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is always reckoned in signs, degrees, minutes, &c, allowing thirty degrees to a sign. Thus, for example, when the sun has gone a hundred and seventy-four degrees from his apogee at A, he is said to be five signs twenty-four degrees from it, which is his mean anomaly. And, in like manner, when he has gone three hundred and fifty-five degrees from his apogee, he is said to be eleven signs twenty-five degrees from it; although he be but five degrees short of A, in coming round to it again.

So that from what has been said, it appears, that when the sun's anomaly is less than six signs, that is, when he is any where between ▲ and c, in the half of his orbit ABC, the solar noon will precede the clock noon: but when his anomaly is more than six signs, that is, when he is any where between c and A, in the half of his orbit CDA, the clock noon will precede the solar noon. On the contrary, when his anomaly is O signs 0 degrees, that is, when he is in his apogee at a; or, when it is exactly six signs, which is when he is in his perigee at c, he will come to the meridian at the same time with the star, and it will be noon by them both at the same instant.

The obliquity of the ecliptic to the equator, which is the first mentioned cause of the equation of time, would make the sun and clocks agree on four days of the year, which are when he enters Aries, Cancer, Libra, and Capricorn; but the other cause, which arises from his unequal motion in his orbit, would make the sun and clocks agree

only twice a year, that is when he is in his apogee and perigee; and, consequently, when these two points fall in the beginnings of Cancer and Capricorn, or of Aries, and Libra, they will concur in making the sun and clocks agree in those points. But the apogee, at present, is in the ninth degree of Cancer, and the perigee in the ninth degree of Capricorn; and, therefore, the sun and clocks cannot be equal about the beginnings of those signs, nor at any other time of the year, except when the swiftness or slowness of equation, resulting from one of the causes, just balances the slowness or swiftness arising from the other.

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About the first of November, the absolute equation of time resulting from both these causes will be the greatest; the time shown by an equally going clock being then about sixteen minutes and a quarter slower than the time shown by the sun. And, as this equation is of the utmost importance in all computations where time is concerned, astronomers have calculated tables, by which it be found for every day of the year. So that by means of these tables we can always correct the apparent time, by reducing it to mean time, which is the principal end, or object proposed. For though the time shown by the sun appears to be the most obvious and natural, yet it is of no other use, but as it may be employed in finding the mean time, or that whose essence is equality or perfect uniformity; all the celestial revolutions, and every other epoch and period, being always

referred to this standard, which is properly considered as the only true and adequate measure of duration.

The equation of time was known as early as the time of Ptolemy, as appears from what he has said upon this subject in the Sd Book of his Almagest; but notwithstanding it was employed both by Tycho Brahe and Kepler, it was not generally adopted till the year 1672, when Flamsteed published a dissertation upon the subject, at the end of the works of Horrox. Since that time, it has been found that some irregularities are also occasioned by the attractions of the planets; but as they depend upon principles which are not easily explained, and can, in no case, produce an error of more than a few seconds, I have altogether omitted them.

As the sun's place and anomaly are subject to continual variations, no general equation Tables can be so constructed as to be perpetual; and, therefore, when great accuracy is required, reference must be had to the Nautical Almanac, or some other performance of that kind. The following concise Table, however, which is adapted to the 2d year after Leap Year, will always be found within about a minute of the truth, and is, therefore, sufficiently accurate for the regulating of common clocks and watches, which are only divided into minutes.

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Where it is to be observed, that those columns which are marked + show that the clock or watch is faster than the sun, and those marked - that it is slower.

LETTER XIV.

OF THE REFORMATION OF THE CALENDAR.

ONE of the first cares of every society, after providing for its most pressing wants and necessities, has always been to establish some uniform method of reckoning time. Without such a standard to refer to, as occasion requires, the administration of public affairs, and the common concerns of life, would be subject to perpetual confusion. A well regulated calendar is, therefore, a matter of the most extensive utility and importance. It is by this means, that we are able to ascertain the returns of the seasons, and to point out the proper times for cultivating the earth; to adjust the observance of civil and ecclesiastical institutions, and to transmit to posterity the dates of such events as are worthy of remembrance.

A computation of time by certain regular periods, is a custom that has been observed by all nations, where arts and sciences have been cultivated; but as nature has afforded us no fixed or permanent measure of duration, the manner of estimating those periods has been various and uncertain. In some countries the natural day is supposed to commence with the rising of the sun, and in others with his setting; some begin to reckon from midnight, and others from noon. The Jews and Romans divided the artifical day into twelve parts, whether long or short, and the night in the same manner; so that their hours, except at the equinoxes, were always

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