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

Thus in a very easy Method may the Course of the New Moons be pointed out, either by the Golden Numbers, or by the Epacts, according to the Julian Account or Manner of adjusting the Year, which goes on regular and uniform without any Variation.

But the regulating these things for those who use the Gregorian Account, is an Affair of more Intricacy; and for them it will require more Consideration to determine, when the Epacts are to be more than ordinarily augmented, and at what Times they are to continue in their usual Course; nay, to know when they are not only not to be extraordinarily augmented, but also when they are to be diminished by an Unit, by increasing one of them by 10 only instead of 11 as usual: and this happens much oftener with the Gregorians, than the increasing one of them by 12 instead of 11. For, in every Gregorian Solar Year, whose Date consists of any Number of entire Hundreds not divisible by 4, it is supposed that the Equinox has anticipated one whole Day; and therefore one Day, that which ought to be the intercalary one, is omitted; and consequently the preceding Solar Year, where one Day was lost, exceeded the Lunar Year by 10 Days only instead of 11.

In order therefore to adapt the before-mention'd Rule to the Gregorian Account, and to know in what Years the Epacts should either be extraordinarily augmented or diminished, and the Golden Numbers should either be set backwards or forwards in the Calendar; the following Rules and Directions must be observed.

First. That in the Years 1800, 2100, 2700, 3000, &c. where the Number of entire Hundreds is divisible by 3, but not by 4, the Gregorian Solar, as well as the Lunar Year, will have lost a Day; and consequently the Difference betwixt them will be the same as usual: Therefore in those Years there must be no Alteration, either in the Epacts or the Golden Numbers; but the former must go on in the same manner, and the latter stand prefixed to the same Days in the Calendar, for another, as they did for the last hundred Years.

2dly. The like will happen in the Years 2000, 2800, 3200, &c. where the Number of entire Hundreds is divisible by 4, but not by 3: For neither the Gregorian Solar nor the Lunar Year is to be altered; and therefore the Epacts must go on, and the Golden Numbers stand, as they did before.

But, 3dly, In the Years 2400, and 3600, whose Number of entire Hundreds is divisible both by 3 and 4, the Gregorian Solar Year goes on as usual, and the Lunar Year has lost a Day. The Difference therefore betwixt them being 12, the Epact of the preceding Year must be augmented by that Number instead of 11, in order to form the Epact of the then present Year; whereby a new Set of Epacts will be introduced, exceeding their precedent corresponding Epacts by an Unit: And the Golden Numbers must be set one Day back in the Calendar.

4thly and lastly, In the Years 1900, 2200, 2300, 2500, &c. where the Number of Hundreds is divisible neither by 3 nor 4; the Gregorian Solar Year having lost one Day, and the Lunar none, the Difference betwixt them being only 10; that Number only, and not 11, is to be added to the Epact of the preceding, in order to form the Epact of that, the then present Year; whereby a new Set of Epacts will be introduced, all of them less by an Unit than their precedent corresponding Epacts: And the Golden Numbers must be set a Day forwarder in the Calendar; that is, be prefixed to the Day following that, against which they stood in the precedent hundred Years.

This Method would preserve a sort of Regularity betwixt the Solar and the Lunar Years; and, by means of the Rules and Directions before-mentioned, the Days of the New Moons might be pointed out, either by the Golden Numbers or by the Epacts, placed in the Calendar for that Purpose; according to the Julian Account for ever, and according to the Gregorian Account till the Year 4199 inclusive, after which there must be some little Variation made in the four last Precepts or Rules, but it would be to little Purpose now, to attempt the framing of a new Set of Rules for so distant a Time.

The Gregorians have chosen to make use of the Epacts to determine the Days of the New Moons, and follow pretty nearly the Rules prescribed above; except that they order the Epacts to have an additional Augmentation of an Unit eight times in 2500 Years, beginning with the Year 1800, as at the End of 400 Years; to which 400 Years if there be added three times seven hundred, or 2100 Years, the Period of 2500 Years will be completed in the Year 3900. After which they do not make their extraordinary Augmentation of an Unit in the Epacts, till at the End of another Term of 400 Years; which defers that Augmentation from the Year 4200 to the Year 4300. And this is the Reason that the Rules above delivered will require a Variation in the Year 4200; whereas it is directed in this Paper that the Epacts should be augmented, or (which is the same thing) the Golden Numbers be set back in the Calendar nine times in 2800 Years. This arises from the Gregorians supposing, that the Difference betwixt 19 Solar and as many Lunar Years would not amount to a whole Day in less than 312 Years and a half; whereas it has appeared above, that it would amount to a whole Day in 310.7 Years. But although the Rule prescribed in this Paper comes much nearer to the Truth, yet the Error in either Case is very inconsiderable, being so small as not to amount to a whole Day in many thousand Years; and therefore is not worth regarding.