Remarks upon the solar and the lunar years, the cycle of 19 years, commonly called the golden number, the epact, and a method of finding the time of Easter, as it is now observed in most parts of Europe

by Earl of George Parker Macclesfield

The mean Tropical Solar Year, or that mean Space of Time wherein the Sun, or Earth, after departing from any Point of the Ecliptic returns to the same again, consists, according to Dr. Halley's Tables, of 365^d, 5^h, 48^´, 55^´´: Which is less by 11^´, 5^´´, than the mean Julian Year, consisting of 365^d, 6^h, 0^´, 0^´´.

Hence the Equinoxes and Solstices anticipate, or come earlier than the Julian Account supposes them to do by 11´, 5´´, in each mean Julian Year; or 44^´, 20^´´ in every four; or 3^d, 1^h, 53^´, 20^´´, in every four hundred Julian Years.

In order to correct this Error in the Julian Year, the Authors of the Gregorian Method of regulating the Year, when they reformed the Calendar in the Beginning of October 1582, directed that three intercalary Days should be omitted or dropped in every four hundred Years; by reckoning all those Years, whose Date consists of a Number of entire Hundreds not divisible by 4, such as 1700, 1800, 1900, 2100, &c. to be only Common, and not Bissextile or Leap Years, as they would otherwise have been; and consequently omitting the intercalary Days, which, according to the Julian Account, should have been inserted in the Month of February in those Years. But at the same time they order'd that every fourth hundredth Year, consisting of a Number of entire Hundreds, divisible by 4, such as 1600, 2000, 2400, 2800, &c. should still be consider'd as Bissextile or Leap Years, and, of consequence, that one Day should be intercalated as usual in those Years.

This Correction, however, did not entirely remove the Error: For the Equinoxes and Solstices still anticipate 1^h, 53^´, 20^´´ in every four hundred Gregorian Years.

But that Difference is so inconsiderable as not to amount to twenty-four Hours, or to one whole Day, in less than 5082 Gregorian Years.

Of the Lunar Year, Cycle of 19 Years, and the Epact.

The Space of Time betwixt one mean Conjunction of the Moon with the Sun and the next following, or a mean Synodical Month, is equal to 29^d, 12^h, 44^´, 3^´´, 2^´´´, 56^IV according to Mr. Pound's Tables of mean Conjunctions.

The Common Lunar Year consists of 12 such Months.

The Intercalary or Embolimæan Year consists of 13 such Months.

In each Cycle of 19 Lunar Years, there are 12 Common, and 7 Intercalary or Embolimæan Years, making together 235 Synodical Months.