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
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-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
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-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
may be found by Computing Likewise for time to come There will be an Eclipse of the Moon the 27th Day of June 1694. These are easie and usefull known Characters of Time deduced from those Measures setled by Authority and Use And in all Ages where they did not all Compute by Weeks yet still the Year was measured by Months though sometimes by Solar and sometimes by Lunar Months and differently ordered as it pleased the Authors of those Constitutions And if the Reader by all that has been said find the Satisfaction of seeing plainly the Reasons and Nature and Use of the Measures for Time and of the Constitutions and Alterations and Reformations of those Measures it is what the Author designed To that end this Discourse has been carried on with all possible plainness suitable to those for whose sake it is made Public the Author not pretending nor owning ability to perform great Matters in this kind or any other or to make new Discoveries Though on another Subject concerning the Letters of the Alphabet more accurately considered by him for a further End than a bare Philosophical Contemplation on the Alphabet viz. The Application of it to a Dumb Person then with him in his house which obliged and urged him to more Sedulity in bending his Thoughts upon it such as are since published Anno 1669 in a Treatise Of the Elements of Speech He thinks he may without Vanity because not without sufficient Provocation Commend and Submit to the Readers impartial judgment a certain new Hypothesis of the Natural Production and Differences of the Letters of the Alphabet Reducing all different Articulations of Consonants to instance in them made by the Organs of Speech to the Number of Nine and Supplying the Essential Differences of the remaining Number of those Letters by finding out 4 sufficient Discriminations of Letters from their Material Part i.e. Sound which is Articulated there being four Differences of Sound which go to the making of Letters viz. Breath Oral as in Whispering Voice Oral Breath Ore-Nasal and Voice Ore-Nasal Thus P B M and a Spirital M‘ which is not in use are distinguished by those Differences of Sound though they all have the same and but one Articulation by the Organs of Speech Like as we may with one Seal Impressed upon Wax of four several Colours suppose Yellow and Green and Red and Black make four as different Signs as from four different Seals upon the same Coloured Wax Thus Every single Articulation Impressed upon those four distinct Matters of Sound produceth four distinct Consonant Letters which ought to be ranged in every single Classis of Articulation Thus to one and the same Articulation by the Lips belong B P M M' and differ only in Sound as hath been said Now nine Articulations Impressed upon four sorts of different Matter of Sound make in all thirty six Consonants wherein are comprised all possible Consonants used by any Nation in the World And they do Orderly and Equally fill up the Abacus and Classes of Consonants Like as nine distinct Seals Impressed upon four sorts of Wax viz. of four several Colours may serve to make thirty six Sensible Discriminations for Signs to be agreed upon for Mutual Communication For the Impression of a Lyon upon Blackwax will differ from that which is made upon Red as sensibly as a Lyon differs from a Boar on the same coloured Wax We may impute the Formal Differences to the nine Seals which give the Impression and the Differences Material to the four sorts of Wax which receive them resembling the 9 Articulations in Speech giving Form and four sorts of Sound being the Material Part which receives the Impressions of the Articulating Motions Whereas other Writers on this Subject taking for granted the Number of Articulations to be equal to the Number of Letters each Letter having a peculiar distinct Articulation in their Table or Abacus of Letters rank some of those Letters in Ternaries some in Pairs and let some stand Single not giving any Reason for the void Spaces in the Abacus nor for the Order in which they are placed Except as to the latter by referring to the Parts of the Mouth where the Articulations are formed beginning ex gr at the Labial Letters of which they find three and suppose them to be framed by three several Articulations by the Lips whereas there is indeed but one Articulation which differenceth the Labial Letters from those made by other Organs but between themselves these three are differenced by the Matter of Sound Articulated Then rejecting and laying aside such Letters of those thirty six as are not Gracefull nor Easie to be pronounced having enough besides Seventeen Consonants are cast off for reasons there assigned and marked in the Abacus with an Obelisk and 19 are retained for the use of Speech And it is no wonder if they who considered but 19 or about that number could not tell how to Rank them in Equal Classes whereas in the Author's Abacus or Table of Letters the whole number of Consonants viz. 36 will be found Equally ranged with their proper Differences and Productions 19 of them being owned for the use of Speech and the remaining 17 noted with a Mark of Rejection For which the Reader is referred to the aforesaid Treatise Which Treatise lying not so plain for want of an Index here is annexed a short View of the Contents of it Contents to the Treatise Of the Elements of Speech OF Speech in General Pag. 1. Of Letters in General 6 Of the Alphabet Form and Matter 16 Of the Organs of Speech and of the Material Part 22 Organs of the Formal Part 25 Variety of Motions and Materials 32 Consonants Their Differences 36 By Close Appulse P. B. M. T. D N. 37 By Close Appulse K. G. Ng. 38 Scheme of Occluse Consonants 40 By Pervious Appulse ibid. F.V. Th. Dh. 41 S. Z. Sh. Zh. 42 L. R. 48 Scheme of Pervious Consonants 52 Table of all Consonants in use 53 Explication of it 54 Table universal of Consonants 62 Short Review 63 Concerning H. 67 Concerning Gh. Pag. 72 Differences by peculiar Tone of several Nations 75 Of Vowels 79 Scheme of the whole Alphabet 96 Of Accent and Emphasis 98 Copies of these Contents are Printed and put into Mr. Luke Meredith's hand to be delivered gratis to any Possessor of the said Treatise Gentleman or Bookseller to be prefixed to the Book Addendum as an Appendix to the Paragraph ending after the Moon and Sun's Month. pag. 88. line 5. It is here needfull to be better explained how the Moon is said to be Behind and how Before the Sun both which or either of them it may be understood to be The Moon goes round her Circuit above 12 times whilst the Sun passeth once about his And so many times overtakes and also goes beyond the Sun In every time to keep her habitude to the Sun she goes more than a Round having the whole Zodiac and about
A DISCOURSE Concerning TIME With Application of The Natural Day and Lunar Month and Solar Year as Natural And of such as are derived from them As Artificial Parts of Time for Measures in Civil and Common Use For the better understanding of The Julian Year and Calendar THE First Column also in our Church Calendar explained With other Incidental Remarks By WILLIAM HOLDER D. D. Canon Residentiary of St. Paul's London and Fellow of the Royal Society London Printed by J. Heptinstall for L. Meredith at the Star in St. Paul's Church-Yard 1694. THE PREFACE THE Reader is not to expect here an Elaborate Methodical or Just Treatise for the entertainment of the Learned but will find a Collection of several Memoirs such as may be all of considerable use to those who are not Proficients in this kind of Knowledge The Author having casually discoursed on the ensuing Heads to one or two Ingenious young Gentlemen and for their better Comprehension and Remembrance put many of them dispersedly in Writing He has now revised those Papers and enlarged them Digressing sometimes and taking in some Astronomical Chronological and other Remarks very worthy and equally needfull to be known though not so directly pertinent or necessary to the Explication of the Julian Year and Ecclesiastick Calendar which was his chief Intention but yet giving some light unto them He hath since been prevailed with to let them be published as being thought profitable for the use of Younger Students whereby to possess them with some usefull Notions such as may prepare and induce them with more Pleasure and Ease to advance into the Study of deeper and larger Contemplations of this kind And for the use also of such as have not considered these things but are content for want of easie Introduction to be ignorant and careless of this so necessary Knowledge of whom there are too many to be found the more the Pity That they if they please may see the Grounds of our Calendar and Measures of Time and know the Reason of the Differences between the Reformed Calendar and our old Julian in respect of Accounts of the Progress of the whole Year and of the Moveable Feasts c. 'T is hoped also This plain Discourse may be usefull to many of our Clergy whom it concerns to have some knowledge of these Matters CONTENTS CHAP. I. Of Measure in General page 1 c. More particularly of Time and Difficulties concerning it p. 10. CHAP. II. Of the Sun's Motion Measuring Days and Years page 22. And making them our ordinary Measures of Time page 24. Difficulties of Accounting by them page 28. The Inequality of the Sun's Motion and of the Solar Days briefly mentioned ibid. From Day and Year other Measures derived page 31. And their Vsefulness ibid. and page 36. The Division of a Circle into 360 Degrees page 33. CHAP. III Of Epocha's Cycles or Periods page 39. Of the Dionysian Period page 41. Of the Cycle of the Sun and Changes of the Dominical Letter p. 43. Containing also an Account of the Week ibid. and Bissextile 45. With a Table of the Dominical Letter page 47 c. Some other Periods particularly that called the Julian page 48. The Indiction page 49. Some principal Aera's and Periods with Tables reducing them to the Year of our Lord page 52 c. CHAP. IV. Of the Day as applied to measure the Year page 55. Different Accounts of Years among the Ancients and Confused page 57. The Julian Year p. 58. Inequality of Natural Days and Reasons thereof page 59. With a short Table of Equation p. 64. CHAP. V. The Deficiency of the Julian Year and Calendar p. 65. And from thence Defects in our Ecclesiastical Computation and how to Reform it page 67 68. CHAP. VI. Of the Lunar Month and Motion of the Moon her Quarters and Years page 69. Epacts explained page 73. The Golden Number page 75 c. Their Vses ibid. c. with Tables 79 80. and particularly in relation to the first Column of the Calendar in the Common-Prayer-Book 81 85 and 96. Several Difficulties about it resolved page 88 c. Imperfections and Intricacies in these Accounts page 90. 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 page 92. The Sun's Account above ten days too late and the Moon 's above four and needs Rectification page 94. CHAP. VIII Conclusion containing some short Observations and Practical Deductions page 97. 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 page 105 c. Of which the Contents also are annexed page 111. A DISCOURSE Concerning TIME c. CHAP. I. Of Measure in General § More particularly of Time and Difficulties concerning it GOD made all things in Number Weight and Measure and gave them to be considered by us according to these Properties which are inherent in Created Beings But without an Act of the Rational Soul comparing these in their several kinds one to another they would be as nothing And therefore the ancient Greeks very fitly termed the Habitude of any one of these to another of the same kind 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the Ratio of it because it is our Rational Notion of their Equality or Difference when we apply one Number or Weight or Measure to another of the same kind and consider and compute what Proportion one bears to the other It cannot be expressed what universal and necessary Use there is of the Consideration of Number Weight and Measure in Common Life Not to speak of Order and Beauty which consist of Symmetry nor of Building Houses and Ships all humane Society is upheld and managed by the use of these No Commerce or Exchange or Trade can be without them and consequently no Benefit of Society And therefore the Sagacity of Learned Men has advanced Arts and Sciences for the better knowledge and use of them For Number Arithmetick for Weight Staticks and for Measure Geometry And for finding out the Original Measures of Time of which I shall have occasion to speak Astronomy All Magnitudes are capable of being measured but it is the application of one to another which makes Actual Measures and Things Actually measured Measures ought to be Stated and known before they be applied to measure other Quantities A Measure therefore has reference to something that is or may be measured by it with application of the Mind Any given Length of a known Line under a certain Denomination may serve to measure out any other Length be it Equal or Unequal A Concave Measure of known and denominated Capacity serves to measure the Capaciousness of any other Vessel In like manner To a given Weight the Weight of all other Bodies may be reduced and so found out And Number in its way
2 93 33 3 94 14 4 95 25 5 96 36 6 97 17 7 98 28 8 99 39 9 1700 20 10 1 31 11 2 12 12 3 23 13 4 34 14 5 15 15 6 26 16 7 37 17 8 18 18 9 29 19 1710 11 1 11 22 2 12 33 3 13 14 4 14 25 5 c. c. c. Â Epacts as in the Month of July answering the Golden Numbers and Days of the Month as they stand in the Calendar Anno Dom. Epacts Golden Numb Month July 1709 29 19 D. 1 1698 28 8 2 27 Â +3 1706 26 16 4 1695 25 5 5 24 Â +6 1703 23 13 7 1692 22 2 8 21 Â +9 1700 20 10 10 19 Â +11 1708 18 18 12 1697 17 7 13 16 Â +14 1705 15 15 15 1694 14 4 16 13 Â +17 1702 12 12 18 1691 11 1 19 10 Â +20 1699 9 9 21 8 Â 22 1707 7 17 +23 1696 6 6 24 5 Â +25 1704 4 14 26 1693 3 3 27 2 Â +28 1701 1 11 29 Â Â +30 1709 29 19 31 So that as the Epact is i. e. the number of days by which the end of the Moon 's 12 Months at the end of the Solar year is found to fall short of the Sun 's New year So is the course of the Moon or her distance from the Sun accounted for the whole ensuing year and for every Nineteenth year after for ever as was supposed And the Golden Number is the Index or Character of the Epacts in a perpetual Cycle to find which of those 19 years the present or any given year is and consequently what is then the Epact and so shews for ever the yearly course of the Moon in relation to the Sun The Golden Number being the Index and Cycle of Epacts the principal use of it is to find the Epacts and so they both serve indifferently for the Accounts of the Moon and furnish you with many usefull Rules and Tables for several purposes As by the Golden Number and Dominical Letter given to find Easter-day for ever Such a Table you have before the Book of Common-Prayer By the Epact and Day of the month is found the Distance at any time how many days the Moon is from the Sun It is thus applied to find the Moon 's Age i. e. how many days are past since the last Conjunction which shews withall how near she is to her Quarters Full or next New-moon and is usefull to find her coming to the South and consequently the Tides c. The Moon 's age is thus found for any given day of any Month Add to the Epact the Day of the month and the Ordinal Number of that month from March inclusive because the Epact begins at March and the Sum of these casting away 30 or 29 as often as it ariseth is the Age of the Moon Ex. gr Febr. 2.1691 2 to find the Moon 's Age say thus Epact 11 Day of month 2 Month from March 12 Sum of these 25 The Moon is then 25 days old Again if it be sought March 25 1692 Epact 22 Day of month 25 Month 1 in all 48 cast away 30 and 18 is the Moon 's Age. The reason why you are so to reckon the Months from March by addition of an Unite every succeeding Month is because the Moon 's year of Twelve Months being 11 days shorter than that of the Sun it is in effect a Day for every Month which is thus accounted for You see then the chief use of the Epacts is as well as we can to reconcile the Twelve Months of the Moon to the Sun's year or Twelve-month and to measure every single Lunar month all along by the days of the Solar month i. e. to make any day of any Solar month so to correspond by help of the Epacts as to shew the present day of the Month of the Moon which day according to the number of it is called the Age of the Moon which might have succeeded a little better if it had pleased the Institutors of the Civil Months of the Sun to have ordered and placed them alternately odd and even of 31 and 30 days beginning suppose at March and ending at February And February in Common years to have 29 days and in the Leap-year 30. But since the old way obtains by Prescription we must follow it though with some inconveniency The foregoing Rule to find the Age of the Moon at all times on any day of any Solar month cannot shew precisely an exact account of the Moon because of the Inequality of the Motions of the Sun and of the Moon and of the Number of days of the Solar months though the last of these is somewhat helped by observing the old Rule Impar Luna pari Par fiat in Impare Mense i. e. by casting out for a whole Month of the Moon when there is occasion 29 in Solar months of 30 days and 30 when the Month consists of 31 days I say though the aforesaid Rule is not exact yet it comes so near that it is very fit and necessary for common use being always at hand or in memory If the Lunations be observed and set down for a whole course of the Golden Number or Cycle of 19 years which is the Cycle of the Moon the same Observations will serve and be verified through the next Cycle of 19 years in the same order and so on for succeeding Cycles as hath been supposed for ever And therefore the Golden Number in the first Column of the Calendar before the Book of Common-Prayer is as a Rule for ever set before the Day of each Month in which the Change or Conjunction of the Moon shall happen whensoever such is the Golden Number as is there set down As if you look ex gr upon the Month of July you will see 19 before or against the first day 8 before the second 16 before the fourth 5 before the fifth c. That is whensoever the Golden Number is 19 there will be New-moon on the first day of July when 8 on the second if 16 on the fourth if 5 then on the fifth day c. And though in the aforesaid Column the Numbers which denote the Golden Number seem to stand confusedly without any order 19 8 and after a space between 16 5 yet they precisely follow the Progressive order of the Epacts of which they are but Indices beginning at the greatest Epact viz. 29 and so descending in order till they come to the least viz. 1 as you may see in the two middle Columns of the second Table preceding where the Golden Numbers 19 8 16 5 13 2 10 c. are Indices of the Epacts in order viz. 29 28 26 25 23 22 20 c. And the reason why they fall in that order in the Calendar from the greatest Epacts progressively to the least is because the greatest Epacts denote a greater distance of the Moon behind the Sun and consequently
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
one of the 12 Signs more to pass after her Conjunction before she overtakes the Sun again And if she may be said to overtake the Sun she may not improperly be said to be behind him untill she overtake him If we look back upon the last pass'd Conjunction Then the Moon was joyned with the Sun and moving swifter is now got before him If upon the next approaching Conjunction Then the Moon is drawing towards him and is behind him Thus when the Epact is 1 the Moon at the end of the year will be 11 days in her progress beyond or before the Sun having got so far since the last Conjunction But in respect of the next ensuing Conjunction to which her Motion tends she will be found about 19 days behind the Sun Thus she is both before and behind the Sun 12 or in some years 13 times in a year But since the Epact is properly the Number of Days by which the Moon has finished her 12 Months sooner than the Sun his or which amounts to the same the Number of Days of the Age of the Moon viz. which have passed between her last Conjunction and the Close of the Sun's year tho' in the Remainder or Complement of Days which respect her next ensuing Conjunction she be behind the Sun yet in the former Respect she must be said to be before him And therefore it may be less exceptionable to Consider her as before the Sun and Correct those Passages which seem to look otherwise To explain this more clearly If two run a Race he that comes first to the Post is propeâ—ly said to be before the other So the Moon beginning her 12 Months with the Sun and arriving at the End of them 11 days before the Sun is properly said to be so much before him And Consequently both of them continuing their Course of Revolutions she keeps on throughout the whole ensuing year 11 days before the Sun in her Synodic Chase besides her gaining more over about a Day in every Solar Month i. e. 11 days in 12 Solar Months Therefore as was said p. 82. to accommodate the Course of the Month of the Moon to that of the Sun we add all along to the day of the Solar month the Number of those days in the foregoing year between the latest Conjunction of the Moon and the End of the Sun's year which are therefore called Epacts together with the Number of Months from March We might more properly reckon by the Day of the Moon 's Month as we do by that of the Sun but then The Day of the Month would be an ambiguous term relating as well to the Moon as to the Sun Therefore it is usually termed The Age of the Moon which is the same with the Day of her Month but wholly avoids the ambiguity Now the Epacts varying every Year by progression of 11 It is so that the Greater the Epact i. e. the Age of the Moon at the End of the Sun's year happens to be so much Shorter will be the Remainder or Complement of days to the next Conjunction which shews the Reason of the Order of Epacts pointed at by the Golden Number in the first Column of the Church Calendar I take the Month of July there in which to make Instance because it begins with the greatest Epact 29 pointed at by the Golden Number 19 The Reader will find those Columns in the said Calendar very carelesly Printed but they may be easily corrected by the Table foregoing observing the order of those Numbers When the Epact is 29 and Golden Number 19 as it was 1690 and will be 1709 The true Complement to the next New-moon will be but half a Day So the Moon will be in her Change not truly but according to that Rule by the Golden Number the First of July and that will be the first day both of the Sun 's and of the Moon 's Month and you may reckon the Age of the Moon by the Day of the Month throughout that one Lunation Otherwise the Moon 's Age must be reconciled to the Day of the Month by the Epacts and Number of Months from March The Solar month being made the Standard to which other Measures are reduced When the Moon Changeth according to the same account on the second day of July as Anno Dom. 1698 the Epact will be 28 Golden Number 8 and the Second of July will be the First of the Moon When on the Fourth of July as Anno Domini 1687 1706. Then the Epact is 26 and Golden Number 16 and the Fourth of July the First of the Moon And thus still the Epacts decrease in order as the Days of the month go forward Now this shews plainly the Reason of the Regular progressive Order by Decrease of the Epacts and of the seeming Disorder of the Golden Number in that Calendar throughout the Month of July And in the same manner in all other Months always allowing for the Differences in the Places of those Numbers which will arise from the Inequality of the Solar and Lunar months From whence it is That in the Year 1709 Epact 29 the Moon 's Change will be allotted to Apr. 4. May 3. June 2. July 1 and 31. August 29. September 27 c. If you ask Why c. p. 88. FINIS CORRIGENDA PAg. 73. lin 7. before or beyond the Sun lin ult 11. days before him Pag. 87. l. 13 14. of the Moon before the Sun and consequently a nearer approach Pag. 88. l. 20. against 19 Days of 29 or 30 in the Calendar l. 23. against them and sometimes an Eleventh day viz. the Space between the end of one Cycle and beginning of another Pag. 95. l. 3. for Allowing r. Abbridging