a more Remote approach to her Conjunction Therefore the Indices of these Epacts are set earlier in the Calendar of the Sun's Month to keep some accord as the Sun 's longer and Uneven Months will permit between the Moon 's Month and that of the Sun And for the same reason as the Epacts decrease so they fall later in the Calendar month If you find one or two or more of the less Epacts set in the beginning and one or two or more greater at the end of the Calendar-month it happens through the Inequality of the Moon 's and Sun's Months If you ask Why there are void Spaces in that first Column of the Calendar some days of the Month having no Golden Numbers set against them You must remember and consider that there are no more Varieties of Epacts than 19 so measured by the Golden Number and they arise out of their Annual Progression by 11 till you go through all Variations and begin again at 11 which is done in 19 Progressions or 19 years as you may see in the first Table So that they are but enough to set against 19 days of 29 in the Calendar and 10 of the days â—aving no Epact can have no Golden Number against them Take an instance of the Month of July in the second Table the Days whereof are set Laterally after and against the Columns of Golden Number and of Epacts and of the correspondent years of our Lord within one Cycle Now there are no Epacts in the aforesaid Progression by 11 which happen to fall on any of these ten Numbers following viz. 27 24 21 19 16 13 10 8 5 2. So that those Days of that Month where those Numbers should in order fall because they have no Epact can have no Golden Number set before them and therefore that Space is left void viz. as to this Month of July the 3d 6 9 11 14 17 20 22 25 28th days and 30th of the next Cycle By which you may plainly see the reason of those void Spaces in this or any other Month of the Ecclesiastical Calendar It was said before that the Rule to find the Moon 's Age is not Precise and the reason is partly because of the Inequality of her Motion sometimes swifter sometimes slower and partly because of the Sun 's unequal Motion and partly because of the odd measure of the Solar year spoken of before So that I may say No General Rule in these Cases without Limitations and Equations can be exact I will insist only on the last Incumbrance viz. the odd measure of the Solar year I mean the odd or Supernumerary 6 hours which are not accounted in the three years after the Leap-year which as I said consists of no more than 365 days without the odd six hours Suppose you apply this Rule to find the Moon 's Age and suppose it exactly true which indeed it is not for any Day or Month in a year that is the first year after Bissextile you will find it not agree exactly to the succeeding three years For the second year after Bissextile takes his beginning six hours before the end of the foregoing year be fulfilled Therefore the Computations of the Motions and Places of the Sun and Moon will be six hours earlier all that year than they will be pointed at by the Rule And for the same reason in the next year viz. the third after Leap-year the Sun and Moon 's places will be computed twelve hours sooner and in the Leap-year for the former two Months viz. till after the Intercalar day 18 hours sooner and in the remainder of that year six hours later You see how considerable it is in which of these four years you make use of Rules or Tables for the Heavenly motions because there may be near 6 or 12 or 18 hours difference in the true Age of the Moon from the time assigned by the Rule And the like happens to the computation of the Sun's entrance into the four Cardinal Signs and of his whole yearly Progress in the Leap-year and the three years after it respectively and so likewise of the other Planets CHAP. VII An Important defect in Ecclesiastical Computations by the Nicene Rule arising from hence that the Golden Number does not exactly measure the Moon 's Cycle § The Sun's Account above ten days too late and the Moon 's above four and needs Rectification BUT besides these Astronomical Intricacies of Calculation which I have transiently mentioned there remains one most considerable Important Defect in Ecclesiastical Computations after the Nicene Rule in relation to the Moon For the Golden Number does not so exactly comply with and measure the Moon 's Cycle but that there is found an Anomaly like that of the Sun's Anticipation of 10′ 44″ For though the Moon in 19 years seems to renew her same course respective to the Sun yet it is found she falls short in that time almost an hour and half which in 16 Decennoval Cycles amount to 24 hours or a Natural Day viz. 16 hours and 16 half hours And thus 16 Cycles are compleated in 304 years or rather as some more accurately seem to calculate in 312 years making the Anticipation of the Moon at the end of every Cycle to be somewhat less viz. 1 H 27′ 32″ 42‴ Now as the Nicene Council fixed the Equinox upon the 21 of March for the finding out of Easter which has caused the Misguidance from the Sun which we lie under in respect of Easter and the moveable Feasts so the fame Council likewise fixed the Accounts of the Moon upon the Cycle of the Golden Number as it then pointed out the Lunations and therefore placed it in the Calendar for a perpetual Rule as is said before But now we find for the reasons before assigned that the Golden Number so fixed gives us the New-moon's and Full and other Accounts of the Moon more than four days too late by reason of the aforesaid Anticipation and our neglect of it Which also wants Reformation like that which is attempted in the Gregorian Calendar For at this time the Sun's Account by our old Julian year is above ten Days too late and that of the Moon above four Days When therefore the Accounts of the Moon are also rectified and reformed and the Golden Numbers once rightly applyed to the Days of the Months they may be kept so for many Ages and kept right by allowing one day at every end of 312 years for an Equation of the Moon 's Cycle The Council of Nice was celebrated Anno Domini 325 since which there have passed four times 312 years to the year 1573 which then caused an Error of four Days and was reformed soon after viz. 1582. From thence viz. 1573 to this present year 1693 there have passed 120 years which contain six Cycles of the Moon and six years Currant which cause a farther Anticipation of almost nine hours So much the Rule by the Golden Number assigns the Aspects
Account of these Changes there is appropriated a Cycle which comprehends in order all the Variations of the Sunday Letter and is therefore called the Cycle of the Sun composed of 4 which makes the Leap-year and 7 the change of the one odd Day throughout the Septimana or Week 4 times 7 gives 28. This Cycle begins at that Leap-year wherein G and F are the Sunday Letters and is terminated at 28. By the Table annexed you may see how it proceeds I have added to it the Cycle of the Moon or Golden Number that you may view their Progress from their being joined and beginning together in the Year 1672. A. D. Cyc ☉ D. Letter Cyc ☽ 1672 1 G. F 1 73 2 E 2 74 3 D 3 75 4 C 4 76 5 B. A 5 77 6 G 6 78 7 F 7 79 8 E 8 1680 9 D. C 9 81 10 B 10 82 11 A 11 83 12 G 12 84 13 F. E 13 85 14 D 14 86 15 C 15 87 16 B 16 88 17 A. G 17 89 18 F 18 1690 19 E 19 91 20 D 1 92 21 C. B 2 93 22 A 3 94 23 G 4 95 24 F 5 96 25 E. D 6 97 26 C 7 98 27 B 8 99 28 A 9 1700 1 G. F 10 701 2 E 11 702 3 D 12 703 4 C 13 704 5 B. A 14 c. It is likely the aforesaid Period was made by Dionysius or whoever else first attempted it in imitation of Calippus who many Ages before in like manner and for the like reason joined four of Meton's Lunary Decennoval Cycles what they are you will see hereafter out of which he made a Period of 76 Years which had its beginning at the New-moon next after the Summer Solstice after the Victory of Alexander the Great over Darius And in the same manner after the third Revolution of this Period Hipparchus enlarged it by adding together four of these Calippic Periods and so obtain'd a greater Period of 304 years containing 16 Metonic Cycles Upon the same Principle but with a greater and nobler Design and Event Joseph Scaliger formed a Period which is become as it were a Standard to all others including and comprehending them all and excells them all for Certainty because we can when we please by Calculation of the Course of the Cycles of which it consists trace up to the Head or Beginning of it and so infallibly determine in what year of this Period any given year is to be placed which by him was thus contrived Upon the Dionysian Period formed as I have shewn out of two Cycles viz. of the Sun and Moon he grafted another most excellent one for Largeness and Certainty beyond all other commencing 764 years before the reputed Epocha of the Creation in use with us serving for many thousand years And it was by joining the Roman Indiction a Cycle of 15 to the other two Cycles i. e. to the Period of Dionysius The Indiction instituted by Constantine the Great is properly a Cycle of Tributes orderly disposed for 15 years And by it Accounts of that kind were kept Afterwards in memory of the great Victory obtained by Constantine over Maxentius 8. Cal. Octob. 312 by which an entire Freedom and as it were a new Life was given to Christianity the Council of Nice for the Honour of Constantine ordain'd that the Accounts of years should be no longer kept by the Olympiads which till that time had been done but that instead thereof the Indiction should be made use of by which to reckon and date their years which hath its Epocha Anno Dom. 313. Jan. 1. Now this Cycle as was said was by Scaliger joined to the other two making the Epocha or Beginning when all three Cycles begin together at 1 which comprehends a Period of 7980 years having its Epocha 764 years before that of the Creation now in use And this is stiled the Julian Period The Golden Number has its Period in 19 years the Cycle of the Sun in 28 the Indiction in 15 The two former as before multiplied one by the other give 532 which multiplied by 15 gives 7980. This Period is of great use in Chronology and they apply all other Periods and Epocha's to it Chronologers differ amongst themselves about most other Great Epocha's as particularly that most principal Epocha of the Creation which is accounted by Arch-bishop Usher to have been 4003 years compleat before the Vulgar Aera of Christ by Scaliger 3949 by Petavius 3983 c. So that when I read of an Action said to be done in such a year of the Creation I am in uncertainty whose Opinion amongst them my Author follows and consequently know not what year he means But the Julian Period is so fixed by Certain Calculation of the Revolutions of those Cycles which make it that it can lie under no Mistake or Doubt but is an Infallible Character of that one year to which therefore all other Aera's must be reduced as well as we can It is necessary to know the different Periods and Epocha's as they were in use amongst several Nations and to know how to reduce them to our way of Accounting else we cannot understand their Historians as to the true Date and Time of Occurrences which they Relate and Account after their own way The Greeks accounted by the Olympiads chiefly the Romans from the Building of Rome and by their Fasti Consulares as the Athenians did by their Archontes The Astronomers from Nabonassar The Aera of Dioclesian or of the Coptites or Martyrs in many places was used until the Christian Aera took place and is still in use as Helvicus relates amongst Arabian and Aethiopic Christians The Arabians and Turks account from the Hegira or Flight of Mahomet The Persians from Jezdagird c. I have for this cause in the following Tables endeavoured to reduce the principal Aera's and Periods to the Year of our Lord Some having their Epocha's before the Nativity and some after Scaliger An. Do. 1 1600 1695 1700 Julian Period 4714 6313 6408 6413 Creation 3950 5549 5644 5649 Judaic Period 3761 5360 5455 5460 Deluge 2294 3893 3988 3993 Exodus Aegypt 1498 3097 3192 3197 Troy Destr 1183 2782 2877 2882 Solomon's Temple 1018 2617 2712 2717 Olympiad 1.195 4.594 3.618 4.619 Iphitus 777 2376 2471 2476 V. C. 753 2352 2447 2452 Nabonassar 749 2349 2444 2449 Julian Calendar 46 1645 1740 1745 Heads of some Aera's after Christ A. D. Years expanded since to the year of our lord 1600 1695 1700 Destruction of Jerusalem 70 1530 1625 1630 Dioclesian's Aera 284 1316 1411 1416 Indiction 313 13. 1287 3. 1382 8. 1387 Hegira 622 978 1073 1078 Jezdagird 632 968 1063 1068 Conquest 1066 534 629 634 Calendar reformed 1582 18 113 118 As to these Tables the Reader may observe that Authors differ about fixing some of the principal Aera's as I said before especially that of the Creation about which many Learned Men dissent from one another But chiefly the
Account of the Septuagint and that likewise which a great part of the Eastern Churches do follow and the Western did even after St. Jerom's time are very widely distant from that used by us at present grounded as 't is thought upon a different Reading of the Ancient Text of the Hebrew Bible where it relates to the Lives of the Patriarchs and some other Circumstances And as the Number of years are differently computed so the Years themselves also have different Beginnings some in Summer and others in Winter c. and consequently some about the middle compared with other years whence one half of such a year seeming to belong to the preceding the other to the following year of another Aera the Epocha thereof is placed by some a year sooner by others a year later So that by reason of these and other Confusions incident to Chronologie it is very difficult I may say beyond humane Industry to come to an Exact and Correct Determination and therefore every one may and will take leave to abound in his own sense CHAP. IV. Of the Day as applyed to measure the Year § Different Accounts of Years among the Ancients and Confused § The Julian Year § Inequality of Natural Days and Reasons thereof With a short Table of Equation HAving no visibly distinct Periods or Measures of our Time for all other Motions but the Day and Year and Lunar Month the Day is best known to us being but of a short and easie observation and having so visible change of parts and easie to be measured by Mechanic Motions But the Year is more obscure though we are sensible of the Seasons yet it is hard to find the Beginning and End of it We are therefore constrained to make the Day serve to measure the Year as well as we can though not commensurately to each year as has been shewed before but by collecting the Fractions of Days in several Years till they amount to an even Day and then by Addition or Subtraction reducing the Year as near as may be to his just course I say by Addition or Subtraction of a Day when it is so collected to or from the Account of the Days of the Year at certain Periods As at every Fourth Year to add the Bissextile-day and at every Period of about 134 Years to omit it which is to subtract it Not regarding the smaller Inequalities in the mean time all along which will never exceed the compass of a Day before the Year be set right For the reason of this Subtraction see more afterwards This uneven Measure of the Year by collection of Days and the Measure not being then so perfectly known to the Ancients rendered it very difficult for them to keep a just Account of Years and to transmit a true Chronology to succeeding Ages Their Civil Constitutions of the Year were after different manners in several Nations some using the Sun's Year but in divers fashions and some following the Moon finding out Embolism's or Equations even to the addition of whole Months to make all as Even as they could But it may be thought that whatever Methods the Ancients did apply in their Computations and Setlements of the Spaces of Years yet they might probably have been kept in some Bounds of their Accounts by the visible Characters of those Stated Measures viz. Day and Year and most especially of the Year For the Night and Day always made a Natural Day of 24 hours in all places remote from the Unhabitable Poles of the World and Winter and Summer always measured a Year So that if they observ'd but Winter and Summer they could not lose a Year in their Accounts though they were perhaps not able to measure the Year exactly by Days therefore it was as usual to them to express a large Space of Time by so many Winters or Harvests as by so many Years I must not dissemble that they who inhabit just under the Line may seem to have two Winters and two Summers But there also they have four Interchangeable Seasons which is enough whereby to measure the Year But at last Julius Caesar a year before his Death and 44 or 45 before Christ with the help of Sosigenes an Aegyptian universally setled the Account of the Year which we of England follow to this day and which from him is stiled the Julian year He supposed the Solar year to contain just 365 days and a quarter or 6 hours and ordered the continuance of the Account of years by adding a day to every fourth year collected from the odd six hours remaining above 365 days at the end of the year making three years successively to consist of 365 days neglecting the odd 6 hours and the fourth year Bissextile or Leap-year of 366 days making thus as he thought a perpetual Equation of the yearly Account Having before taken notice of the Inequality of Natural days I shall before I pass farther say somewhat more of it in this place It is to be thought that of himself the Sun moves Equally through the Degrees of the Ecliptic But by reason of the Sun's Excentricity to the Earth and Obliquity to the Equator he appears to us to move Unequally The Sun passeth 360 Degrees of the Ecliptic i. e. round it in 365 days and almost a quarter of a day So it is plain that the Sun does not pass a whole Degree of the Ecliptic in a day one with another but somewhat less viz. 59′ 8″ but he is found sometimes to exceed that Number and sometimes to fall short of it So that 59′ and 8″ must be called his Middle or Mean Motion being between his two Extreams of sometimes going faster and sometimes slower which makes the Inequality of Natural days About the Summer Solstice being in his Apogaeum he is found by Observation to pass but 57 Minutes in a Day And at the Winter Solstice in his Perigaeum 61′ according to his Apparent Motion The Consequence whereof is That the Natural day of 24 hours is shorter in Summer than in Winter So that the Sun is 8 or 9 days longer in passing the Northern half of the Ecliptic than the Southern Take but your Almanack in hand and number the days of the Sun's passage between the Equinoctial Points and you will find that from the Sun's Entrance into Aries to his Entrance into Libra are about 4 or 5 hours above 186 days And from thence to his Entrance into Aries are so much less than 179 days 7 or 8 days difference Which Entrances vary every year as Influenced by the Unequal Measures of the Julian year in respect of the Leap-year and the three following years This in general might be supposed to be caused by the Sun's Excentricity to the Earth but amongst Astronomers there is a farther account of Inequality of days and lately confirmed by experience of our Watches and Clocks which has 4 Periods in a Year and seems so Irregular that Excentricity alone cannot solve it which else might
answer the general Variations by Half-years But this having four Periods in a Year must have another joint Cause which is the Obliquity of the Ecliptic to the Equator and from thence the Diurnal differences of the Sun 's Right Ascensions which finish their Variations in each Quadrant of the Circle of the Ecliptic and this being joined to the former Inequality arising from Excentricity makes these Quarterly and seeming Irregular Inequalities of Natural days But yet these Differences are not so sensible to us as to give any disturbance to our Account and Use of Natural days but rather affect the Measures of the Seasons of the Year This Inequality hath been diligently observed by several of our Ingenious Clock-makers and Equations been made and used by them But the most Authentic Tables of Equation of Natural days are handed to us by the Skill and Diligence of our Great Master in Astronomy Mr. Flamstead and published in Mr. Parker's Almanacks for the Years 1692 and 1693. Out of which we may take a Compendious View only of the Days of Extreme Inequality and of the Mean between them referring to the whole Table for a daily Account Supposing a Watch or a Clock to be made and set so exactly to correspond with the Day of the Middle Motion of the Sun that it will continue to go truly according to that Motion of the Sun for a whole Year the Sun's days sometimes lengthning and sometimes shortning I mean the Natural days the Accounts of the hours in the Sun-dial will vary from those of the Equal going Watch according to the Table following Month. Equation Watch. Jan. 31 14′ 49″ Too Fast Apr. 4 0. 0  May 4 4. 13 Too Slow Jun. 6 0. 0  July 15 5. 46 Too Fast Aug. 19 0. 0  Oct. 22 16. 1 Too Slow Dec. 12 0. 0  Jan. 31 14. 49 Too Fast CHAP. V. The Deficiency of the Julian Year and Calendar § And from thence Defects in our Ecclesiastical Computation and how to Reform it BUT to come nearer to our purpose in reference to the Calendar There is in this long tract of time a great Incongruity crept into our Calendar by the Deficiency of the Julian Year as we measure it The true Solar Year is computed to be constituted of 365 days 5 H hours 49′ Minutes and 16″ second Minutes so it falls short of the odd 6 hours by 10′ 44″ The Julian Year is made to consist of 365 days six hours neglecting the odd Minutes which neglect in tract of time has made a considerable Variation For the odd Deficient Minutes Deficient I mean in the true year from the Julian year of 365 days and full 6 hours viz. 10′ 44″ multiplyed by 134 as being collected in so many years arise to 24 hours or a whole day And as many times 134 years as are passed since Julius Caesar's time so many days will the true Account of the Sun's Motion and the Seasons caused by it vary and fall sooner than by the Julian Account We of England retain the Julian constitution of the year as at first established throughout the Roman Empire Unreformed without consideration of the said defective Minutes and continue our Accounts by it making our Dates Stylo veteri as they who follow the Gregorian Reformation do Stylo novo They have set their Calendar 10 days forward making our tenth of March their twentieth so that the Equinoctial day and all the other Accounts fall 10 days sooner in our Calendar than in theirs and will still in tract of time fall sooner till it be reformed In Caesar's time the true Vernal Equinox or Sun's entrance into Aries was reputed to be about March 24th which now by the aforesaid Defect of 10′ 44″ is fallen back to about the 10th of March The Ecclesiastical Computation of the Moveable Feasts regards the time of the Nicene Council Anno 325 at which Easter-day on which the rest depend was setled and fixed to be always on the first Sunday after the first Full-moon after the Vernal Equinox The Equinox was then on March 21 and in regard that we are now guided not by the true Equinox but by the Nicene Rule which supposed the Equinox to be always the 21 of March and we still follow the same Rule It hath caused a great Anomaly or Irregularity in our Calendar and wants to be reformed and the Equinox to be rightly computed as was designed in the Gregorian Reformation And being once reformed and set right it may be kept so as to the Sun without any considerable variaation for many Ages by omitting one Leap-year i.e. the Additional day at the end of every 134 years As we add a day every fourth year to adjust the odd six hours so to subtract a day in 134 years to adjust the deficient Minutes As for other nicer Observations in the course of the Sun as the variations of his Excentricity of his Apogaeum of his Declination c. which have very long Periods Astronomers may be consulted by those that are Curious since those Motions are not our Measures of Time Having therefore touched so far as we are concerned upon some Phaenomena of the Motions of the Sun we proceed now to those of the Moon CHAP. VI. Of the Lunar Month and Motion of the Moon her Quarters and years § Epacts explained § The Golden Number § Their Uses with Tables and particularly in relation to the first Column of the Calendar in the Common-prayer-book Several Difficulties about it resolved § Imperfections and Intricacies in these Accounts THE Moon has two Accounts of her Circuit which are her Months or as her Years of Revolution One her Periodic month or Month of Peragration which chiefly respects her own proper Motion or place in the Zodiac by which she like the Sun in his Year performs her Revolution round the Zodiac from any one Point of it to the same again And this is made in 27 D 74 H 43′ The other is her Synodic month or Month of Consecution and has relation to the Sun and Earth more particularly in respect of her Phases or various Shapes and of her Aspects to the Sun and therefore this Month of hers is chiefly or almost only consider'd in regard that the Sun is the chief Regulator of Time and of the Moon 's appearances to our Sight This is her Circuit from one Conjunction with the Sun which we call New-moon Change Prime to another Conjunction with the same and because when she passeth from her Conjunction by what time she shall have accomplish'd her Month of Peragration in the same Space of time the Sun will be advanced almost a Sign of the Zodiac which is 30 Degrees viz. about 27 Degrees Therefore she must overtake the Sun before she can be in Conjunction with him which requires about two days the Sun also in that time getting forwards about two Degrees more This Month consists of 29 days and a half Middle-motion in which her relation to the Sun