_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. _Being Part of a Letter from the Right Honourable_ George _Earl of_ Macclesfield _to_ Martin Folkes _Esq_; President _of the_ Royal Society. _Of the_ Solar Year. [_Read_ May 10. 1750.] 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 365d, 5h, 48´, 55´´: Which is less by 11´, 5´´, than the mean _Julian_ Year, consisting of 365d, 6h, 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 3d, 1h, 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 1h, 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 29d, 12h, 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.