is as for the use of it Certain and not liable to any Error or Mistake It was stiled Aera Dionysiana or Aera Christiana and afterwards Vulgaris was added to it to distinguish it from Aera Christiana Vera as contended for though never in use Till then the Accounts in use were the Olympiads the Consuls Urbs Condita Indictions The Olympiads were a small Cycle but of four Years still repeated and numbring withall the Repetitions But Iphitus made them an Aera by accompting a continual Series of Expanded Years from the first Olympick and they were used both ways but chiefly the Olympiads by Quaternions CHAP. III. Of Epocha's Cycles or Periods § Of the Dionysian Period § Of the Cycle of the Sun and Changes of the Dominical Letter Containing also an Account of the Week and Bissextile With a Table of the Dominical-letter c. § Some other Periods particularly that called the Julian § The Indiction § Some Principal Aera's and Periods with a Table reducing them to the Year of our Lord. HERE if I may have leave to Digress and take in Notions though not so Pertinent to our present Design yet equally Profitable and Usefull to Young Students for whom this Discourse is intended I would in this Place say something more of Epocha's and Periods And first I take Epocha to be the Head or Beginning the Pause 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or Stop if you reckon up or backwards as far as you can And Aera the Continuation or Series of any Account of Years which is or may be supposed to be Extended and Numbred onwards as long as Time shall have a Being Secondly a Cycle or Period is an Account of Years that has a Beginning and an End too And then begins again and again as often as it ends and so obtains a Perpetuity The Aera has but one Beginning which is the Epocha if we speak strictly though the Words are often Promiscuously used And from thence a Continual Extension The Cycle or Period has its Continuation by beginning again as oft as it ends going as it were in a Circle and thence it has its Name Thus the Cycle of the Moon after every Space of 19 Years begins again toties quoties in infinitum I think we do more commonly use these words so as to stile a lesser Space a Cycle and a greater by the Name of Period and you may not improperly call the Beginning of a large Period the Epocha thereof For the Derivation of these Words Epocha and Aera I refer you to the Etymologists The aforesaid Dionysius or as some affirm Victorius Aquitanus about 70 Years before him considering that a small Cycle of Years by reason of its often Revolution cannot give so certain a Character of Time as a large Period contrived a Period usefull for Computation consisting of 532 years by applying the Cycle of the Sun 28 to that of the Moon 19 which multiplied together give the Number of 532 beginning as oft as those two Cycles take their Rise together at 1 as they did lately in the Year 1672. Dionysius however gave it a new Beginning by applying it to the Year of our Lord and therefore it was generally stiled the Dionysian Period This Period has had but 4 Beginnings since Christ viz. A. D. 76 608 1140 1672 and this present Year 1693 is the 22d year of this Period As the Cycle of the Moon serves to shew the Epacts and that of the Sun the Dominical Letter throughout all their Variations So this Dionysian Period serves to shew these two Cycles both together and how they proceed and vary all along till at last they accomplish their Period and both together take their Beginning again after every 532d year And it serves farther also which was the chief Design of it for more Certain Computation by how much it is a Larger and more Comprehensive Period and under a more Undeceivable Calculation The two Cycles which make this Period are or ought to be very well known to all One of them that of the Moon or Golden Number is at large explicated in the following Discourse The other that of the Sun so called because it shews the Sunday Letter being a Table or Cycle of the Changes of the Dominical Letter I shall briefly here explain Instead of the ancient Roman division of the Month into Nones Ides and Calends we reckon the Days of the Month in Order And instead of their accompting by their Nundinae quasi Novendinae their Mercates or Fayrs for the Country-People to come to Town every 9th Day for Commerce and Trade and to receive their Laws as the Greeks reckoned by Ten 's dividing their Month into 3 Parts we as the Hebrews number our Days by Weeks and their Returns after every 7 Days which the Jews did in relation to their Sabbath and possibly the Assyrians c. in relation to the Quarters of the Moon consisting each of about 7 days and we as Christians for our Lord's day We describe the Days of the Week by seven several Names as Sunday Monday Tuesday c. And to distinguish them in the Calendar there are 7 Letters appropriated and set in Alphabetical order before them and so repeated throughout the whole Year viz. A B C D E F G and some one of these is the Dominical Letter or the Letter for Sunday and the Letters following for the other Days as they follow But the Sunday Letter is not constantly the same but is changed once in every Common Year and in every Fourth or Leap-year twice And the reason is First because the Common Year does not consist of just Weeks but of 52 Weeks and one Day So that as the Year begins with A set before New-year's-day So it ends with A set before the last Day And the Year beginning again at A there will be two A A falling together Dec. 31 and Jan. 1. and if one of them the former happen to be Sunday the other in course must stand for Monday and then reckoning onward Sunday must fall upon the first following G and G will be the Dominical that ensuing Year Thus the odd Day shifts back the Dominical Letter every Year by one Letter And this Revolution would be terminated in 7 Years But secondly there comes in another odd Day every 4th Year being Leap-year And in that Year there are consequently two such Shifts the Sunday Letter being changed twice Once at the beginning of the Year and the 2d time towards the latter end of February by Interposition of the Bissextile or Intercalar Day called Bissextile because the 6th of the Calends of March is twice repeated And the reason why this was done in that Month and not rather at the end of the Year seems to be because by Numa's Institution for the better regulating the Year in imitation of what the Greeks had done before there had been an Intercalation of several Days at that very time in February To take a more easie
Foot Cubits Fathoms Furlongs Miles c. as the Quantity proposed shall require So if I be asked concerning Duration How long is the Age of a Man The common Answer must be with the Psalmist Threescore Years and Ten which are indeed measured by the Time so long as the Sun is in making seventy Revolutions round the Ecliptic which Revolutions we by Divine and Humane Authority call Years as a Stated Measure of Time by which we keep our Accounts And in the same manner less Durations are measured by Months or Weeks or Days And if they be yet less Then by the Parts of a Day viz. Hours Minutes c. The Celestial Motions numbred by an Act of the Mind as the Parts of them succeed one another secundùm prius posterius are the Original Measures of Time and by help of the Lights in the Firmament are so perceptible and easily known to us by the Interchanges of Light and Darkness and Succession of Seasons and Termination of Revolutions and the manifest Effects of them that from thence we have a more Familiar Secondary Measure of Time a kind of Standard measure of all other Motions or Rest or Duration alluding to those other Standard-measures spoken of before but with some Differences which I shall touch upon And these are principally the Day the Lunar Month and the Year I do not intend to fall upon nice Philosophical Disquisitions about the Nature of Time and Curious Questions relating to it But upon the Use of it in Vitâ communi from the visible Secondary Measures thereof agreed upon and practised according to both Divine and Humane Institution If the Revolution of the Primum Mobile be to the Curious the first Equal Standard-measure of Time and we may have such a Conception of it yet I see not how we can so easily discern and usefully apply this Motion as a Measure of Time but remotely by the guidance of the Lights in the Firmament For the Light of those Bodies doth immediately discover to us the Succession of their own Motion and Mediately that of the Primum Mobile whose Parts are numbred upon the Degrees of the Aequator Where we treat more generally of Time the nearest and easiest way is to be guided immediately by those Lights and make the Day and Month and Year our Measures of Time And as all other Measures of Time are reducible to these Three so we labour to reduce these Three though strictly of themselves Incommensurate to one another for Civil use measuring the greater by the less viz. the Year by Months and the Year and Month by Days and Parts of Days So that they may be indifferently used as one agreeable Measure of Time greater or less as there may be occasion to apply the Measure There is a great Difference which renders the Account of the Measures of Time to be of much more difficult and curious Contemplation than the other because the other Original Measures are to be found every where on Earth and the Standards of them Arbitrary whereas both Original and what we may call Standard-measures of Time are above in the Heavenly Sphears And because the other Measures before spoken of are of Continued Quantity Permanent and Visible and for the most part Tractable whereas Time is always Transient in a continual Flux neither to be seen nor felt nor reserved but only measured by an Act of the Mind by Observation and Application of those Motions which are the Measures of it We cannot keep by us settled and Permanent Material Standards of the Measures of Time as we do of the other There is another Difference That the Heavenly Motions though intricate are more Stated and Certain than the Terrestrial Models of the Measure of those other Quantities before discoursed of and are indeed both Originals and Standards And if we will also call the Day and Year Standard Measures it is because they are Unalterably Constituted by those Motions and are better known to us whilst we follow that Light which goes along with those moving Bodies and because they have some Stamp of Authority from the Almighty Lord of Heaven and Earth and from Regulations of the Calendar by Public Authority in several Governments And though from the former of these Differences I conceive we cannot so properly call the Celestial Motions Standard Measures because we cannot make any such Standing Measures to be reserved and kept for Public Use and produced when we please that they may be resorted unto and applied to the Measures which are used as is done in the Material Standard Measures and Weights as Yard Gallon Pound c. Yet from their Certainty which is the other Difference we may in some manner look upon them as a kind of Standard Measures because all Measures of Time are reduced to those we commonly use But they are improperly called Standards because as was said they cannot be made Standing Measures for to be such does not comport with the Nature of Time I had rather call them Stated Measures and we may conceive them to correspond with and supply the use of those other kinds of Standard Measures and having also some Stamp of Authority by which they are Setled and Stated something also different from Nature For as was said of Measures of Length and of Capaciousness and likewise of Weights So here also the Measures of Time are in their way subjected more or less to Civil Sanction Thus in Rome not to speak of other Nations Romulus and Numa and after them Julius Caesar Ordered and Constituted the Account and Computation of Years and Months which last Order we of England still follow though in long Tract of Time some Anomalies are crept in which makes our Calendar vary from the true Account of Time There is one remarkable Instance of this how we measure our Time by Law and not by Nature and that is the Solar Month which tho' it be no Periodical Motion and not easily Mensurable and the Months unequal amongst themselves and not to be measured by Even Weeks or Days as naturally consisting according to the Mean Motion of the Sun of 30 Days 10 Hours and near half an hour Yet by Civil Sanction and Constitution this is made to us the chiefest Measure of the Year And these Months are measured by Integer Days though unequally some by 31 days some by 30 and one by 28 and every fourth Year by 29. This Solar Month I say is by Civil Sanction and Authority notified in Authentic Calendars made for our use the chief Measure of the Year a kind of Standard by which we measure out our Time But these Months do not so much come under my Consideration but more properly in order to Ecclesiastical Computations the Lunar Month which is Natural and Periodical and by which the Moveable Festivals of the Christian Church are regulated We read in Moses That God created Lights in the Firmament of Heaven to divide the Day from the Night and appointed
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