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
them for Signs and for Seasons and for Days and for Years Gen. 1.14 The visible Motions of all the other Lights of Heaven might afford us several Measures of Time if we could number them But because most of those Motions are not so evident to us and the great Lights are sufficient and serve also to measure even the Motions of those other we therefore following the Guidance and declared Design of the Almighty Providence deduce our Measures of Time from the successive Motions of the Sun and Moon and most from the Sun Both of them having Signal Motions and giving sensibly Apparent Signs the Sun of Seasons and of Light and Darkness i.e. of Years and of Days The Moon of her changeable Habitudes to the Sun and consequently of her Phases or different Appearances to us and of her Seasons For she makes also four Quarterly Seasons within her little Year or Month of Consecution I need not add how Generally and how Much those Quarterly Seasons of the Moon are observed CHAP. II. Of the Sun's Motion Measuring Days and Years and making them our Ordinary Measures of Time § Difficulties of Accounting by them § The Inequality of the Sun's Motion and of Solar Days briefly mentioned sect From Day and Year other Measures derived § And their Usefulness § The Division of a Circle into 360 Degrees WHether the Sun actually moves out of his place or else is fixed upon his own Center and only seems to move and the Motions be attributed to the Earth after the Copernican way which of late is more generally favoured because it does much better and more easily solve all the Phaenomena Yet it is still the Sun which according to the Scripture by his Light governs the Day and by his Light and Heat makes the Seasons of the Year and terminates to us and discovers unto us the Revolutions of the Earth supposing the Motion thereof both in it self and also about the Sun And it is all one as to our Sight and Calculation of Time whether the Motion be attribured to the Earth or to the Sun As the Distance is still the same whether we fansie the Shore to recede from the Ship or the Ship to move from the Shore I shall therefore in this Discourse because of Prepossession of the one and Prejudice against the other suppose the Sun to move according to the Ptolemaic System First then from the Motions of the Sun as Original Measures are constituted for our use Two most Signal Universal Natural Distinct Perceptible Measures of Time which are as Standards for us Mortals to measure our Time by And these are the Day and the Year The Day i. e. the Natural Day 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 though it be accounted in General to be measured by one whole Revolution of the Primum Mobile and with it of the Equator upon the Axis of the World Yet more precisely and truly it is measured by the Revolution of the Sun carried along with the Motion of the Primum Mobile upon the same Axis either in the Equator or in less Circles very near Parallel to the Equator which are therefore called Parallels For the Day being visibly governed by the Sun is a little longer than the Revolution of the Equator so much as is occasioned by the Advance of the Sun in his Annual contrary Motion along the Ecliptic in that Space of Time which is about one Degree of the Ecliptic and which the Sun passeth in about four minutes of an hour I say the Solar Day from the Meridian of a Place on Earth round to the same Meridian again is a little longer than the same Revolution of the Equator viz. so much longer as the same Point of the Equator is returned sooner to the same Meridian than is the Sun which in that Space of time by his Annual contrary Motion Eastward will be advanced near a Degree of the Ecliptic cross to the Motion of the Equator As suppose the Sun to be in the first Point of Aries i. e. in the Equinoctial then by what time the first Point of Aries will be carried round with the Diurnal Motion of the World contrary to the Order of Signs from one Meridian to the same again In that time the Sun will be advanced as was said near one Degree of Aries contrary to the other Motion and so will be found distant from the said first Point about a Degree and will require about four minutes of an hour to be brought back by the Motion of the Primum Mobile to the same Meridian i. e. The first Point will return to the Meridian sooner by about four minutes of an hour than the first Degree of Aries whereabout the Sun will be found at that time And so much the Sun 's Diurnal Motion is longer than the Revolution of the Equator As a Natural Day is measured by the Revolution of the Sun from any one Meridian to the same Meridian again So a Year is measured by the Motion of the Sun round the Ecliptic upon the Axis of the same from one Point of the Ecliptic suppose from the first Point of Aries to the same Point again And this Revolution is performed Obliquely and Contrary to the other so that the Day and Year seem not to correspond with or regard each other The Year is measured to us by the Revolution of the Sun in the Ecliptic The Day by his Motion in or Parallel with the Equator The Year by the Sun's Motion Eastward in Consequentia or secundùm Seriem Signorum The Day by his Motion Westward in Antecedentia or contra Seriem Signorum The Day is no aliquot part of the Year strictly speaking neither to Compound or Divide the Year so much as by Units If the Year comprehend Days it is but as any Greater Space of Time may be said to comprehend a Less though the Less Space be Incommensurate to the Greater And from these differing Properties of Day and Year arise Difficulties in carrying on and reconciling the Supputations of Time especially in long Measures Although it must be confessed that for Vulgar Use where is no need of or regard to Exact Calculation we have no better Measure of a single Year than the Day and the Artificial Solar Month consisting of Even Days Because the Succession of Days is so visible and so easily Numbred that by these we may keep as good an Account of the Year as is needfull to our Common Occasions But if we thus measure many Ages of Years by Even Days our Computation will be perplexed For the Year without regard to Days ends and is terminated with an odd day and odd hours and odd minutes and odd second minutes if we go no farther So that it cannot be measured by any even Number of Days or Hours or Minutes The Circle of Degrees in the Ecliptic which make a Year are 360 the Circle of Days within a Year is broken into 365 and almost a Quarter The Sun is
carried round the World backward the daily Motion compared with the Annual 365 times and almost a Quarter while he makes his own Round forwards of 360 Degrees of the Ecliptic So no Circle of Even Days can make a Year which as was said creates difficulty in keeping account of Years And the very Steps which the Sun appears to us to make through the Ecliptic are Unequal as also the Days if one be compared to another successively throughout the Year are found not to be Equal and will not justly correspond with any Artificial or Mechanic Equal Measures of Time as by Watch Clock c. So that we are to find out the Extremities on both Sides and from and between them the Midle dayly Motions of the Sun along the Ecliptic and to frame Tables of Equation of Natural days to be applied to the mean Motion by Addition or Subtraction as the Case shall require which are styled Prosthaphaereses The Greek word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 being fitted to comprehend both addition and subtraction The Day is limited to us by the Interchanges of Light and Darkness and the Year by the successive Seasons of Winter Spring Summer and Autumn And these are Signal and Certain tho' not Original Measures of Time constituted by the Revolutions and manifested to us by the Light of the Sun And we have no other Measure save one of the Moon but are as we say Artificially made out of these by Compounding or Dividing them No other Measure of Time deduced from any other Original than the Motion of the Sun can be so evident to us For these are apparent at least after a gross manner to all Mankind and to almost all Living Creatures others only to the Learned in Astronomy or else derived from these by Institution for Civil Use And from these Constituted Measures and Denominations of Time viz. Day and Year not excluding the Lunar Month all other Measures of Duration or Successive Motion are Artificially contrived for Civil Use by dividing these into less parts or Collecting and Compounding them The Day for Small Measures chiefly by Partition and the Year for Great by Collection of Numbers of Years Or we may measure by Numbers of Days and Parts of a Year Some divided the Natural day comprizing Day and Night into four Parts or Quarters for the Day and four for the Night and each of these Quarters consisted of three Planetary Hours The Artificial day from Sun-rise to Sunset be it longer or shorter being divided into 12 Equal Hours and the Night likewise into 12 Three of which Hours made one Part or Quarter But the Hours of the Day were always unequal to the Hours of the Night according to the Increase or Decrease of the Lengths of Days and Nights Only if the Sun were in the Equinoctial or the Inhabitants under the same then the Days and Nights being Equal so would the Hours be also But the General Usage is to divide the whole Natural day into 24 Equal Hours an Hour into 60 I Minutes a Minute into 60 II Second Minutes a Second Minute into 60 III Thirds and so on And by thus dividing the Day we compute the smallest Measures of Time and by Compounding Years we measure the Greater Spaces of Duration But we must observe that the Day is not thus divided by Nature as it is into Light and Darkness and by the Meridian into Noon and Midnight But this Division as most others are is Artificial and at our pleasure by Consent of Nations We may observe likewise that the common Division of a Circle into 360 Degrees or Parts is also Artificial and Arbitrary But it is well chosen and pitched upon as being a Number that abounds with Integer Aliquot Parts and therefore most apt for Partition and being as near as may be suited to the number of Days which the Sun makes in a Year in compassing his whole Circle of the Ecliptic viz. 360 to 365. And in both respects it is best fitted for Astronomical Uses Of the former of these the Aliquot Parts of the Number 360 take a short View as follows 1 360 2 180 3 120 4 90 5 72 6 60 8 45 9 40 10 36 12 30 15 24 18 20 In toto 23 several Aliquot parts The Number 6 is celebrated for having all Aliquot Parts viz. 3 2 and 1 and for being composed of the Aggregate of them all and therefore is stiled The Perfect Number And 10 is the first of the Saracenical Characters or Figures with Cypher that great Friend to Calculation or rather which changeth Calculation strictly so called into easie Computation Now the Number 360 consists of the Square of 6 viz. 36 multiplied by 10 or having a Cypher added to it Of these 360 Degrees or Parts of a Circle every one may be supposed to be subdivided into Minutes Seconds Thirds c. And these Parts are marked alike with the Parts of an Hour ex gr For Hours 3 H 2 I 5 II 4 III and so onwards For Degrees 3 Gr or 3° 2 I 5 II 4 III c. i. e. 3 Hours or 3 Degrees 2 Minutes 5 Seconds 4 Thirds and so forwards A Minute being 1 60 of an Hour or of a Degree a Second 1 60 of a Minute a Third 1 60 of a Second c. So that one Hour or Degree contains 60 I 3600 II 216000 III and as many Fourths IIII as is the last Number multiplied by 60 viz. 12960000 IIII almost 13 Millions By Composition or Joint Number of Days besides such as have been formerly in use we have now chiefly the Week made of seven Days and a Month made of 4 Weeks or 28 Days By Partition or Gross Dividing of the Year we have the 4 Quarters or Seasons of the Year we have 12 Calendar Months intended however now Unequaly constituted at Pleasure to measure the Movement or Passage of the Sun through every of the 12 Signs of the Zodiac Lastly by Compounding or Numbring Years we keep Account of Ages and Publick Transactions and Memorable Accidents we make Cycles and Periods of Years as Decads Centuries Chiliads c. chiefly for the use of Computations in History Chronology Astronomy c. The Numbers of Years by which we measure the Spaces of Time having their several Epocha's or Beginnings as from the Creation of the World from the Floud from the first Olympiad from the Building of Rome or from any remarkable Passage or Accident giving us a pleasant Prospect into the Histories of Antiquity and of former Ages We Christians make the Reputed Year of the Nativity of our Blessed Saviour our chief Epocha from which to make our Dates brought in use first by Dionysius Exiguus Abbas who lived in Justinian's Reign about the Year of our Lord 528 And tho' his Computation may perhaps differ two Years from Truth as Helvicus or more Years as others are of opinion yet since it is and has been universally received over all Christendom our Compute by it
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
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
of the Moon to the Sun later than by true account they are found to be Therefore in the aforesaid first Column in the Calendar before our Book of Common-Prayer in any of the Months having found out amongst those Figures of that Column the Golden Number for the present year instead of the Day of the Month over against it reckon four Days and nine Hours before it and you have the Day of the Moon for Common use or which amounts to the same reckon that Day of the Month which has the Golden Number belonging to it over against it for the fifth Day of the Moon 's Age. Thus much hath been said of the Accounts of the Sun and Moon principally for the better understanding of our Calendar which being constituted after the old Julian year we may see what need there is of Rectifying it from those Anomalies which in this long tract of time since the Nicene Council have crept into it tending to the displacing of the Seasons of the year and misplacing the Festivals of the Church And to shew also the Grounds and Reasons of the Cycle of the Moon 's Epacts viz. the Golden Number which so often occurrs to us and of which we may make so frequent and continual use CHAP. VIII Conclusion containing some short Observations and Practical Deductions § With a brief Account of the Author 's New Hypothesis concerning the Natural Production and Differences of the Letters of the Alphabet relating to a Treatise formerly Published by him Of the Elements of Speech Of which the Contents also are annexed FRom what hath been said the Reader may amongst other things observe the Agreements and Differences of the Measures of Time to and from those other Material Permanent Measures of Distance and Capacity and Weight first spoken of And that of the Measures of Time some are Natural and Universal and some Arbitrary and Artificial and confined diversly to several Nations The Noctidial Day the Lunar Periodic Month and the Solar Year are Natural and Universal but Incommensurate each to other and difficult to be reconciled Yet we are constrained to make use of them as Measures to one another reducing the Disagreements by Observing and Collecting and allowing for their Differences Other Measures as Hour Week Month of Weeks Solar Calendar Months are more Artificial and Arbitrary for the use of Common Life and serve for Measures by Public Sanction Consent and Usage of so many Nations as are agreed to them and so are made very usefull by which to measure the other The former also though Natural and Universal yet are subject to the like Regulations If we measure the Year by Days there will be found a Remainder at last of about six Hours above 365 Days Whence Julius Caesar ordained that in the Account of Years the odd 6 Hours should be omitted in the First and a Second and a Third Year and collected every Fourth Year adding the bissextile-Bissextile-day to that year So you see we follow a Calendar not exactly true in Nature nor Equal but Artificially contrived for common Use by the Julian Institution And the Calendar Months are likewise Arbitrarily and Unequally setled by the same Power by which Months we to this day Account and they measure and make up that which we call the Julian year Now take a short Review of some Measures relating to the Calendar which have been more largely treated in the foregoing Discourse Measure the Year by Days and the remaining odd Part of a Day which 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or Numero rotundo is accounted six hours shews the Reason of the Bissextile or Leap-year Again Measure the Year by Weeks ' and the remaining odd Day for three Years successively and two odd Days in the fourth or Leap-year shew the Reason of the yearly Change of the Dominical Letter and the Nature and Use of the Cycle of the Sun which is 28. Again Measure the Year by Lunar Synodic Months and the remainding 11 days by which 12 Lunar months fall short of the Solar year make the Epacts and shew the Reason of their Observation and Use Again Pursue and Observe all the Variations of Epacts till they return to the same again and you will find that Revolution to be made at the end of every Ninteenth year which Number of Nineteen constitutes the Cycle of the Moon viz. the Golden Number And thus proceeds our Julian year But then Consider more narrowly that the odd Hours at the end of the Solar Year are not indeed fully six but are deficient 10′ 44″ which Deficiency in 134 years collected amounts to a whole Day And hence may be seen the Reason why the Vernal Equinox which at the time of the Nicene Council fell upon the 21st of March falls now above 10 days sooner viz. about the 10th of March which was one Reason of the Gregorian Reformation of the Calendar Again Consider that the Golden Number does not perfectly correspond with so many Revolutions of the Moon as are made in that time but the Period of those Revolutions is accomplished in somewhat less space than full 19 years viz. near an hour and half sooner which sets her back so much in every Cycle and collected amounts to a whole day in about 312 years which is called the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or Anticipation of the Moon So that following the Accounts of the Moon as directed by that perpetual Cycle of the Moon called the Golden Number placed for that purpose at the Nicene Council before and along the Ecclesiastic Calendar and continued still in ours we now find above four days difference viz. so much later than the true Account which was another Reason of the Reformation of the Calendar Remember lastly what has been observed before to shew the power of Legislative Authority and Consent and Practice in ordering and using Measures That the Measure of the Year by Solar months as constituted by Julius Caesar and a little altered by Augustus his Successor tho' it be Irregular Imperfect Unequal and wholly Artificial having little agreement with the Natural Measures of Time Yet because it is made to consist of Integer days and consequently more easie and Certain to be applied viz. Days to Months and Months to Years is become by the help of Authentic Calendars one of the Principal Measures of Time for Common use especially when joined with the other We measure the Beginning and Progress and End of the Year by these Months and the Days of which they consist we Date all Affairs Actions and Accidents of Humane Life and Reflect back upon them by the help of this certain Character of Time when joyned with other Measures as Such a Day of such a Month of such a Year in some certain Period or Epocha Ex. gr King CHARLES the Second was Crowned on the 23d Day of the Month of April in the Year of our Vulgar Christian Aera 1661 and the time elapsed to this is so many Years Months and Days as