show the fractional parts, or days of the lunar month, with which each year of the cycle ends; and, consequently, they show the age of the moon at the beginning of the years against which they are severally set. By deducting that number, therefore, from 30, the remainder gives the day of the month for the new moon in January, for each year of the cycle.

This series of numbers, proceeding always by elevens, and showing the age of the moon at the beginning of each year, is called THE EPACT; from a Greek word, signifying addition.

The seven lunar months, or 210 days, which are added to the general account to make it equal to 19 solar years, are the difference between 19 solar and 19 lunar years. For 19 solar years, contain 6939 days; 19 lunar years, contain 6729 days; add seven lunar months, or 210 days, and the sum makes 6939 days: omitting fractions.

From the correspondence of the epacts with the years of the lunar cycle, it is easy to find the newmoons, and consequently the full-moons, for every month of the year.

Yrs.of the

L. Cycle. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

Epacts.

0.11.22. 3. 14.25. 6, 17. 28.9. 20. 1. 12. 23. 4. 15. 26. 7. 18

To find the new moon for any given month, we must, 1st, know the current year of the lunar cycle; 2dly, the epact corresponding to that year: 3dly, we must deduct the number of the epact of that year from 30, for January, and the remainder will be the day of the new moon in that month. Thus, if the epact be 12, (that is, if the moon be 12 days old at the end of the year,) we must deduct 12 from 30, (the sum of a lunar month,) and 18 will remain; therefore it will be newmoon on the 18th of January following. For February, we must deduct the epact from 28; for March, from 30. For the other ten months, we must add to the epact, 2 for April, 3 for May, 4 for June, and so on; and deduct from 30; and the remainder will give the day for the moon's change, or new moon, in each of those ten months. But, if the epact together with the number added exceed 30, then we must deduct from 60, (or 2 months,) instead of from 30; and the remainder will equally show the day of the new moon.

Since therefore the new moons, after every nineteen years, fall again upon the same days of the month, a table of the new moons for one entire cycle of nineteen years will show the new moons for the succeeding cycles; with sufficient accuracy

for every purpose of common life, though not for the exactness of astronomical calculations. And, since the full moons are always 14 days and 18 hours before, and after, the new moons; by finding the new moon for any month, we find also the full moon, by counting 14 days and a half either forward or backward. This method may sometimes err, by one day, or thirty-six hours; but that difference is immaterial for common life, and in most instances it will be found exact even to a day.

It is upon this principle, that Table II. has been arranged; in which we may trace the beautiful order uniformly maintained by that splendid luminary, "the faithful witness in HEAVEN." This Table shows the New-Moons, upon a mean calculation, for every month of the year in the recurrent CYCLE of NINETEEN years. It is digested from the ecclesiastical Table of Epacts, compared throughout with the two last lunar cycles in the Nautical Almanack, and with the years of the present cycle, of which the present year, 1812, is the 8th year. In order to use it, first find the number of the current year in the lunar cycle; corresponding to which number in the same line are the days

Psalm lxxxix. 37.

of the New-Moons, for each of the twelve months of the year. To find the Full-Moon of any month, reckon 14 days and a half, backward or forward, from the day of the New-Moon. The Epact of each year is subjoined, which shows the Moon's age at the beginning of that year.

HEBDOMADAL* TIME.

§. Of Weeks.

We have now seen the operations of the SUN and MOON, as the natural indexes of time; and we have found the means of adjusting the indications of the latter, to the days depending upon the former, so as to know, with sufficient accuracy, upon what days of the solar year the new and full moons shall fall.

But there remains another rule of time, of the utmost benefit and importance, which it is equally necessary for us to adjust to the days of the solar

* From the Greek, irra, hepta-seven.

year; this is, the seven constantly recurring days of THE WEEK; by means of which, the measures of months are subdivided into smaller portions, and more convenient measures, of time.

This division of time has no relation, either to the sun, or to the moon, or to any natural index whatsoever; but is the positive institution, and perpetual evidence of the intervention, of THE AUTHOR

OF TIME.

Some eminent astronomers, chiefly of the late French school, attempted (for obvious reasons,) to get rid of the institutional origin of THE WEEK; by representing it as an invention of man, to mark the fourth parts, or quarters, of the lunar month. But they must have been able to see, what every common observer may at once discern, that the rule of weeks would be at variancė with that of the lunar motions, before three of them could pass; and that the variance would be continually increasing. There is, indeed, a perpetual and essential discordance, between the ratio of weeks and that of the lunar motions; since one lunar year contains only 48 of those quarters, while it embraces 50 weeks and four days. Let us, then, humbly recognise and adore the Almighty power, who so graciously superadded to His natural dividers of time, this inestimable, unchan