was too enlightened not to perceive, that his system was in fact almost as repugnant to the laws of mechanics as that of Ptolemy. His true glory is the having been an excellent observer, and having laid or strengthened the foundations of the new astronomical theories, either by his own labours, or by those of his disciples and coadjutors, whom he had assembled in his little town of Uraniburg.

We know, that the motion of the Moon is subject to a great number of inequalities. The four principal of these are the equation of the centre, the evection, the variation, and the annual equation. The first, we have seen, was discovered by Hipparchus, and the second by Ptolemy; and what they consist in has been explained. Tycho discovered both the others.

The variation is an alternate increase and diminution of the motions of the Moon, which depend on it's position with regard to the syzygies, or the line which joins the centres of the Sun, Moon, and Earth, when these three bodies are in conjunction or opposition. Tycho observed, that in setting off from the point of conjunction, for instance, the velocity of the Moon diminished till the first quarter; that it increased from the first quarter to the point of opposition; that it diminished in the third quarter of it's revolution, and again increased in the fourth : and so on alternately in it's succeeding revolutions.

The annual equation arises from an inequality, which is found in the duration of the lunar months, according to the different seasons of the year. It is to be observed, that the periodical revolutions of the Moon are of the same duration only at the same

seasons; while from one season to another they increase or diminish. The longest take place in the

january; the shortest in Hence result in the theory equations, proportional to

months of december and those of june and july. of the Moon three small the equation of the Sun's centre: one for the notions of the Moon in it's orbit, the other for the motion of it's apogee, and the third for the motion of the nodes of the lunar orbit.

Beside these four principal inequalities, which have deen detected by the immediate assistance of observation, the motion of the Moon is subject to several other little inequalities, which the theory of universal gravitation has occasioned to be remarked; and which we are at present obliged to introduce into astronomical calculation, when we would have it represent the state of the heavens with all the accuracy, which it is possible to attain.

Tycho likewise improved the theory of the Moon in another essential part: he determined the greatest and least inclination of the lunar orbit to the plane of the ecliptic with more care, and with greater precision, than had ever before been done. The same research he also extended to the different planets.

The ancients had a general knowledge of the effects of refraction. Every person might perceive, that the brightness of the Sun, when seen at the horizon, was much less, than when it has reached the meridian. The reason of this is, the Earth being surrounded with a dense atmosphere, which extends fifty miles from it's surface according to the common supposition, the rays of the Sun coming from the

horizon

horizon traverse a greater space in the atmosphere, and consequently experience more resistance, and are more enfeebled, than the rays that come from the meridian. This difference should have led the ancients to suspect, that refraction might produce some change in the apparent position of the heavenly bodies above the horizon; a change which in fact is known to take place. But we do not find, that the ancients paid any attention to it. Tycho was the first who felt the necessity of introducing this important element into astronomical calculation, and who began to employ it. But as the laws of refraction were not yet known in his time, he could only give general and somewhat vague results.

To the same astronomer we are indebted for the elements of the theory of comets. The opinion, that comets are only meteors, was not yet subverted; notwithstanding the judicious reflections of Seneca, quoted above. Tycho completed the demonstration, that they are solid bodies like the planets, and subject to the same revolutions round the Sun. He observed a great number of comets in which he recognized this character of resemblance, which ought naturally to have dissipated the prerogatives ascribed to them. But his authority and his reasonings did not prevent comets from being still for a long time considered as the harbingers of great events: so powerfully is the unhappy race of mankind enchained by errours, with which religious superstitions are connected.

The great star which suddenly appeared in the constellation of Cassiopeia, in 1572, attracted the: attention of every astronomer, and Tycho has rc

corded the history of this extraordinary astronomical event. It was first seen on the 7th of november, both at Wittemberg and Augsburg at the same time. Bad weather prevented Tycho from observing it before the 11th, when he found it almost as bright as Venus when stationary. It continued thus for some weeks, when it's magnitude gradually diminished. It was seen for seventeen months, at the end of which time, in march 1574, it disappeared entirely. According to all probability, had astronomers been assisted by the telescope, it would have been longer visible. Tycho very accurately observed the periods of magnitude through which it passed during the time of it's appearance: and he noted with similar attention the singular changes of colour it underwent. At first it was of a bright whiteness: then it became of a reddish yellow, like Mars, Aldebaran, and the right shoulder of Orion; after which it changed to a leaden white, like that of Saturn; and thus it remained, till it disappeared: it twinkled like a common star: &c.

Similar phenomena have been seen on many other occasions. The ancient poets, particularly Ovid in his Fasti, book IV, relate that one of the stars of the Pleiades was extinguished. Pliny says, that Hipparchus undertook to number the stars, in consequence of the appearance of a new one in his time. Nearer our own times, in the years 945 and 1264, it is said, that a new star was seen in the same place of the heavens. In 1600 a star was observed for the first time in the breast of the Swan, which appeared and disappeared alternately; in 1616 it was of the

third magnitude; after which it diminished for some years, and then disappeared. It was seen again in 1655, and disappeared once more, to reappear in 1665; &c. In the neck of the Whale there is a star, which changes it's magnitude periodically, and appears and disappears at regular intervals. It would be superfluous here to adduce a greater number of these extraordinary facts, and I shall hereafter relate the reasons, which modern astronomers have given to explain them.

Contemporary with Tycho several eminent astronomers flourished, among whom William 1v, landgrave of Hesse Cassel, and Kepler, deserve particu larly to be distinguished. Of both of them I shall speak, after I have given a brief account of the reform of the calendar in 1582, under the pontificate of Gregory XIII.

Great confusion had long taken place in the perplexing and defective method, which the church had adopted for fixing the celebration of Easter every year, which, as is well known, regulates all the other movable feasts. The jews celebrate their Passover on the fourteenth day of the first month; that is to say, of that lunar month in which the fourteenth day fell on the vernal equinox, or nearest after it. The primitive church made no change in this system, except directing, that the christian festival of Easter should be kept on the sunday next following the fourteenth day. When this fourteenth day happened to be on sunday, some churches made no scruple of celebrating their Easter on that day, notwithstanding it's coincidence with the jewish Passover: but the council held at Nice in 325 prohibited this practice, and ordered,

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