autumn season, from the autumnal equinox, on the 23d of September; and the winter season from the winter solstice, on the 21st of December. At the two equinoxes, the days and nights are of equal length; viz. twelve hours each: the sun rising and setting at six o'clock. From the vernal to the autumnal equinox, the days are longer than the nights; and from the autumnal to the vernal equinox, the nights are longer than the days. At the summer solstice, the day is the longest; at the winter solstice, the day is the shortest.-See Table IV.

But here it must be observed, that although we compute time by the true solar year, yet the twelve solar months and our twelve calendar months differ in their divisions and periods. The cause of this difference is, that our civil year does not begin exactly at any one of the four great solar points, of the solstices and equinoxes, but is made to begin eleven days after the winter solstice, which happens on the 21st of December; and the same difference continues throughout the year, between the divisions of the months. But this difference does not prevent our common year from being altogether a solar year.-See Table V.

Years are numbered by CENTURIES, or hundreds ;

M

and are reckoned from some fixed period, which is called AN EPOCHA; and the reckoning of years from the particular epocha, is called THE ERA of that epocha.

The SOLAR days, months, seasons, and years, constitute the rule of time by which the common business of human life is regulated; so that it is necessary, to reduce all other measures of time to that rule.

LUNAR TIME.

THE MOON.

THE second great natural index of time, is THE MOON. But, as the revolutions of this luminary do not correspond in measure with any revolutions depending upon the SUN, some rule of equation, or artificial adjustment, is requisite, in order to reconcile their motions with each other.

The revolution of the moon round the earth is completed in 29 days, 12 hours, 44 minutes, and 3 seconds; (or, by a round number, in 30 days.) This revolution is called a lunation, or lunar month. Twelve of these lunar months, constituting one

lunar year, are therefore completed in 354 days; that is to say, 10 days, 15 hours, 11 minutes, and 27 seconds, before the twelve of the solar year months are completed. Hence it follows; 1st, that the lunar year comprehends only 354 days; and, 2dly, that it is constantly departing from the rule of the solar year, at the rate of about eleven days every year.

§ Correspondence of Solar and Lunar Time.

As it is of great importance to the uses of mankind to reconcile the two computations, in order that we may be able to know when each lunation begins; that is to say, to know on what days of the solar year the new-moons will fall; the following method has been devised, for adjusting the two

measures.

When the solar and the lunar year begin together, that is, when it is new-moon upon the first day of January, the moon (as has been said) will complete her twelfth month, 10 days, 15 hours, 11 minutes, 27 seconds, before the sun will have completed his twelfth month; and, consequently, the moon will be already advanced those 10 d.

15 h. 11 m. 27 s. into her 13th lunation, and second year, when the sun is only beginning his second year. It will follow, that at the end of the second year the moon will have completed her year, twice 10 days, 15 hours, 11 minutes, 27 seconds, before the sun has completed his and so on, for each succeeding year.

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But it is found, that at the end of every nineteen solar years, (which are equal to 19 lunar years and 7 months,) the moon and the sun meet again on the 1st of January; and begin their years again in coincidence. And thus, after a cycle, or recurrence, of 19 solar years, called THE LUNAR CYCLE, all the new moons fall again upon the same days of the solar months that they did 19 years before.

Now, as the difference between the solar and lunar year is in the proportion of 10 days, 15 hours, 11 minutes, 27 seconds, for each of those 19 years; or, speaking by a round number, 11 days; by always adding eleven days to the lunar years, for the difference between solar and lunar measure, the two sums will be kept at par; and the appearances of the moon will be always fixed to the standard of solar time.

The eleven days, thus successively added to the

lunar years throughout the 19 solar years of the cycle, are reduced into lunar months, in the follow

After the last, or 19th, year of the cycle, twelve days are added instead of eleven, (viz. 18+12=30,) which completes the lunar month; and the new cycle finds the sun and moon in conjunction on the first day of the first year, as they had been nineteen years before.

It is evident, that the numbers in the last column