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ordered, that on such occasions Easter should not be kept till the sunday following. After this general arrangement, nothing more was necessary, but to fix the day of the equinox, and the age of the Moon with respect to the Sun.

The vernal equinox happening on the 21st of march in the year 325, the council of Nice believed, or supposed, that the same phenomenon would always occur on the same day, and at the same hour, throughout the course of time. On the other hand it decreed, that the age of the Moon should be regulated by the metonic cycle; so that all the years which had the same golden number, or which should be equally distant from the beginning of each period of nineteen solar years, must have their new Moons on the same days. The fathers assembled at this council, however, however, though in other respects very ignorant, having some confused notions of the im perfection of the metonic cycle, directed the patriarch of Alexandria, in which city the celebrated school of mathematics flourished, to verify the paschal moons by astronomical calculation, and communicate the results to the pontiff at Rome, who should announce the precise day of Easter to all the christian World: but this judicious regulation was neglected,

In the system of the calendar adopted by the council of Nice there were two little astronomical errours, the effects of which, accumulating through a series of ages, were become very considerable. Ouc of these was, that the duration of the solar year extended to 365 days, six hours: the other, that £35 lunations composed exactly nineteen solar years. The first supposition errs in excess about eleven mi


nutes; and hence it followed, that the vernal equinox, which fell on the 21st of march in the year 325, happened on the 11th in 1582. The second errs by defect; and about the middle of the sixteenth century, the new moons indicated by the calendar preceded the true new moons, as shown by observation, four days.

The defects of the calendar had long been known; and several attempts had been made to correct them, but always in vain. The great progress of astronomy in the sixteenth century gave hopes of better success to Gregory XIII, who was desirous of rendering his pontificate illustrious by a signal and necessary reform, in which his predecessors had failed. Accordingly he issued a solemn invitation to all the astronomers of Christendom, to deliver their thoughts on the best means of correcting the calendar, and giving it an accurate and permanent form.

This invitation produced a multitude of schemes, among which that of Aloysius Lilius, an astronomer of Verona, obtained the preference, and was established by a bull, issued in the month of march 1582. It is a little complicated; and, to acquire a perfect knowledge of it, recourse must be had to the works, which treat of it expressly. I shall confine myself here to a few general remarks.

In the first place it was decreed, that, in the year 1582, the day after the 4th of october should be called the 15th, or that this month should be reduced to twenty-one days only, to make the equinox of

For a fuller account of the reformation of the Calendar, see Bonnycastle's Introduction to Astronomy.


the following year, 1583, fall on the 21st of march. 2dly: To prevent the return of the anticipation of the equinoxes in future, as well on account of the eleven minutes surplus of the julian year, as of the precession of the equinoxes, the quantity of which then began to be pretty accurately known, it was regulated, that of four secular years, all which would be bissextile according to the julian calendar, in future one only should be so, and the other three remain common years: thus for example, of the four secular years 1600, 1700, 1800, and 1900, the first alone would be bissextile. 3dly: With respect to the Moon, the motion of which makes here the most perplexing part of the problem, Lilius substituted instead of the golden numbers, or metonic cycle, the epacts, which are the numbers that express the Moon's age at the commencement of every year, or the excess of the solar year above the lunar. This arrangement, which easily admitted the addition or subtraction of certain days at determinate epochs, had the advantage of reconciling the motions of the Sun and Moon better than the simple metonic cycle. The days of the year were preceded by letters indicating little calculations, which it was necessary to make, in order to find the age of the Moon at every moment, and to regulate the festival of Easter with the other movable feasts.

This new calendar was received and adopted with universal applause in all catholic countries. But it had not the same success among the protestants, who retained the julian calendar as far as regarded the Sun's motion, and had recourse to astronomical cal


culation for fixing the celebration of Easter. However, as the practical form of the gregorian calendar is level to every capacity, the protestants of Germany at length adopted it in 1700, as the english did in 1752. It is equally in use among the other nations of the north, Prussia alone excepted.

On this subject I shall add only one word more. The convenience of any calendar whatever is not a sufficient reason for adopting or retaining it: the essential condition is, that it should be perfectly accurate. But, whatever plan be pursued, this is unattainable. Happily the common calendars are of very little use, since the most celebrated academies in Europe have begun to publish ephemerides, the utility of which I have already had occasion to make known, when speaking of the ancient cycles.

The landgrave of Hesse Cassel, William IV, who died in 1592, at the age of sixty, was very early instructed in astronomy; and not only patronized the science, but gave himself up to the practice of observations with a zeal and success, which would have done honour to a private individual. He built an observatory in his capital, and furnished it with the best instruments then to be obtained. Among his excellent observations are quoted those he made of the positions of several stars, and of the solstitial altitudes of the Sun in the years 1585 and 1587.

Tycho has been called the great observer; and for a similar reason Kepler should be styled the creator of true physical Astronomy. Born in 1571, he soon began to render himself eminent by his works; which were so numerous, that an abstract, or even a simple


catalogue of them, would carry us too far. From the various proofs he gave of his genius I shall select his discovery of the laws, which the planets obey in their motions: a discovery, to which he was led by combining with profound sagacity his own observations with those of Tycho.

The ancients made the planets revolve in perfect circles, the centre of which they supposed at first to be occupied by the Earth. But they soon found themselves obliged to remove the Earth to a greater or less distance from the centre of this revolution, that they might account for the changes observed in the diameters of the planets, whence it was to be inferred, that their distances from the Earth likewise changed. Tycho, while he left the Earth fixed in the centre of the mundane system, had at least avowed, that Mercury, Venus, Mars, Jupiter, and Saturn, revolved round the Sun, as I have already said. The numerous observations he made on the motions of Mars in particular furnished Kepler with the means of convincing himself by immense calculations, that all these motions could not be explained by the supposition of a circular orbit, in whatever situation the Sun might be supposed to be placed. He tried several other orbits in vain, till at length he found, that the common ellipsis, by placing the Sun in one of it's foci, agreed with the results of his calculations. This was the first step toward the grand discovery we have announced. Having afterward determined the dimensions of the elliptical orbit of Mars; and comparing together the times, which the planet took in making a complete revolution from


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