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diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..d7b82bc --- /dev/null +++ b/.gitattributes @@ -0,0 +1,4 @@ +*.txt text eol=lf +*.htm text eol=lf +*.html text eol=lf +*.md text eol=lf diff --git a/LICENSE.txt b/LICENSE.txt new file mode 100644 index 0000000..6312041 --- /dev/null +++ b/LICENSE.txt @@ -0,0 +1,11 @@ +This eBook, including all associated images, markup, improvements, +metadata, and any other content or labor, has been confirmed to be +in the PUBLIC DOMAIN IN THE UNITED STATES. + +Procedures for determining public domain status are described in +the "Copyright How-To" at https://www.gutenberg.org. + +No investigation has been made concerning possible copyrights in +jurisdictions other than the United States. Anyone seeking to utilize +this eBook outside of the United States should confirm copyright +status under the laws that apply to them. diff --git a/README.md b/README.md new file mode 100644 index 0000000..8b3c9eb --- /dev/null +++ b/README.md @@ -0,0 +1,2 @@ +Project Gutenberg (https://www.gutenberg.org) public repository for +eBook #62764 (https://www.gutenberg.org/ebooks/62764) diff --git a/old/62764-8.txt b/old/62764-8.txt deleted file mode 100644 index d70919c..0000000 --- a/old/62764-8.txt +++ /dev/null @@ -1,1055 +0,0 @@ -The Project Gutenberg EBook of 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 George Parker - -This eBook is for the use of anyone anywhere in the United States and most -other parts of the world at no cost and with almost no restrictions -whatsoever. You may copy it, give it away or re-use it under the terms of -the Project Gutenberg License included with this eBook or online at -www.gutenberg.org. If you are not located in the United States, you'll have -to check the laws of the country where you are located before using this ebook. - -Title: 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 - -Author: George Parker - -Release Date: July 26, 2020 [EBook #62764] - -Language: English - -Character set encoding: ISO-8859-1 - -*** START OF THIS PROJECT GUTENBERG EBOOK REMARKS UPON SOLAR AND LUNAR YEARS *** - - - - -Produced by MWS, Eleni Christofaki and the Online -Distributed Proofreading Team at https://www.pgdp.net (This -file was produced from images generously made available -by The Internet Archive) - - - - - - - - - -Transcriber's note - -A list of the changes made can be found at the end of the book. -Formatting and special characters are indicated as follows: - - _italic_ - =bold= - +gesperrt+ - - - - - =+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_, - - and by him communicated to the same, - _May_ 10. 1750. - - _LONDON_: - - Printed for CHARLES DAVIS, Printer to the - _Royal Society_. - M.DCC.LI. - - - - -A TABLE, shewing, by means of the Golden Numbers, the several Days on -which the Paschal Limits or Full Moons, according to the _Gregorian_ -Account, have already happened, or will hereafter happen; from the -Reformation of the Calendar in the Year of our Lord 1582, to the Year -4199 inclusive. - -To find the Day on which the Paschal Limit or Full Moon falls in any -given Year; Look, in the Column of Golden Numbers belonging to that -Period of Time wherein the given Year is contained, for the Golden -Number of that Year; over-against which, in the same Line continued to -the Column intitled _Paschal Full Moons_, you will find the Day of the -Month, on which the Paschal Limit or Full Moon happens in that Year. -And the _Sunday_ next after that Day is _Easter_ Day in that Year, -according to the _Gregorian_ Account. - - +-----------------------------------------------------------+ - |Golden Numbers from the Year 1583 to 1699, and so on to | - | 4199, all inclusive. | - +----+----+----+----+----+----+----+----+----+----+----+----+ - |1583|1700|1900|2200|2300|2400|2500|2600|2900|3100|3400|3500| - | to | to | to | to | to | to | to | to | to | to | to | to | - |1699|1899|2199|2299|2399|2499|2599|2899|3099|3399|3499|3599| - +----+----+----+----+----+----+----+----+----+----+----+----+ - | 3 | 14 | .. | 6 | 17 | 6 | 17 | .. | 9 | .. | 1 | 12 | - | .. | 3 | 14 | .. | 6 | .. | 6 | 17 | .. | 9 | .. | 1 | - | 11 | .. | 3 | 14 | .. | 14 | .. | 6 | 17 | .. | 9 | .. | - | .. | 11 | .. | 3 | 14 | 3 | 14 | .. | 6 | 17 | .. | 9 | - | 19 | .. | 11 | .. | 3 | .. | 3 | 14 | .. | 6 | 17 | .. | - | 8 | 19 | .. | 11 | .. | 11 | .. | 3 | 14 | .. | 6 | 17 | - | .. | 8 | 19 | .. | 11 | .. | 11 | .. | 3 | 14 | .. | 6 | - | 16 | .. | 8 | 19 | .. | 19 | .. | 11 | .. | 3 | 14 | .. | - | 5 | 16 | .. | 8 | 19 | 8 | 19 | .. | 11 | .. | 3 | 14 | - | .. | 5 | 16 | .. | 8 | .. | 8 | 19 | .. | 11 | .. | 3 | - | 13 | .. | 5 | 16 | .. | 16 | .. | 8 | 19 | .. | 11 | .. | - | 2 | 13 | .. | 5 | 16 | 5 | 16 | .. | 8 | 19 | .. | 11 | - | .. | 2 | 13 | .. | 5 | .. | 5 | 16 | .. | 8 | 19 | .. | - | 10 | .. | 2 | 13 | .. | 13 | .. | 5 | 16 | .. | 8 | 19 | - | .. | 10 | .. | 2 | 13 | 2 | 13 | .. | 5 | 16 | .. | 8 | - | 18 | .. | 10 | .. | 2 | .. | 2 | 13 | .. | 5 | 16 | .. | - | 7 | 18 | .. | 10 | .. | 10 | .. | 2 | 13 | .. | 5 | 16 | - | .. | 7 | 18 | .. | 10 | .. | 10 | .. | 2 | 13 | .. | 5 | - | 15 | .. | 7 | 18 | .. | 18 | .. | 10 | .. | 2 | 13 | .. | - | 4 | 15 | .. | 7 | 18 | 7 | 18 | .. | 10 | .. | 2 | 13 | - | .. | 4 | 15 | .. | 7 | .. | 7 | 18 | .. | 10 | .. | 2 | - | 12 | .. | 4 | 15 | .. | 15 | .. | 7 | 18 | .. | 10 | .. | - | 1 | 12 | .. | 4 | 15 | 4 | 15 | .. | 7 | 18 | .. | 10 | - | .. | 1 | 12 | .. | 4 | .. | 4 | 15 | .. | 7 | 18 | .. | - | 9 | .. | 1 | 12 | .. | 12 | .. | 4 | 15 | .. | 7 | 18 | - | .. | 9 | .. | 1 | 12 | 1 | 12 | .. | 4 | 15 | .. | 7 | - | 17 | .. | 9 | .. | 1 | .. | 1 | 12 | .. | 4 | 15 | .. | - | 6 | 17 | 17 | 9 | .. | 9 | .. | 1 | 12 | 12 | 4 | 15 | - | 14 | 6 | 6 | 17 | 9 | 17 | 9 | 9 | 1 | 1 | 12 | 4 | - | | | | | | | | | | | | | - +----+----+----+----+----+----+----+----+----+----+----+----+ - - +---------------------------------------------------------+ - |Golden Numbers from the Year 1583 to 1699,| Paschal | - |and so on to 4199, all inclusive. | Full Moons. | - +----+----+----+----+----------------------+--------------+ - |3600|3700|3800|4100| Days of the | - | to | to | to | to | Month, and | - |3699|3799|4099|4199| Sunday Letters| - +----+----+----+----+----------------------+--------------+ - | 1 | 12 | .. | 4 | March 21. C | - | .. | 1 | 12 | .. | 22. D | - | 9 | .. | 1 | 12 | 23. E | - | .. | 9 | .. | 1 | 24. F | - | 17 | .. | 9 | .. | 25. G | - | 6 | 17 | .. | 9 | 26. A | - | .. | 6 | 17 | .. | 27. B | - | 14 | .. | 6 | 17 | 28. C | - | 3 | 14 | .. | 6 | 29. D | - | .. | 3 | 14 | .. | 30. E | - | 11 | .. | 3 | 14 | 31. F | - | .. | 11 | .. | 3 | April 1. G | - | 19 | .. | 11 | .. | 2. A | - | 8 | 19 | .. | 11 | 3. B | - | .. | 8 | 19 | .. | 4. C | - | 16 | .. | 8 | 19 | 5. D | - | 5 | 16 | .. | 8 | 6. E | - | .. | 5 | 16 | .. | 7. F | - | 13 | .. | 5 | 16 | 8. G | - | 2 | 13 | .. | 5 | 9. A | - | .. | 2 | 13 | .. | 10. B | - | 10 | .. | 2 | 13 | 11. C | - | .. | 10 | .. | 2 | 12. D | - | 18 | .. | 10 | .. | 13. E | - | 7 | 18 | .. | 10 | 14. F | - | .. | 7 | 18 | .. | 15. G | - | 15 | .. | 7 | 18 | 16. A | - | 4 | 15 | 15 | 7 | 17. B | - | 12 | 4 | 4 | 15 | 18. C | - | | | | | 19. D | - | | | | | 20. E | - | | | | | 21. F | - | | | | | 22. G | - | | | | | 23. A | - | | | | | 24. B | - | | | | | 25. C | - +----+----+----+----+-------------------------------------+ - - - - - _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. - -It was thought, at the time of the General Council of _Nice_, which was -holden in the Year of our Lord 325, that 19 _Julian_ Solar Years were -exactly equal to such a Cycle of 19 Lunar Years, or to 235 Synodical -Months; and therefore, that, at the End of 19 Years, the New Moons -or Conjunctions would happen exactly at the same Times, as they did -19 Years before: And upon this Supposition it was, that, some time -afterwards, the several Numbers of that Cycle, commonly called the -Golden Numbers, were prefixed to all those Days in the Calendar, on -which the New Moons then happened in the respective Years corresponding -to those Numbers; it being imagined, that whensoever any of those -Numbers should for the future be the Golden Number of the Year, the New -Moons would invariably happen on those Days in the several Months, to -which that Number was prefixed. - -But this was a Mistake: - - d h ´ ´´ ´´´ - For 19 _Julian_ Solar Years contain 6939, 18, 0, 0, 0 - Whereas 235 Synodical Months - contain only 6939, 16, 31, 56, 30 - ---------------------- - And are therefore less than 19 - _Julian_ Solar Years by 0, 1, 28, 3, 30. - -This Difference amounts to a whole Day very nearly in 310.7 Years, the -New Moons anticipating, or falling earlier, by 24 Hours in that Space -of Time, than they did before: And therefore now in the Year 1750, the -New Moons happen above four Days and a half sooner, than the Times -pointed out by the Golden Numbers in the Calendar. - -In order therefore to preserve a sort of regular Correspondence betwixt -the Solar and the Lunar Years, and to make the Golden Numbers, prefixed -to the Days of the Month, useful for determining the Times of the New -Moons, it would be necessary, when once those Golden Numbers should -have been prefixed to the proper Days, to make them anticipate a Day -at the End of every 310.7 Years, as the Moons will actually have done; -that is to set them back one Day, by prefixing each of them to the Day -preceding that, against which they before stood. - -But as such a Rule would neither be so easily comprehended or retained -in Memory, as if the Alteration was to be made at the End or at the -Beginning of complete Centuries of Years; the Rule would be much more -fit for Practice, and keep sufficiently near to the Truth, if those -Numbers should be set back nine Days in the Space of 2800 Years; by -setting them back one Day, first at the End of 400 Years, and then at -the End of every 300 Years for eight times successively: whereby they -would be set back, in the whole, nine Days in 2800 Years. After which -they must again be set one Day back at the End of 400 Years, and so on, -as in the preceding 2800 Years. By which means the Golden Numbers would -always point out the mean Times of the New Moons, within a Day of the -Truth. - -It is plain however that the Lunar Year will have lost one Day more -than ordinary, with respect to the Solar Year, whenever the New Moons -shall have anticipated a whole Day; as they will have done at those -times, when it is necessary that the Golden Numbers should, by the -Rule just now given, be set back one Day: and consequently the Epact, -for that and the succeeding Years, must exceed by an Unit the several -corresponding Epacts of the preceding 19 Years. - -For the Epact is the Difference, in whole Days, betwixt the common -_Julian_ Solar and the Lunar Year; the former being reckoned to consist -of 365, and the latter of only 354 Days. If therefore the Solar and -the Lunar Year at any time should commence on the same Day, the Solar -would, at the End of the Year, have exceeded the Lunar by 11 Days; -which Number 11 would be the Epact of the next Year: 22 would be -the Epact of the Year following, and 33 the Epact of the Year after -that, the Epacts increasing yearly by 11. But as often as this yearly -Addition makes the Epact exceed 30, those 30 are rejected as making -an intercalary Month, and only the Excess of the Epact above 30 is -accounted the true Epact for that Year. Thus when the Epact would -amount to 31, 32, 33, 34, _&c._ the 30 is rejected, and the Epact -becomes 1, 2, 3, 4, _&c._ - -Since therefore the Lunar Year will have lost a Day more than ordinary, -in respect of the Solar Year, whenever it is necessary to set the -Golden Numbers one Day back, as was before observed; it follows, that -the Epact must at the same time be increased by an Unit more than -usual: the Difference betwixt the Solar and the Lunar Year having been -just so much greater than usual. That is, 12 must be added, instead of -11, to the Epact of the preceding, in order to form what will be the -Epact of the then present Year. Which Addition of an Unit extraordinary -to one Epact will occasion all the subsequent Epacts (which will follow -each other in the usual manner, each exceeding the foregoing by 11) to -be greater by an Unit than their respectively corresponding Epacts of -the preceding 19 Years. - -If therefore, instead of the Golden Numbers, the Epacts of the several -Years were prefixed, in the manner the _Gregorians_ have done, to the -Days of the Calendar, in order to denote the Days on which the New -Moons fall in those Years whereof those Numbers are the Epacts; there -would never be Occasion to shift the Places of those Epacts in the -Calendar; since the Augmentation by an Unit extraordinary of the Epacts -themselves would answer the Purpose, and keep all tolerably right. - -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. - - - - -_A Method of finding the Time of_ Easter, _as it is observed in most -Parts of_ Europe. - - -From what has been already said, a Method may be obtained, for fixing, -with sufficient Exactness, the Time of the Celebration of the Feast -of _Easter_, which is governed by the _Vernal Equinox_, and by the -Age of the Moon nearest to it. The former whereof, when once rightly -adjusted, may (by the Corrections mentioned in that Part of this Paper -which relates to the Solar Year) be made to continue to fall at very -near the same time with, or at most not to differ a whole Day from the -true _Equinox_: and the same Rules and Directions, which, as was before -shewn, would, without any great Error, point out the Times of the first -Day of the Moon, would with equal Certainty point out the fourteenth, -fifteenth, or any other: And thus the Times of the Oppositions or -the Full Moons might be as well marked out thereby, as those of the -Conjunctions or the New Moons. - -I shall not at present take notice of the Canon of the Council of -_Nice_, in the Year of our Lord 325, which directs the Time of -celebrating the Feast of _Easter_, or of the Reasons upon which that -Canon was founded. Nor shall I endeavour to explain the Rule now in -Use in the Church of _England_ for finding _Easter_: For, besides that -such an Explanation would extend this Paper to an improper Length, -those Points have already been treated of by several much abler -Hands, and particularly by our Countryman the learned Dr. _Prideaux_. -Nor is it my Intention to enter far into the Methods used by the -_Gregorians_, or those of the Church of _Rome_, or by any other Nations -or Countries, for finding the Time of that Feast. As to our own, I -shall only observe, that the Method now used in _England_, for finding -the fourteenth Day of the Moon, or the Ecclesiastical Full Moon, on -which _Easter_ dependeth, is, by Process of Time, become considerably -erroneous: as the Golden Numbers, which were placed in the Calendar, to -point out the Days on which the New Moons fall in those Years of which -they are respectively the Golden Numbers, do now stand several Days -later in the same than those New Moons do really happen. Which Error, -as was before observed, arises from the Anticipation of the Moons since -the Time of the Council of _Nice_: And as the _Vernal Equinox_ has also -anticipated eleven Days since that time; neither that Equinox, nor -the New Moons, do now happen on those Days upon which the Church of -_England_ supposes them so to happen. - -When Pope _Gregory_ XIII. reformed the _Julian_ Solar Year, he likewise -made a Correction as to the Time of celebrating the Feast of _Easter_, -by placing the Epacts (which he directed to be made use of for the -future instead of the Golden Numbers) much nearer to the true Times of -the New Moons than the Golden Numbers then stood in the old Calendar: -I say, _much nearer to the true Times_; because in fact the Epacts, as -placed by him, were not prefixed to the exact Days upon which the New -Moons then truly fell. And this was done with Design, and for a Reason -which it is not material to the Purpose of this Paper to mention. - -But the Church of _England_, and that of _Rome_ or the _Gregorians_, do -still agree in this; that both of them mark (the former by the Golden -Numbers, and the latter by the Epacts corresponding to them) the Days -on which their Ecclesiastical New Moons are supposed to happen: And -that fourteenth Day of the Moon inclusive, or that Full Moon, which -falls upon, or next after, the 21st Day of _March_, is the Paschal -Limit or Full Moon to both: And the _Sunday_ next following that Limit -or Full Moon, is by both Churches celebrated as _Easter_ Day. But the -21st of _March_ being reckoned, according to the _Gregorian_ Account or -the New Style, eleven Days sooner than by the _Julian_ Account or the -Old Style, which is still in Use amongst us; and their Ecclesiastical -New Moons being three Days earlier than those of the Church of -_England_; it happens that although the Church of _England_ and that of -_Rome_ often do, yet more frequently they do not, celebrate the Feast -of _Easter_ upon the same natural Day. - -It might however be easier for both, and could occasion no -Inconvenience, now that Almanacks, which tell the exact Times of the -New Moons, are in most Peoples Hands; if all the Golden Numbers and -Epacts now prefixed to those Days of the Calendar, in our Book of -Common Prayer, and in the _Roman Breviary_, on which the respective -Ecclesiastical New Moons happen, were omitted in the Places where they -now stand; and were set only against those fourteenth Days of the Moon, -or those Full Moons, which happen betwixt the 21st Day of _March_ and -the 18th of _April_, both inclusive. Since no fourteenth Day or Full -Moon, which happens before the 21st of _March_, or after the 18th Day -of _April_, can have any Share in fixing the Time of _Easter_. By which -means the Trouble of counting to the fourteenth Day, and the Mistakes -which sometimes arise therefrom, would be avoided. - -We do as yet in _England_ follow the _Julian_ Account or the Old Style -in the Civil Year; as also the Old Method of finding those Moons upon -which _Easter_ depends: Both of which have been shewn to be very -erroneous. - -If therefore this Nation should ever judge it proper to correct the -Civil Year, and to make it conformable to that of the _Gregorians_, it -would surely be adviseable to correct the Time of the Celebration of -the Feast of _Easter_ likewise, and to bring it to the same Day upon -which it is kept and solemnized by the Inhabitants of the greatest Part -of _Europe_, that is, by those who follow the _Gregorian_ Account. For -tho' I am aware, that their Method of finding the Time of _Easter_ is -not quite exact, but is liable to some Errors; yet I apprehend, that -all other practicable Methods of doing it would be so too: And if they -were more free from Error, they would probably be more intricate, -and harder to be understood by Numbers of People, than the Method of -determining that Feast either by a Cycle of Epacts, as is practiced by -the _Gregorians_, or by that of 19 Years or the Golden Numbers, in the -manner proposed in the following Part of this Paper: And it is of no -small Importance, that a Matter of so general a Concern, as the Method -of finding _Easter_ is, should be within the Reach of the Generality of -Mankind, at least as far as the Nature of the thing will admit. - -For which Reason, in case the Legislature of this Country should before -the Year 1900, think fit to make our Civil Year correspond with that -of the _Gregorians_, and also to celebrate all the future Feasts of -_Easter_ upon the same Days upon which they celebrate them; this last -Particular might be easily effected, without altering the Rule of the -Church of _England_ for the finding of that Feast: And this only by -advancing the Golden Numbers, prefixed to certain Days in the Calendar, -8 Days forwarder for the New Moons, or 21 Days forwarder for the -fourteenth Days or Full Moons, than they now stand in our Calendar. - -In order to explain this, it must be observed, that the _Gregorian_ -Account or the New Style is eleven Days forwarder than the _Julian_ -Account or the Old Style, which we still make use of; that is, the last -Day of any of our Months is the eleventh Day of their next succeeding -Month. If therefore their Ecclesiastical New Moons fell on the same -Days with those of the Church of _England_, the Golden Number 14, -which now stands against the last Day of _February_ in our that is the -_Julian_ Calendar, should, when we should have adopted the _Gregorian_ -Calendar, be prefixed to the 11th Day of _March_. But since their -Ecclesiastical New Moons happen 3 Days earlier than our Ecclesiastical -New Moons at present do; so much should be deducted from those 11 Days, -by which the Golden Numbers ought otherwise to be advanced; and the -Golden Number 14 should not be placed against the 11th, but the 8th Day -of _March_: Which being reckoned the first Day of the Moon, if we count -on to the fourteenth Day of the same inclusive, that would be found -to fall on the a 21st Day of _March_; on which Day the _Gregorian_ -Paschal Limit or Full Moon will happen when the Golden Number is 14. -And the like Course should be taken with the rest of the 19 Golden -Numbers; which ought to be placed 8 Days forwarder than they now stand, -if they are to point out the New Moon; or 21 Days forwarder than they -are at present, if they are to mark the fourteenth Day of the Moon or -the Full Moon: The latter of which, as has been shewn, would be more -eligible, than to prefix those Numbers to the Days on which the New -Moons happen. - -Thus may the Rule and Method now used in the Church of _England_, be -most easily adapted to shew the Time of _Easter_, as it is observed by -the _Gregorians_, till the Year 1900; at which Time, and at the other -proper succeeding Times, if the Golden Numbers in the Calendar shall -either be advanced or set backward a Day, according the foregoing Rules -and Directions for that Purpose, they will continue to shew us the New -or the Full Moons, of the Church of _Rome_ or the _Gregorian_ Calendar -with great Exactness, till the Year 4199: when, as has been already -mentioned, there must be a little Variation made in those Rules and -Directions. - -There is however one Exception to those General Rules and Directions, -which will be taken notice of in the next Paragraph. - -Upon these Principles I framed the Table accompanying this Paper, -and shewing, by means of the Golden Numbers, all the _Gregorian_ -Paschal Limits or Full Moons, from the Reformation of the Calendar, -_&c._ by Pope _Gregory_ to the Year 4199 inclusive. Which Space of -Time is therein divided into sixteen unequal Portions or Periods; at -the Beginning of each of which, all the Golden Numbers, when once -they shall have been properly placed in the Calendar, must either be -advanced or set back one Day, with respect to the Place where they -stood in the preceding Period, agreeably to the foregoing Rules: Except -those Numbers which shall happen to stand against the 4th and 5th of -_April_ to shew the Paschal New Moons, or against the 17th and 18th of -the same Month to mark out the Paschal Full Moons; both which Numbers -at some Times, and only one of them at others, must keep the same Place -for that, which was allotted to them in the immediately preceding -Period. - -In order to determine at what Times, and on what Occasions, this -Exception is to take Place; let it be observed, that, in the Months of -_January_, _March_, _May_, and some others in our present Calendar, -as well as in the Table above mentioned, some of the Golden Numbers -stand double or in Pairs, and follow one the other immediately; whilst -others, on the contrary, generally stand single and by themselves. - -Now, when any of those Pairs, or two Numbers which usually accompany -each other, happen, in pursuance of the foregoing Rules, to be prefixed -the one to the 4th and the other to the 5th of _April_ for the New -Moons, or the one to the 17th and the other to the 18th of _April_ -for the Paschal Limits or Full Moons: And when any of those Numbers, -which generally stand single, are prefixed, according to the said -Rules, to the 5th of _April_ for the New Moons, or to the 18th for the -Full Moons: In these Cases those Pairs or single Numbers that are so -situated; must not be set forward or advanced at the Beginning of the -next Period, but must keep their Places during another Period, if the -foregoing Rules direct all the Golden Numbers to be advanced a Day; -which must be complied with in respect to all the other Golden Numbers, -except those so situated as above. Instances whereof may be seen in -the Table, under the respective Periods beginning with the Years 1900, -2600, 3100, and 3800. - -But if, in Conformity to the foregoing Rules, all the Golden Numbers -are to be set one Day backward; those Pairs or single Numbers, tho' -situated as is above-mentioned, must not keep their Places, but must -move one Day backward like all the other Golden Numbers; as they may be -seen to do in the Periods beginning with the Years 2400 and 3600. - -To give a plain and intelligible Account of the Reason, on which the -Directions now given with respect to this Exception are founded, -would extend this Paper, already too long, far beyond its due and -proper Bounds. I shall therefore content myself with observing, that -it depends chiefly upon the Nature of the _Menses Pleni_ and _Menses -Cavi_, into which the Lunar Year is usually divided: and that, in -order to make use of the Golden Numbers for finding the Time of the -_Gregorian Easter_, it will be necessary not only to conform to -the general Rules laid down in the former Part of this Paper; but -also to follow the Directions just now given, with respect to the -above-mentioned Exception to those general Rules. - -But I should not do Justice to _Peter Davall_ of the _Middle Temple_, -Esq; Secretary of the _Royal Society_, did I not here acknowledge, -that, before I had so fully considered these Matters as I have since -done, I had the first Hint of applying the Golden Numbers to find the -_Gregorian_ Paschal Limit or full Moon, from him; who has since that -time composed and drawn up Tables, _&c._ which may possibly be of -considerable and general Use in this Nation hereafter. - - -_FINIS._ - - - - -Transcriber's Note - -Variable spelling and hyphenation have been retained. Minor punctuation -inconsistencies have been silently repaired. - -Corrections. - -The first line indicates the original, the second the correction. - -p. 7 - - what Years the Epacts should either be extraordinariy - what Years the Epacts should either be extraordinarily - - - - - -End of the Project Gutenberg EBook of 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 George Parker - -*** END OF THIS PROJECT GUTENBERG EBOOK REMARKS UPON SOLAR AND LUNAR YEARS *** - -***** This file should be named 62764-8.txt or 62764-8.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/6/2/7/6/62764/ - -Produced by MWS, Eleni Christofaki and the Online -Distributed Proofreading Team at https://www.pgdp.net (This -file was produced from images generously made available -by The Internet Archive) - -Updated editions will replace the previous one--the old editions will -be renamed. - -Creating the works from print editions not protected by U.S. copyright -law means that no one owns a United States copyright in these works, -so the Foundation (and you!) can copy and distribute it in the United -States without permission and without paying copyright -royalties. 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You may copy it, give it away or re-use it under the terms of -the Project Gutenberg License included with this eBook or online at -www.gutenberg.org. If you are not located in the United States, you'll have -to check the laws of the country where you are located before using this ebook. - -Title: 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 - -Author: George Parker - -Release Date: July 26, 2020 [EBook #62764] - -Language: English - -Character set encoding: ISO-8859-1 - -*** START OF THIS PROJECT GUTENBERG EBOOK REMARKS UPON SOLAR AND LUNAR YEARS *** - - - - -Produced by MWS, Eleni Christofaki and the Online -Distributed Proofreading Team at https://www.pgdp.net (This -file was produced from images generously made available -by The Internet Archive) - - - - - - -</pre> - -<div class="transnote"><h3>Transcriber's note</h3> - -<p>A <a href="#Transcribers_Note">list</a> of the changes made can be found at the end of the book.</p></div> -<hr class="chap" /> -<h1>REMARKS<br /> <small>UPON</small><br /> -<small>THE SOLAR AND THE LUNAR YEARS</small>,<br /> The Cycle of 19 Years, commonly called -<br /> -THE GOLDEN NUMBER, -<br /> -THE EPACT, -<br /> -And a Method of finding the Time of<br /> -<i>Easter</i>, as it is now observed in most<br /> -Parts of <i>Europe</i>.</h1> - -<hr class="chap" /> -<div class="figcenter"> -<img src="images/titlepage.jpg" width="600" height="800" alt="" /> -</div> -<hr class="chap" /> -<p class="center"><big><strong><em class="gesperrt">REMARKS</em></strong></big> -<br /> -<small><em class="gesperrt">UPON</em></small> -<br /> -<small>THE SOLAR AND THE LUNAR YEARS,</small> -<br /> -The Cycle of 19 Years, commonly called -<br /> -<em class="gesperrt">THE GOLDEN NUMBER</em>, -<br /> -<em class="gesperrt">THE EPACT</em>, -<br /><br /> -And a Method of finding the Time of<br /> -<i>Easter</i>, as it is now observed in most<br /> -Parts of <i>Europe</i>.</p> - -<p class="center p2">Being Part of a LETTER from -<br /><br /> -The Right Honourable -<br /><br /> -GEORGE EARL OF MACCLESFIELD -<br /><br /> -to -<br /><br /> -<i>Martin Folkes</i> Esq; <i>President</i> of the <i>Royal Society</i>, -<br /><br /> -and by him communicated to the same,<br /> -<i>May</i> 10. 1750.</p> - -<p class="center p2"><i>LONDON</i>: -<br /> -Printed for <span class="smcap">Charles Davis</span>, Printer to the -<i>Royal Society</i>.</p> -<p class="center">M.DCC.LI. -</p> -<hr class="chap" /> -<div class="bbox"> -<p class="hang">A TABLE, shewing, by means of the Golden Numbers, the several Days on which the -Paschal Limits or Full Moons, according to the <i>Gregorian</i> Account, have already happened, -or will hereafter happen; from the Reformation of the Calendar in the Year of -our Lord 1582, to the Year 4199 inclusive.</p> - -<p class="hang">To find the Day on which the Paschal Limit or Full Moon falls in any given Year; Look, in the -Column of Golden Numbers belonging to that Period of Time wherein the given Year is contained, -for the Golden Number of that Year; over-against which, in the same Line continued to the Column -intitled <i>Paschal Full Moons</i>, you will find the Day of the Month, on which the Paschal Limit or Full -Moon happens in that Year. And the <i>Sunday</i> next after that Day is <i>Easter</i> Day in that Year, according -to the <i>Gregorian</i> Account.</p> </div> - -<table id="golden" summary="numbers"> - -<tr><td colspan="16" class="bt bb">Golden Numbers from the Year 1583 to 1699, and so on to 4199, all inclusive.</td> -<td class="bt bb">Paschal <br /> Full Moons. </td> </tr> - -<tr><td class="bb bt center">1583 - to -1699</td> - -<td class="bb bt center">1700 - to -1699</td> - -<td class="bb bt center">1900 - to -2199</td> - -<td class="bb bt center">2200 - to -2299</td> - -<td class="bb bt center">2300 - to -2399</td> - -<td class="bb bt center">2400 - to -2499</td> - -<td class="bb bt center">2500 - to -2599</td> - -<td class="bb bt center">2600 - to -2899</td> - -<td class="bb bt center">2900 - to -3099</td> - -<td class="bb bt center">3100 - to -3399</td> - -<td class="bb bt center">3400 - to -3499</td> - -<td class="bb bt center">3500 - to -3599</td> - -<td class="bb bt center">3600 - to -3699</td> - -<td class="bb bt center">3700 - to -3799</td> - -<td class="bb bt center">3800 - to -4099</td> - -<td class="bb bt center">4100 - to -4199</td> - - <td class="bb bt">Days of the - Month, and -Sunday Letters</td></tr> - -<tr> <td class="tdr">3</td> - <td class="tdr">14</td> -<td class="tdr">..</td> - <td class="tdr">6</td> -<td class="tdr">17</td> - <td class="tdr">6</td> -<td class="tdr">17</td> -<td class="tdr">..</td> - <td class="tdr">9</td> -<td class="tdr">..</td> - <td class="tdr">1</td> - <td class="tdr">12</td> - <td class="tdr">1</td> -<td class="tdr">12</td> - -<td class="tdr">..</td> -<td class="tdr">4</td> - <td class="tdr">March 21. C </td></tr> - - <tr><td class="tdr">..</td> -<td class="tdr">3</td> - <td class="tdr">14</td> -<td class="tdr">..</td> -<td class="tdr">6</td> -<td class="tdr">..</td> <td class="tdr">6</td> -<td class="tdr">17</td> -<td class="tdr">..</td> -<td class="tdr">9</td> -<td class="tdr">..</td> <td class="tdr">1</td> <td class="tdr">..</td> <td class="tdr">1</td> - <td class="tdr">12</td> - <td class="tdr">..</td> - <td class="tdr">22. D </td></tr> - <tr><td class="tdr">11</td> -<td class="tdr">..</td> <td class="tdr">3</td> <td class="tdr">14</td> -<td class="tdr">..</td> <td class="tdr">14</td> -<td class="tdr">..</td> <td class="tdr">6</td> <td class="tdr">17</td> -<td class="tdr">..</td> <td class="tdr">9</td> -<td class="tdr">..</td> <td class="tdr">9</td> - <td class="tdr">..</td> <td class="tdr">1</td> <td class="tdr">12</td> - <td class="tdr">23. E </td> </tr> -<tr> <td class="tdr">..</td> <td class="tdr">11</td> - <td class="tdr">..</td> <td class="tdr">3</td> <td class="tdr">14</td> - <td class="tdr">3</td> <td class="tdr">14</td> -<td class="tdr">..</td> <td class="tdr">6</td> <td class="tdr">17</td> -<td class="tdr">..</td> <td class="tdr">9</td> -<td class="tdr">..</td> <td class="tdr">9</td> -<td class="tdr">..</td> <td class="tdr">1</td> - <td class="tdr">24. F </td></tr> -<tr> <td class="tdr">19</td> -<td class="tdr">..</td> <td class="tdr">11</td> - <td class="tdr">..</td> <td class="tdr">3</td> -<td class="tdr">..</td> <td class="tdr">3</td> -<td class="tdr">14</td> - <td class="tdr">..</td> <td class="tdr">6</td> <td class="tdr">17</td> - <td class="tdr">..</td> <td class="tdr">17</td> -<td class="tdr">..</td> <td class="tdr">9</td> - <td class="tdr">..</td> - <td class="tdr">25. G </td> </tr> - <tr> <td class="tdr">8</td> <td class="tdr">19</td> -<td class="tdr">..</td> <td class="tdr">11</td> - <td class="tdr">..</td> <td class="tdr">11</td> - <td class="tdr">..</td> <td class="tdr">3</td> <td class="tdr">14</td> - <td class="tdr">..</td> <td class="tdr">6</td> <td class="tdr">17</td> - <td class="tdr">6</td> <td class="tdr">17</td> - <td class="tdr">..</td> <td class="tdr">9</td> - <td class="tdr">26. A </td></tr> - <tr><td class="tdr">..</td> <td class="tdr">8</td> <td class="tdr">19</td> -<td class="tdr">..</td> <td class="tdr">11</td> - <td class="tdr">..</td> <td class="tdr">11</td> -<td class="tdr">..</td> <td class="tdr">3</td> <td class="tdr">14</td> - <td class="tdr">..</td> <td class="tdr">6</td> - <td class="tdr">..</td> <td class="tdr">6</td> <td class="tdr">17</td> -<td class="tdr">..</td> - <td class="tdr">27. B </td> - </tr> -<tr><td class="tdr">16</td> - <td class="tdr">..</td> <td class="tdr">8</td> - <td class="tdr">19</td> - <td class="tdr">..</td> <td class="tdr">19</td> - <td class="tdr">..</td> <td class="tdr">11</td> - <td class="tdr">..</td> <td class="tdr">3</td> <td class="tdr">14</td> - <td class="tdr">..</td> <td class="tdr">14</td> - <td class="tdr">..</td> <td class="tdr">6</td> <td class="tdr">17</td> - <td class="tdr">28. C </td></tr> - <tr><td class="tdr">5</td> <td class="tdr">16</td> - <td class="tdr">..</td> <td class="tdr">8</td> <td class="tdr">19</td> - <td class="tdr">8</td> <td class="tdr">19</td> - <td class="tdr">..</td> <td class="tdr">11</td> - <td class="tdr">..</td> <td class="tdr">3</td> <td class="tdr">14</td> - <td class="tdr">3</td> <td class="tdr">14</td> - <td class="tdr">..</td> <td class="tdr">6</td> - <td class="tdr">29. D </td></tr> - <tr><td class="tdr">..</td> <td class="tdr">5</td> <td class="tdr">16</td> - <td class="tdr">..</td> <td class="tdr">8</td> -<td class="tdr">..</td> <td class="tdr">8</td> <td class="tdr">19</td> - <td class="tdr">..</td> <td class="tdr">11</td> - <td class="tdr">..</td> <td class="tdr">3</td> - <td class="tdr">..</td> <td class="tdr">3</td> <td class="tdr">14</td> -<td class="tdr">..</td> - <td class="tdr">30. E </td></tr> - <tr><td class="tdr">13</td> -<td class="tdr">..</td> <td class="tdr">5</td> <td class="tdr">16</td> - <td class="tdr">..</td> <td class="tdr">16</td> -<td class="tdr">..</td> <td class="tdr">8</td> <td class="tdr">19</td> -<td class="tdr">..</td> <td class="tdr">11</td> - <td class="tdr">..</td> <td class="tdr">11</td> -<td class="tdr">..</td> <td class="tdr">3</td> <td class="tdr">14</td> - <td class="tdr">31. F </td></tr> - <tr><td class="tdr">2</td> <td class="tdr">13</td> -<td class="tdr">..</td> <td class="tdr">5</td> <td class="tdr">16</td> - <td class="tdr">5</td> <td class="tdr">16</td> - <td class="tdr">..</td> <td class="tdr">8</td> <td class="tdr">19</td> - <td class="tdr">..</td> <td class="tdr">11</td> - <td class="tdr">..</td> <td class="tdr">11</td> -<td class="tdr">..</td> <td class="tdr">3</td> -<td class="tdr">April 1. G </td></tr> -<tr> <td class="tdr">..</td> <td class="tdr">2</td> <td class="tdr">13</td> - <td class="tdr">..</td> <td class="tdr">5</td> -<td class="tdr">..</td> <td class="tdr">5</td> <td class="tdr">16</td> -<td class="tdr">..</td> <td class="tdr">8</td> <td class="tdr">19</td> - <td class="tdr">..</td> <td class="tdr">19</td> -<td class="tdr">..</td> <td class="tdr">11</td> -<td class="tdr">..</td> - <td class="tdr">2. A </td></tr> - <tr><td class="tdr">10</td> - <td class="tdr">..</td> <td class="tdr">2</td> <td class="tdr">13</td> - <td class="tdr">..</td> <td class="tdr">13</td> -<td class="tdr">..</td> <td class="tdr">5</td> <td class="tdr">16</td> - <td class="tdr">..</td> <td class="tdr">8</td> <td class="tdr">19</td> - <td class="tdr">8</td> <td class="tdr">19</td> - <td class="tdr">..</td> <td class="tdr">11</td> - <td class="tdr">3. B </td> </tr> - <tr><td class="tdr">..</td> <td class="tdr">10</td> - <td class="tdr">..</td> <td class="tdr">2</td> <td class="tdr">13</td> - <td class="tdr">2</td> <td class="tdr">13</td> -<td class="tdr">..</td> <td class="tdr">5</td> <td class="tdr">16</td> - <td class="tdr">..</td> <td class="tdr">8</td> - <td class="tdr">..</td> <td class="tdr">8</td> <td class="tdr">19</td> -<td class="tdr">..</td> - <td class="tdr">4. C </td></tr> -<tr> <td class="tdr">18</td> - <td class="tdr">..</td> <td class="tdr">10</td> -<td class="tdr">..</td> <td class="tdr">2</td> - <td class="tdr">..</td> <td class="tdr">2</td> <td class="tdr">13</td> - <td class="tdr">..</td> <td class="tdr">5</td> <td class="tdr">16</td> -<td class="tdr">..</td> <td class="tdr">16</td> -<td class="tdr">..</td> <td class="tdr">8</td> <td class="tdr">19</td> - <td class="tdr">5. D </td></tr> - <tr> <td class="tdr">7</td> <td class="tdr">18</td> -<td class="tdr">..</td> <td class="tdr">10</td> - <td class="tdr">..</td> <td class="tdr">10</td> -<td class="tdr">..</td> <td class="tdr">2</td> <td class="tdr">13</td> - <td class="tdr">..</td> <td class="tdr">5</td> <td class="tdr">16</td> - <td class="tdr">5</td> <td class="tdr">16</td> -<td class="tdr">..</td> <td class="tdr">8</td> - <td class="tdr">6. E </td></tr> - <tr><td class="tdr">..</td> <td class="tdr">7</td> <td class="tdr">18</td> - <td class="tdr">..</td> <td class="tdr">10</td> - <td class="tdr">..</td> <td class="tdr">10</td> -<td class="tdr">..</td> <td class="tdr">2</td> <td class="tdr">13</td> - <td class="tdr">..</td> <td class="tdr">5</td> - <td class="tdr">..</td> <td class="tdr">5</td> <td class="tdr">16</td> - <td class="tdr">..</td> - <td class="tdr">7. F </td> </tr> - <tr><td class="tdr">15</td> - <td class="tdr">..</td> <td class="tdr">7</td> <td class="tdr">18</td> - <td class="tdr">..</td> <td class="tdr">18</td> -<td class="tdr">..</td> <td class="tdr">10</td> -<td class="tdr">..</td> <td class="tdr">2</td> <td class="tdr">13</td> -<td class="tdr">..</td> <td class="tdr">13</td> -<td class="tdr">..</td> <td class="tdr">5</td> <td class="tdr">16</td> - <td class="tdr">8. G </td></tr> - <tr> <td class="tdr">4</td> <td class="tdr">15</td> -<td class="tdr">..</td> <td class="tdr">7</td> <td class="tdr">18</td> - <td class="tdr">7</td> <td class="tdr">18</td> - <td class="tdr">..</td> <td class="tdr">10</td> - <td class="tdr">..</td> <td class="tdr">2</td> <td class="tdr">13</td> - <td class="tdr">2</td> <td class="tdr">13</td> - <td class="tdr">..</td> <td class="tdr">5</td> - <td class="tdr">9. A </td></tr> - <tr><td class="tdr">..</td> <td class="tdr">4</td> <td class="tdr">15</td> - <td class="tdr">..</td> <td class="tdr">7</td> -<td class="tdr">..</td> <td class="tdr">7</td> <td class="tdr">18</td> - <td class="tdr">..</td> <td class="tdr">10</td> -<td class="tdr">..</td> <td class="tdr">2</td> -<td class="tdr">..</td> <td class="tdr">2</td> <td class="tdr">13</td> -<td class="tdr">..</td> -<td class="tdr">10. B </td></tr> - <tr><td class="tdr">12</td> -<td class="tdr">..</td> <td class="tdr">4</td> <td class="tdr">15</td> - <td class="tdr">..</td> <td class="tdr">15</td> - <td class="tdr">..</td> <td class="tdr">7</td> <td class="tdr">18</td> - <td class="tdr">..</td> <td class="tdr">10</td> - <td class="tdr">..</td> <td class="tdr">10</td> -<td class="tdr">..</td> <td class="tdr">2</td> <td class="tdr">13</td> - <td class="tdr">11. C </td></tr> - <tr><td class="tdr">1</td> <td class="tdr">12</td> -<td class="tdr">..</td> <td class="tdr">4</td> <td class="tdr">15</td> - <td class="tdr">4</td> <td class="tdr">15</td> -<td class="tdr">..</td> <td class="tdr">7</td> <td class="tdr">18</td> -<td class="tdr">..</td> <td class="tdr">10</td> -<td class="tdr">..</td> <td class="tdr">10</td> -<td class="tdr">..</td> <td class="tdr">2</td> -<td class="tdr">12. D </td></tr> - <tr><td class="tdr">..</td> -<td class="tdr">1</td> -<td class="tdr">12</td> -<td class="tdr">..</td> -<td class="tdr">4</td> -<td class="tdr">..</td> -<td class="tdr">4</td> -<td class="tdr">15</td> -<td class="tdr">..</td> -<td class="tdr">7</td> -<td class="tdr">18</td> -<td class="tdr">..</td> -<td class="tdr">18</td> -<td class="tdr">..</td> -<td class="tdr">10</td> -<td class="tdr">..</td> -<td class="tdr">13. E </td></tr> -<tr> <td class="tdr">9</td> -<td class="tdr">..</td> -<td class="tdr">1</td> -<td class="tdr">12</td> -<td class="tdr">..</td> -<td class="tdr">12</td> -<td class="tdr">.. </td> -<td class="tdr">4</td> -<td class="tdr">15</td> -<td class="tdr">..</td> -<td class="tdr">7</td> -<td class="tdr">18</td> -<td class="tdr">7</td> -<td class="tdr">18</td> -<td class="tdr">..</td> -<td class="tdr">10</td> -<td class="tdr">14. F </td> </tr> -<tr> -<td class="tdr">..</td> - <td class="tdr">9</td> - <td class="tdr">..</td> - <td class="tdr">1</td> - <td class="tdr">12</td> - <td class="tdr">1</td> - <td class="tdr">12</td> -<td class="tdr">..</td> - <td class="tdr">4</td> - <td class="tdr">15</td> -<td class="tdr">..</td> - <td class="tdr">7</td> -<td class="tdr">..</td> - <td class="tdr">7</td> - <td class="tdr">18</td> - <td class="tdr">..</td> -<td class="tdr">15. G </td> -</tr> -<tr> -<td class="tdr">17</td> -<td class="tdr">..</td> -<td class="tdr">9</td> -<td class="tdr">..</td> - <td class="tdr">1</td> -<td class="tdr">..</td> - <td class="tdr">1</td> -<td class="tdr">12</td> -<td class="tdr">..</td> - <td class="tdr">4</td> - <td class="tdr">15</td> - <td class="tdr">..</td> -<td class="tdr">15</td> -<td class="tdr">..</td> - <td class="tdr">7</td> - <td class="tdr">18</td> - <td class="tdr">16. A </td> </tr> - <tr><td class="tdr">6</td> -<td class="tdr">17</td> -<td class="tdr">17</td> -<td class="tdr">9</td> -<td class="tdr">..</td> - <td class="tdr">9</td> - <td class="tdr">..</td> -<td class="tdr">1</td> -<td class="tdr">12</td> - <td class="tdr">12</td> -<td class="tdr">4</td> -<td class="tdr">15</td> -<td class="tdr">4 -</td> -<td class="tdr">15</td> -<td class="tdr">15</td> - <td class="tdr">7</td> -<td class="tdr">17. B </td></tr> -<tr><td class="tdr br bl">14</td> -<td class="tdr br bl">6</td> -<td class="tdr br bl">6</td> -<td class="tdr br bl">17</td> -<td class="tdr br bl">9</td> -<td class="tdr br bl">17</td> - <td class="tdr br bl">9</td> -<td class="tdr br bl">9</td> -<td class="tdr br bl">1</td> -<td class="tdr br bl">1</td> - <td class="tdr br bl">12</td> -<td class="tdr br bl">4</td> - <td class="tdr br bl">12</td> -<td class="tdr br bl">4</td> - <td class="tdr br bl">4</td> -<td class="tdr br bl">15</td> -<td class="tdr br bl">18. C </td> </tr> -<tr><td> </td> <td> </td> <td> </td> <td> </td> <td> </td> -<td> </td> <td> </td> <td> </td> <td> </td> -<td> </td> <td> </td> <td> </td> <td> </td> <td> </td> - <td> </td> <td> </td> <td class="tdr">19. D </td> </tr> -<tr><td> </td> <td> </td> <td> </td> <td> </td> <td> </td> -<td> </td> <td> </td> <td> </td> <td> </td> -<td> </td> <td> </td> <td> </td> <td> </td> <td> </td> - <td> </td> <td> </td> <td class="tdr">20. E </td> </tr> -<tr><td> </td> <td> </td> <td> </td> <td> </td> <td> </td> -<td> </td> <td> </td> <td> </td> <td> </td> -<td> </td> <td> </td> <td> </td> <td> </td> <td> </td> - <td> </td> <td> </td> <td class="tdr">21. F </td></tr> -<tr><td> </td> <td> </td> <td> </td> <td> </td> <td> </td> -<td> </td> <td> </td> <td> </td> <td> </td> -<td> </td> <td> </td> <td> </td> <td> </td> <td> </td> - <td> </td> <td> </td> <td class="tdr">22. G </td></tr> -<tr><td> </td> <td> </td> <td> </td> <td> </td> <td> </td> -<td> </td> <td> </td> <td> </td> <td> </td> -<td> </td> <td> </td> <td> </td> <td> </td> <td> </td> - <td> </td> <td> </td> <td class="tdr">23. A </td></tr> -<tr><td> </td> <td> </td> <td> </td> <td> </td> <td> </td> -<td> </td> <td> </td> <td> </td> <td> </td> -<td> </td> <td> </td> <td> </td> <td> </td> <td> </td> - <td> </td> <td> </td> <td class="tdr">24. B </td></tr> -<tr> -<td class="bb"> </td> -<td class="bb"> </td><td class="bb"> </td><td class="bb"> </td> -<td class="bb"> </td><td class="bb"> </td><td class="bb"> </td> -<td class="bb"> </td><td class="bb"> </td><td class="bb"> </td> -<td class="bb"> </td><td class="bb"> </td><td class="bb"> </td> -<td class="bb"> </td><td class="bb"> </td><td class="bb"> </td> - <td class="tdr bb br bl">25. C </td></tr> -</table> -<hr class="chap" /> -<p><span class="pagenum"><a name="Page_1" id="Page_1">[1]</a></span></p> - -<h2 class="hang"><i>Remarks upon the</i> Solar <i>and the</i> Lunar <i>Years</i>, -<i>the</i> Cycle <i>of 19 Years</i>, <i>commonly called the</i> -Golden Number, <i>the</i> Epact, <i>and a Method -of finding the Time of</i> Easter, <i>as it is -now observed in most Parts of</i> Europe. -<i>Being Part of a Letter from the Right -Honourable</i> George <i>Earl of</i> Macclesfield -<i>to</i> Martin Folkes <i>Esq</i>; President <i>of the</i> -Royal Society.</h2> - -<h3><i>Of the</i> Solar Year.</h3> - -<div class="sidenote"><i>Read</i> May 10. -1750.</div> - -<p class="dropcap">T<span class="smcap">he</span> mean <i>Tropical Solar Year</i>, 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. <i>Halley</i>'s Tables, of 365<sup>d</sup>, 5<sup>h</sup>, 48<sup>´</sup>, -55<sup>´´</sup>: Which is less by 11<sup>´</sup>, 5<sup>´´</sup>, than the mean <i>Julian</i> -Year, consisting of 365<sup>d</sup>, 6<sup>h</sup>, 0<sup>´</sup>, 0<sup>´´</sup>.</p> - -<p>Hence the Equinoxes and Solstices anticipate, or -come earlier than the <i>Julian</i> Account supposes them -to do by 11´, 5´´, in each mean <i>Julian</i> Year; or 44<sup>´</sup>, -20<sup>´´</sup> in every four; or 3<sup>d</sup>, 1<sup>h</sup>, 53<sup>´</sup>, 20<sup>´´</sup>, in every four -hundred <i>Julian</i> Years.</p> - -<p>In order to correct this Error in the <i>Julian</i> Year, -the Authors of the <i>Gregorian</i> Method of regulating -the Year, when they reformed the Calendar in the -Beginning of <i>October 1582</i>, directed that three intercalary -Days should be omitted or dropped in every -four hundred Years; by reckoning all those Years, -<span class="pagenum"><a name="Page_2" id="Page_2">[2]</a></span> -whose Date consists of a Number of entire Hundreds -not divisible by 4, such as 1700, 1800, -1900, 2100, <i>&c.</i> 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 <i>Julian</i> Account, -should have been inserted in the Month of -<i>February</i> 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, <i>&c.</i> should still -be consider'd as Bissextile or Leap Years, and, of -consequence, that one Day should be intercalated as -usual in those Years.</p> - -<p>This Correction, however, did not entirely remove -the Error: For the Equinoxes and Solstices still anticipate -1<sup>h</sup>, 53<sup>´</sup>, 20<sup>´´</sup> in every four hundred <i>Gregorian</i> -Years.</p> - -<p>But that Difference is so inconsiderable as not to -amount to twenty-four Hours, or to one whole Day, -in less than 5082 <i>Gregorian</i> Years.</p> - -<h3><i>Of the</i> Lunar Year, Cycle of 19 Years, <i>and -the</i> Epact.</h3> - -<p>The Space of Time betwixt one mean Conjunction -of the Moon with the Sun and the next following, -or a mean <i>Synodical Month</i>, is equal to 29<sup>d</sup>, -12<sup>h</sup>, 44<sup>´</sup>, 3<sup>´´</sup>, 2<sup>´´´</sup>, 56<sup><small>IV</small></sup> according to Mr. <i>Pound</i>'s -Tables of mean Conjunctions.</p> - -<p>The Common Lunar Year consists of 12 such -Months.</p> - -<p><span class="pagenum"><a name="Page_3" id="Page_3">[3]</a></span> - -The Intercalary or <i>Embolimæan</i> Year consists of -13 such Months.</p> - -<p>In each Cycle of 19 Lunar Years, there are 12 -Common, and 7 Intercalary or <i>Embolimæan</i> Years, -making together 235 Synodical Months.</p> - -<p>It was thought, at the time of the General Council -of <i>Nice</i>, which was holden in the Year of our -Lord 325, that 19 <i>Julian</i> Solar Years were exactly -equal to such a Cycle of 19 Lunar Years, or to 235 -Synodical Months; and therefore, that, at the End -of 19 Years, the New Moons or Conjunctions would -happen exactly at the same Times, as they did 19 -Years before: And upon this Supposition it was, that, -some time afterwards, the several Numbers of that -Cycle, commonly called the Golden Numbers, were -prefixed to all those Days in the Calendar, on which -the New Moons then happened in the respective -Years corresponding to those Numbers; it being -imagined, that whensoever any of those Numbers -should for the future be the Golden Number of the -Year, the New Moons would invariably happen on -those Days in the several Months, to which that Number -was prefixed.</p> - -<p>But this was a Mistake:</p> - -<table summary="solar years"> - -<tr><td>For 19 <i>Julian</i> Solar Years contain</td> - -<td class="tdr">6939<sup>d</sup>,</td> -<td class="tdr">18<sup>h</sup>,</td> -<td class="tdr">0<sup>´</sup>,</td> -<td class="tdr">0<sup>´´</sup>,</td> -<td class="tdr">0<sup>´´´</sup></td></tr> - -<tr><td>Whereas 235 Synodical Months -contain only </td> -<td class="bb">6939,</td> -<td class="bb">16,</td> -<td class="bb">31,</td> -<td class="bb">56,</td> -<td class="bb">30</td></tr> - -<tr><td>And are therefore less than 19 -<i>Julian</i> Solar Years by -</td> -<td class="tdr">0,</td> - <td class="center">1,</td> -<td class="tdr">28,</td> -<td class="tdr">3,</td> -<td class="tdr">30.</td></tr> -</table> - -<p>This Difference amounts to a whole Day very -nearly in 310.7 Years, the New Moons anticipating,<span class="pagenum"><a name="Page_4" id="Page_4">[4]</a></span> -or falling earlier, by 24 Hours in that Space of Time, -than they did before: And therefore now in the Year -1750, the New Moons happen above four Days and -a half sooner, than the Times pointed out by the -Golden Numbers in the Calendar.</p> - -<p>In order therefore to preserve a sort of regular -Correspondence betwixt the Solar and the Lunar -Years, and to make the Golden Numbers, prefixed -to the Days of the Month, useful for determining -the Times of the New Moons, it would be necessary, -when once those Golden Numbers should have been -prefixed to the proper Days, to make them anticipate -a Day at the End of every 310.7 Years, as the Moons -will actually have done; that is to set them back one -Day, by prefixing each of them to the Day preceding -that, against which they before stood.</p> - -<p>But as such a Rule would neither be so easily comprehended -or retained in Memory, as if the Alteration -was to be made at the End or at the Beginning -of complete Centuries of Years; the Rule would be -much more fit for Practice, and keep sufficiently near -to the Truth, if those Numbers should be set back nine -Days in the Space of 2800 Years; by setting them -back one Day, first at the End of 400 Years, and -then at the End of every 300 Years for eight times -successively: whereby they would be set back, in -the whole, nine Days in 2800 Years. After which -they must again be set one Day back at the End of -400 Years, and so on, as in the preceding 2800 Years. -By which means the Golden Numbers would always -point out the mean Times of the New Moons, within -a Day of the Truth.</p> - -<p><span class="pagenum"><a name="Page_5" id="Page_5">[5]</a></span> - -It is plain however that the Lunar Year will have -lost one Day more than ordinary, with respect to -the Solar Year, whenever the New Moons shall have -anticipated a whole Day; as they will have done at -those times, when it is necessary that the Golden -Numbers should, by the Rule just now given, be set -back one Day: and consequently the Epact, for that -and the succeeding Years, must exceed by an Unit -the several corresponding Epacts of the preceding 19 -Years.</p> - -<p>For the Epact is the Difference, in whole Days, betwixt -the common <i>Julian</i> Solar and the Lunar Year; -the former being reckoned to consist of 365, and the -latter of only 354 Days. If therefore the Solar and the -Lunar Year at any time should commence on the same -Day, the Solar would, at the End of the Year, have exceeded -the Lunar by 11 Days; which Number 11 would -be the Epact of the next Year: 22 would be the Epact -of the Year following, and 33 the Epact of the Year -after that, the Epacts increasing yearly by 11. But as -often as this yearly Addition makes the Epact exceed -30, those 30 are rejected as making an intercalary -Month, and only the Excess of the Epact above 30 is accounted -the true Epact for that Year. Thus when the -Epact would amount to 31, 32, 33, 34, <i>&c.</i> the 30 -is rejected, and the Epact becomes 1, 2, 3, 4, <i>&c.</i></p> - -<p>Since therefore the Lunar Year will have lost a Day -more than ordinary, in respect of the Solar Year, -whenever it is necessary to set the Golden Numbers -one Day back, as was before observed; it follows, -that the Epact must at the same time be increased -by an Unit more than usual: the Difference betwixt -the Solar and the Lunar Year having been just so<span class="pagenum"><a name="Page_6" id="Page_6">[6]</a></span> -much greater than usual. That is, 12 must be added, -instead of 11, to the Epact of the preceding, in order -to form what will be the Epact of the then present -Year. Which Addition of an Unit extraordinary -to one Epact will occasion all the subsequent Epacts -(which will follow each other in the usual manner, -each exceeding the foregoing by 11) to be greater -by an Unit than their respectively corresponding Epacts -of the preceding 19 Years.</p> - -<p>If therefore, instead of the Golden Numbers, the -Epacts of the several Years were prefixed, in the -manner the <i>Gregorians</i> have done, to the Days of the -Calendar, in order to denote the Days on which the -New Moons fall in those Years whereof those Numbers -are the Epacts; there would never be Occasion -to shift the Places of those Epacts in the Calendar; -since the Augmentation by an Unit extraordinary of -the Epacts themselves would answer the Purpose, and -keep all tolerably right.</p> - -<p>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 <i>Julian</i> -Account or Manner of adjusting the Year, which -goes on regular and uniform without any Variation.</p> - -<p>But the regulating these things for those who use the -<i>Gregorian</i> 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<span class="pagenum"><a name="Page_7" id="Page_7">[7]</a></span> -<i>Gregorians</i>, than the increasing one of them by 12 -instead of 11. For, in every <i>Gregorian</i> 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.</p> - -<p>In order therefore to adapt the before-mention'd -Rule to the <i>Gregorian</i> Account, and to know in -what Years the Epacts should either be <span class="err" title="original: extraordinariy">extraordinarily</span> -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.</p> - -<p>First. That in the Years 1800, 2100, 2700, 3000, -<i>&c.</i> where the Number of entire Hundreds is divisible -by 3, but not by 4, the <i>Gregorian</i> 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.</p> - -<p>2dly. The like will happen in the Years 2000, 2800, -3200, <i>&c.</i> where the Number of entire Hundreds is -divisible by 4, but not by 3: For neither the <i>Gregorian</i> -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.</p> - -<p><span class="pagenum"><a name="Page_8" id="Page_8">[8]</a></span> - -But, 3dly, In the Years 2400, and 3600, whose -Number of entire Hundreds is divisible both by 3 -and 4, the <i>Gregorian</i> 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.</p> - -<p>4thly and lastly, In the Years 1900, 2200, 2300, -2500, <i>&c.</i> where the Number of Hundreds is divisible -neither by 3 nor 4; the <i>Gregorian</i> 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.</p> - -<p>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 -<i>Julian</i> Account for ever, and according to the <i>Gregorian</i> -Account till the Year 4199 inclusive, after<span class="pagenum"><a name="Page_9" id="Page_9">[9]</a></span> -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.</p> - -<p>The <i>Gregorians</i> 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 <i>Gregorians</i> -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.</p> - -<p><span class="pagenum"><a name="Page_10" id="Page_10">[10]</a></span></p> - -<h2><i>A Method of finding the Time of</i> Easter, <i>as -it is observed in most Parts of</i> Europe.</h2> - -<p>From what has been already said, a Method may -be obtained, for fixing, with sufficient Exactness, the -Time of the Celebration of the Feast of <i>Easter</i>, -which is governed by the <i>Vernal Equinox</i>, and by the -Age of the Moon nearest to it. The former whereof, -when once rightly adjusted, may (by the Corrections -mentioned in that Part of this Paper which relates to -the Solar Year) be made to continue to fall at very near -the same time with, or at most not to differ a whole -Day from the true <i>Equinox</i>: and the same Rules -and Directions, which, as was before shewn, would, -without any great Error, point out the Times of the -first Day of the Moon, would with equal Certainty -point out the fourteenth, fifteenth, or any other: And -thus the Times of the Oppositions or the Full Moons -might be as well marked out thereby, as those of the -Conjunctions or the New Moons.</p> - -<p>I shall not at present take notice of the Canon of -the Council of <i>Nice</i>, in the Year of our Lord 325, -which directs the Time of celebrating the Feast of -<i>Easter</i>, or of the Reasons upon which that Canon was -founded. Nor shall I endeavour to explain the Rule -now in Use in the Church of <i>England</i> for finding -<i>Easter</i>: For, besides that such an Explanation would -extend this Paper to an improper Length, those Points -have already been treated of by several much abler -Hands, and particularly by our Countryman the learned -Dr. <i>Prideaux</i>. Nor is it my Intention to enter far into<span class="pagenum"><a name="Page_11" id="Page_11">[11]</a></span> -the Methods used by the <i>Gregorians</i>, or those of the -Church of <i>Rome</i>, or by any other Nations or Countries, -for finding the Time of that Feast. As to our -own, I shall only observe, that the Method now used -in <i>England</i>, for finding the fourteenth Day of the -Moon, or the Ecclesiastical Full Moon, on which -<i>Easter</i> dependeth, is, by Process of Time, become -considerably erroneous: as the Golden Numbers, -which were placed in the Calendar, to point out the -Days on which the New Moons fall in those Years -of which they are respectively the Golden Numbers, -do now stand several Days later in the same than those -New Moons do really happen. Which Error, as was -before observed, arises from the Anticipation of the -Moons since the Time of the Council of <i>Nice</i>: And as -the <i>Vernal Equinox</i> has also anticipated eleven Days -since that time; neither that Equinox, nor the New -Moons, do now happen on those Days upon which -the Church of <i>England</i> supposes them so to happen.</p> - -<p>When Pope <i>Gregory</i> XIII. reformed the <i>Julian</i> -Solar Year, he likewise made a Correction as to the -Time of celebrating the Feast of <i>Easter</i>, by placing -the Epacts (which he directed to be made use of -for the future instead of the Golden Numbers) much -nearer to the true Times of the New Moons than -the Golden Numbers then stood in the old Calendar: -I say, <i>much nearer to the true Times</i>; because in -fact the Epacts, as placed by him, were not prefixed -to the exact Days upon which the New Moons then -truly fell. And this was done with Design, and for a -Reason which it is not material to the Purpose of -this Paper to mention.</p> - -<p><span class="pagenum"><a name="Page_12" id="Page_12">[12]</a></span> - -But the Church of <i>England</i>, and that of <i>Rome</i> -or the <i>Gregorians</i>, do still agree in this; that both of -them mark (the former by the Golden Numbers, and -the latter by the Epacts corresponding to them) the -Days on which their Ecclesiastical New Moons are -supposed to happen: And that fourteenth Day of the -Moon inclusive, or that Full Moon, which falls upon, -or next after, the 21st Day of <i>March</i>, is the Paschal -Limit or Full Moon to both: And the <i>Sunday</i> next -following that Limit or Full Moon, is by both -Churches celebrated as <i>Easter</i> Day. But the 21st of -<i>March</i> being reckoned, according to the <i>Gregorian</i> -Account or the New Style, eleven Days sooner than -by the <i>Julian</i> Account or the Old Style, which is still -in Use amongst us; and their Ecclesiastical New -Moons being three Days earlier than those of the -Church of <i>England</i>; it happens that although the -Church of <i>England</i> and that of <i>Rome</i> often do, yet -more frequently they do not, celebrate the Feast of -<i>Easter</i> upon the same natural Day.</p> - -<p>It might however be easier for both, and could -occasion no Inconvenience, now that Almanacks, -which tell the exact Times of the New Moons, are -in most Peoples Hands; if all the Golden Numbers -and Epacts now prefixed to those Days of the Calendar, -in our Book of Common Prayer, and in the <i>Roman -Breviary</i>, on which the respective Ecclesiastical New -Moons happen, were omitted in the Places where -they now stand; and were set only against those fourteenth -Days of the Moon, or those Full Moons, -which happen betwixt the 21st Day of <i>March</i> and the -18th of <i>April</i>, both inclusive. Since no fourteenth -Day or Full Moon, which happens before the 21st<span class="pagenum"><a name="Page_13" id="Page_13">[13]</a></span> -of <i>March</i>, or after the 18th Day of <i>April</i>, can have any -Share in fixing the Time of <i>Easter</i>. By which means -the Trouble of counting to the fourteenth Day, and -the Mistakes which sometimes arise therefrom, would -be avoided.</p> - -<p>We do as yet in <i>England</i> follow the <i>Julian</i> Account -or the Old Style in the Civil Year; as also the -Old Method of finding those Moons upon which -<i>Easter</i> depends: Both of which have been shewn -to be very erroneous.</p> - -<p>If therefore this Nation should ever judge it proper -to correct the Civil Year, and to make it conformable -to that of the <i>Gregorians</i>, it would surely -be adviseable to correct the Time of the Celebration -of the Feast of <i>Easter</i> likewise, and to bring it -to the same Day upon which it is kept and solemnized -by the Inhabitants of the greatest Part of <i>Europe</i>, -that is, by those who follow the <i>Gregorian</i> Account. -For tho' I am aware, that their Method of finding -the Time of <i>Easter</i> is not quite exact, but is liable -to some Errors; yet I apprehend, that all other practicable -Methods of doing it would be so too: And -if they were more free from Error, they would probably -be more intricate, and harder to be understood -by Numbers of People, than the Method of determining -that Feast either by a Cycle of Epacts, as is -practiced by the <i>Gregorians</i>, or by that of 19 Years -or the Golden Numbers, in the manner proposed in -the following Part of this Paper: And it is of no -small Importance, that a Matter of so general a Concern, -as the Method of finding <i>Easter</i> is, should be -within the Reach of the Generality of Mankind, at -least as far as the Nature of the thing will admit.</p> - -<p><span class="pagenum"><a name="Page_14" id="Page_14">[14]</a></span> - -For which Reason, in case the Legislature of this -Country should before the Year 1900, think fit to -make our Civil Year correspond with that of the -<i>Gregorians</i>, and also to celebrate all the future Feasts -of <i>Easter</i> upon the same Days upon which they celebrate -them; this last Particular might be easily effected, -without altering the Rule of the Church of <i>England</i> -for the finding of that Feast: And this only by advancing -the Golden Numbers, prefixed to certain Days in the -Calendar, 8 Days forwarder for the New Moons, or -21 Days forwarder for the fourteenth Days or Full -Moons, than they now stand in our Calendar.</p> - -<p>In order to explain this, it must be observed, that the -<i>Gregorian</i> Account or the New Style is eleven Days -forwarder than the <i>Julian</i> Account or the Old Style, -which we still make use of; that is, the last Day of -any of our Months is the eleventh Day of their next -succeeding Month. If therefore their Ecclesiastical -New Moons fell on the same Days with those of the -Church of <i>England</i>, the Golden Number 14, which -now stands against the last Day of <i>February</i> in our -that is the <i>Julian</i> Calendar, should, when we should -have adopted the <i>Gregorian</i> Calendar, be prefixed to -the 11th Day of <i>March</i>. But since their Ecclesiastical -New Moons happen 3 Days earlier than our Ecclesiastical -New Moons at present do; so much should be deducted -from those 11 Days, by which the Golden -Numbers ought otherwise to be advanced; and the -Golden Number 14 should not be placed against the -11th, but the 8th Day of <i>March</i>: Which being reckoned -the first Day of the Moon, if we count on to -the fourteenth Day of the same inclusive, that would -be found to fall on the a 21st Day of <i>March</i>; on which<span class="pagenum"><a name="Page_15" id="Page_15">[15]</a></span> -Day the <i>Gregorian</i> Paschal Limit or Full Moon will -happen when the Golden Number is 14. And the like -Course should be taken with the rest of the 19 Golden -Numbers; which ought to be placed 8 Days forwarder -than they now stand, if they are to point out the New -Moon; or 21 Days forwarder than they are at present, -if they are to mark the fourteenth Day of the Moon or -the Full Moon: The latter of which, as has been shewn, -would be more eligible, than to prefix those Numbers -to the Days on which the New Moons happen.</p> - -<p>Thus may the Rule and Method now used in the -Church of <i>England</i>, be most easily adapted to shew -the Time of <i>Easter</i>, as it is observed by the <i>Gregorians</i>, -till the Year 1900; at which Time, and at -the other proper succeeding Times, if the Golden -Numbers in the Calendar shall either be advanced or -set backward a Day, according the foregoing Rules -and Directions for that Purpose, they will continue -to shew us the New or the Full Moons, of the Church -of <i>Rome</i> or the <i>Gregorian</i> Calendar with great Exactness, -till the Year 4199: when, as has been already -mentioned, there must be a little Variation made in -those Rules and Directions.</p> - -<p>There is however one Exception to those General -Rules and Directions, which will be taken notice of -in the next Paragraph.</p> - -<p>Upon these Principles I framed the Table accompanying -this Paper, and shewing, by means of the -Golden Numbers, all the <i>Gregorian</i> Paschal Limits -or Full Moons, from the Reformation of the Calendar, -<i>&c.</i> by Pope <i>Gregory</i> to the Year 4199 inclusive. -Which Space of Time is therein divided into sixteen -<span class="pagenum"><a name="Page_16" id="Page_16">[16]</a></span> -unequal Portions or Periods; at the Beginning of -each of which, all the Golden Numbers, when once -they shall have been properly placed in the Calendar, -must either be advanced or set back one Day, with -respect to the Place where they stood in the preceding -Period, agreeably to the foregoing Rules: Except -those Numbers which shall happen to stand against -the 4th and 5th of <i>April</i> to shew the Paschal New -Moons, or against the 17th and 18th of the same Month -to mark out the Paschal Full Moons; both which -Numbers at some Times, and only one of them at -others, must keep the same Place for that, which was -allotted to them in the immediately preceding Period.</p> - -<p>In order to determine at what Times, and on -what Occasions, this Exception is to take Place; let -it be observed, that, in the Months of <i>January</i>, -<i>March</i>, <i>May</i>, and some others in our present Calendar, -as well as in the Table above mentioned, -some of the Golden Numbers stand double or in -Pairs, and follow one the other immediately; whilst -others, on the contrary, generally stand single and -by themselves.</p> - -<p>Now, when any of those Pairs, or two Numbers -which usually accompany each other, happen, in pursuance -of the foregoing Rules, to be prefixed the one -to the 4th and the other to the 5th of <i>April</i> for the -New Moons, or the one to the 17th and the other -to the 18th of <i>April</i> for the Paschal Limits or Full -Moons: And when any of those Numbers, which -generally stand single, are prefixed, according to the -said Rules, to the 5th of <i>April</i> for the New Moons, -or to the 18th for the Full Moons: In these Cases -those Pairs or single Numbers that are so situated; -must not be set forward or advanced at the Begin<span class="pagenum"><a name="Page_17" id="Page_17">[17]</a></span>ning -of the next Period, but must keep their Places -during another Period, if the foregoing Rules direct -all the Golden Numbers to be advanced a Day; -which must be complied with in respect to all the -other Golden Numbers, except those so situated as -above. Instances whereof may be seen in the Table, -under the respective Periods beginning with the Years -1900, 2600, 3100, and 3800.</p> - -<p>But if, in Conformity to the foregoing Rules, all -the Golden Numbers are to be set one Day backward; -those Pairs or single Numbers, tho' situated -as is above-mentioned, must not keep their Places, -but must move one Day backward like all the other -Golden Numbers; as they may be seen to do in the -Periods beginning with the Years 2400 and 3600.</p> - -<p>To give a plain and intelligible Account of the -Reason, on which the Directions now given with -respect to this Exception are founded, would extend -this Paper, already too long, far beyond its due and -proper Bounds. I shall therefore content myself with -observing, that it depends chiefly upon the Nature -of the <i>Menses Pleni</i> and <i>Menses Cavi</i>, into which -the Lunar Year is usually divided: and that, in order -to make use of the Golden Numbers for finding the -Time of the <i>Gregorian Easter</i>, it will be necessary -not only to conform to the general Rules laid -down in the former Part of this Paper; but also to -follow the Directions just now given, with respect to -the above-mentioned Exception to those general -Rules.</p> - -<p>But I should not do Justice to <i>Peter Davall</i> of -the <i>Middle Temple</i>, Esq; Secretary of the <i>Royal<span class="pagenum"><a name="Page_18" id="Page_18">[18]</a></span> -Society</i>, did I not here acknowledge, that, before I had -so fully considered these Matters as I have since done, -I had the first Hint of applying the Golden Numbers -to find the <i>Gregorian</i> Paschal Limit or full Moon, -from him; who has since that time composed and -drawn up Tables, <i>&c.</i> which may possibly be of -considerable and general Use in this Nation hereafter.</p> - -<p class="center"><i>FINIS.</i></p> - -<hr class="chap" /> -<div class="transnote"><h3><a id="Transcribers_Note"></a>Transcriber's Note</h3> - -<p>Variable spelling and hyphenation have been retained. Minor punctuation -inconsistencies have been silently repaired.</p> - -<p class="center">Corrections.</p> - -<p>The first line indicates the original, the second the correction.</p> -<p>p. <a href="#Page_7">7</a></p> - -<ul><li>what Years the Epacts should either be extraordinariy</li> - -<li>what Years the Epacts should either be <span class="u">extraordinarily</span></li></ul> -</div> - - - - - - - -<pre> - - - - - -End of the Project Gutenberg EBook of 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 George Parker - -*** END OF THIS PROJECT GUTENBERG EBOOK REMARKS UPON SOLAR AND LUNAR YEARS *** - -***** This file should be named 62764-h.htm or 62764-h.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/6/2/7/6/62764/ - -Produced by MWS, Eleni Christofaki and the Online -Distributed Proofreading Team at https://www.pgdp.net (This -file was produced from images generously made available -by The Internet Archive) - -Updated editions will replace the previous one--the old editions will -be renamed. - -Creating the works from print editions not protected by U.S. copyright -law means that no one owns a United States copyright in these works, -so the Foundation (and you!) can copy and distribute it in the United -States without permission and without paying copyright -royalties. 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