any given imperfection of structure or adjustment will produce in any given circumstances under which an observation can be made. Suppose, for example, that the principle of an instrument required that a circle should be exactly concentric with the axis on which it is made to turn. As this is a condition which no workmanship can fulfil, it becomes necessary to enquire what errors will be produced in observations made and registered on the faith of such an instrument, by any assigned deviation in this respect; that is to say, what would be the dis

agreement between observations made with it and with one absolutely perfect, could such be obtained. Now, a simple theorem in geometry shows that, whatever be the extent of this deviation, it may be annihilated in its effect on the result of observations depending on the graduation of the limb, by the very easy method of reading off the divisions on two diametrically opposite points of the circle, and taking a mean; for the effect of excentricity is always to increase one such reading by just the same quantity by which it diminishes the other. Again, suppose that the proper use of the instrument required that this axis should be exactly parallel to that of the earth. As it never can be placed or remain so, it becomes a question, what amount of error will arise in its use from any assigned deviation, whether in a horizontal or vertical plane, from this precise position. Such enquiries constitute the theory of instrumental errors; a theory of the utmost importance to practice, and one of which a complete knowledge will enable an observer, with very moderate instrumental means, to attain a degree of precision which might seem to belong only to the most refined and costly. In the present work, however, we have no further concern with it. The few astronomical instruments we propose to describe in this chapter will be considered as perfect both in construction and adjustment.

(114.) As the above remarks are very essential to a right understanding of the philosophy of our subject and the spirit of astronomical methods, we shall elucidate them by taking a case. Observant persons, before the invention of astronomical instruments, had already concluded the apparent diurnal motions of the stars to be performed in circles about fixed poles in the heavens, as shown in the foregoing chapter. In drawing this conclusion, however, refraction was entirely overlooked, or, if forced on their notice by its great magnitude in the immediate neighbourhood of the horizon, was regarded as a local irregularity, and, as such neglected, or slurred over. As soon, however, as the

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 23h 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, -a 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.