reduce the days into 11 parts by multiplying them by 11 and they add thereto 650 elevenths which do make 59 days and 1 11. I find that these 59 days and 1 33 are the artificial days which were elapsed to the day of the Epocha since that an eleventh part of the natural day and an eleventh of the artificial had began together under the meridian of the Indies to which these Rules are accommodated 6. Divide the whole by 703. 7. Keep the Numerator which you shall call Anamaan 8. Take the quotient of the Fraction found Art 6. and substract it from the number found Art 3. The remainder will be the Horoconne that is to say the number of the days of the Aera which you shall keep Explication Having laid apart what is always added by the 5th Article it appears by the 2d. 3d. 4th 6th and 8th operation that as 703 is to 11 so the number of the artificial days which results from the Operations of the 2d. and 3d. Art is to the number of the days deducted to have the number of the natural days which answers to this number of the artificial days whence it appears that by making the lunar month to consist of 30 artificial days 703 of these days do surpass the number of the natural days which equal them above eleven days One may find the greatness of the Lunar Month which results from this Hyphothesis for if 703 Artificial Days do give an excess of 11 Days 30 of these Days which do make a Lunar Month do give an excess of 330 703 in the Day and as 703 is to 330 so 24 Hours are to 11 Hours 15 Minutes 57 Seconds and deducting this Overplus from 30 Days there remains 29 Days 12 Hours 44 Minutes 3 Seconds for the Lunar Month which agrees within a Second to the Lunar Month determined by our Astronomers As to the value of 59 Days and 1 11 which is added before the Division it appears that if 703 Days do give 11 to substract 59 Days and 1 11 do give 650 703 in the Day which do make 22 Hours 11 Minutes and a half by which the end of the Artificial Day must arrive before the end of the Natural Day which is taken for the Epocha The Anamaan is the number of the 703 parts of the Day which remain from the end of the Artificial Day to the end of the current Natural Day Use is made hereof in the sequel to calculate the motion of the Moon as shall be afterwards explained The Quotient which is taken from the number of the Days found by the third Art is the difference of the entire Days which is found between the number of the Artificial Days and the number of the Natural Days from the Epocha The Horoconne is the number of the Natural Days elapsed from the Astronomical Epocha to the current Day It should seem that in rigour the Addition of the Days of the current Month prescribed by the third Article should not be made till after the Multiplication and Division which serves to find the difference of the Artificial Days from the Natural because that the Days of the Current Month are Natural and not Artificial of 30 per mensem but by the sequel it appears that this is done more exactly to have the Anamaam which serves for the calculation of the motion of the Moon III. 1. Set down the Horoconne 2. Divide it by 7. 3. The Numerator of the Fraction is the day of the Week Note That the first day of the Week is Sunday Explication It follows from this Operation and Advertisement that if after the Division there remains 1 the current day will be a Sunday and if nothing remains it will be a Saturday the Astronomical Epocha of the Horoconne is therefore a Saturday If it be known likewise what day of the Week is the day current it will be seen whether the Precedent Operations have been well made IV. 1 Set down the Horoconne 2. Multiply it by 800. 3. Substract it by 373. 4. Divide it by 292207. 5. The Quotient will be the Aera and the Numerator of the Fraction will be the Krommethiapponne which you shall keep Explication The days are here reduced into 800 parts The number 373 of the third Article makes 373 800 of the day which do make 11 hours and 11 minutes They can proceed only from the difference of the Epocha's or from some correction seeing that it is always the same number that is substracted The Epocha of this fourth Section may therefore be 11 hours and 11 minutes after the former The Aera will be a number of Periods of Days from this new Epocha 800 of which will make 292207. The Question is to know what these Periods will be 800 Gregorian Years which very nearly approach as many Tropical Solar Years do make 292194 Days If then we suppose that the Aera be the number of the Tropical Solar Years from the Epocha 800 of these Years will be 13 Days too long according to the Gregorian correction But if we suppose that they are Anomalous Years during which the Sun returns to his Apogaeum or Astral Years during which the Sun returns to the same fixt Star there will be almost no error for in 13 Days which is the overplus of 800 of these Periods above 800 Gregorian Years the Sun by its middle motion makes 12d. 48′ 48″ which the Apogaeum of the Sun does in 800 Years by reason of 57″ 39′″ per annum Albategnius makes the Annual motion of the Sun's Apogeum 59″ 4′″ and that of the fix'd Stars 54″ 34′″ and there are some modern Astronomers which do make this annual motion of the Sun 's Apogaeum 57″ and that of the fix'd Stars 51″ Therefore if what is here called Aera is the number of the Anomalous or Astral Years these Years will be almost conformable to those which are established by the antient and modern Astronomers Nevertheless it appears by the following Rules that they use this form of Year as if it were Tropical during which the Sun returns to the same place of the Zodiack and that it is not distinguished from the other two sorts of Years The Krommethiapponne which remains after the preceeding Division that is to say after having taken all the entire Years from the Epocha will therefore be the 800 parts of the Day which remain after the Sun's return to the same place of the Zodiack and it appears by the following Operations that this place was the beginning of Aries Thus according to this Hypothesis the Vernal middle Aequinox will happen 11 Hours 11′ after the Epocha of the preceeding Section V. 1. Set down the Krommethiapponne 2. Substract from it the Aera 3. Divide the ramainder by 2. 4. Neglecting the Fraction substract 2 from the Quotient 5. Divide the remainder by 7. the Fraction will give you the day of the Week Note That when I shall say the Fraction I mean only of the Numerator Explication Seeing
by 12 the Quoent will be Natti itti The end of the Souriat Explication These three first Operations do serve to reduce the Moon 's distance from the Sun into minutes dividing it by 720 it is reduced to the 30 part of a Circle for 720 minutes are the 30th part of 21600 minutes which do make the whole circumference The ground of this division is the Moons diurnal motion from the Sun which is near the 30th part of the whole Circle They consider then the Position of the Moon not only in the Signs and in her stations but also in the 30th parts of the Zodiack which do each consist of 12 degrees and are called itti dividing the remainder by 12 they have the minutes or sixtieth parts of an itti which do each consist of 12 minutes of degrees which the Moon removes from the Sun in the sixtieth part of a day these sixtieth parts are called natti itti Reflexions upon the Indian Rules I. Of the particular Epocha's of the Indian Method HAving explained the Rules comprised in the preceding Sections and found our several Periods of Years Months and Days which they suppose It remains to us particularly to explain divers particular Epocha's which we have found in the numbers employed in this Method which being compared together may serve to determine the Year the Month the Day the Hour and the Meridian of the Astronomical Epocha which is not spoken of in the Indian Rules which suppose it known By the Rules of the I. Section is sought the number of the Lunary Months elapsed from the Astronomical Epocha The Epocha which they suppose in this Section is therefore that of the Lunar Months and consequently it must be at the Hour of the middle Conjunction from whence begins the Month wherein the Epocha is By the Rules of the II. Section they first reduce the Lunar Months elapsed from the Epocha into Artificial Days of 30 per mensem which are shorter than the Natural Days from one Noon to the other by 11 703 a Day that is to say by 22 Minutes 32 Seconds of an Hour These Artificial Days have therefore their beginning at the new Moons and at every thirtieth part of the Lunar Month but the Natural Days do always begin naturally at Midnight under the same Meridian The Term of the Artificial Days agrees not then with the Term of the Natural Days in the same Hour and same Minute unless when the Month or one of the 30 parts of the Month begins at Midnight under the Meridian given at the choice of the Astronomer After this common beginning the end of the Artificial Day prevents the end of the Natural Day under the same Meridian 11 703 a Day in which does then consist the Anamaan which always augments one 703d of a Day to every eleventh part of the Day until that the number of the 703 parts amounts to 703 or surpasses this number for then they take 703 of these parts for a Day whereby the number of the Artificial Days surpasses the number of the Natural Days elaps'd since the Epocha and the remainder if there is any is the Anamaan The day of this meeting or concourse of the term of the Artificial days with the term of the Natural Days under the Meridian which is chosen is always a new Epocha of the Anamaan which is reduced to nothing or to less than 11 after having attained this number 703 which arrives only at every Period of 64 Days as it appears in dividing 703 by 11 and more exactly eleven times in 703 Days At every time given for the Epocha of the Anamaan they then take the Day of the preceeding rencounter of the beginning of the Artificial Days with the beginning of the Natural Days which under the same Meridian happens only five or six times in a Year Seeing then that in the fifth Article of the II. Section they add 650 elevenths of a Day to those which are elapsed from the Epocha of the I. Section they suppose that this Epocha was proceeded from another Epocha which could only be that of the Anamaan of 650 elevenths of a Day that is to say of 59 Days 1 11â— which do give 650 703 of a Day for the Anamaan under the Meridian of the East Indies to which the Rules of this II. Section are accommodated which shows that under this Meridian the middle Conjunction which gave beginning to the Artificial Day since the Astronomical Epocha was 650 703 of a Day before the end of the Natural Day in which this conjunction happen'd And consequently that it happen'd at one a Clock 49 Minutes in the morning under the Meridian which is supposed in the same Section but in the 9th Article of the 10th Section they deduct 40 Minutes from the motion of the Moon and in the 8th Article of the 7th Section they deduct 3 minutes from the motion of the Sun which removes the Moon 37 minutes from the Sun at the hour that they suppose the middle Conjunction of the Moon with the Sun in the II. Section Wherefore I have judged that the 40 minutes taken from the motion of the Moon and the 3 minutes taken from the motion of the Sun do result from some difference between the meridian to which these Rules were accommodated at the beginning and of another meridian to which they have since reduced them so that under the meridian supposed in the II. Section the new Moon in the Epocha arrived at one a Clock 49 minutes in the morning but under the meridian which is supposed in the 9th Article of the X. Section at the same hour of I. and 49 minutes after midnight the Moon was distant from the Sun 37 minutes which it makes in an hour 13 minutes therefore under the Meridian supposed in the 9th Article of the X. Section the new Moon could not arrive till 3 a Clock 2 minutes after midnight The meridian to which these Rules have been reduced would therefore be more oriental than the meridian chosen at the beginning by 1 hour 13 minutes that is to say 18 degrees and a quarter and having supposed that they have reduced them to the meridian of Siam they would be accommodated from the beginning almost to the meridian of Narsinga What more convinces that this substraction of 40 minutes from the motion of the Moon and of three minutes from the motion of the Sun is caused from the difference of the meridians of 1 hour 13 minutes is that in 1 hour 13 minutes the Moon makes 40 minutes and the Sun 3. 'T is therefore by the same difference of 1 hour 13 minutes that they have deducted 3 minutes from the motion of the Sun and 40 minutes from the motion of the Moon Without this correspondence of what they have deducted from the motion of the Sun with what they have taken from the motion of the Moon which appears to have for foundation the same difference of time and consequently the same difference
6939 days and 18 hours are longer by 1 hour 30 minutes 38 seconds 25 thirds than the Indian That of Numa must be of a number of whole days according to Titus Livius whose words are these Ad cursum Lunae in duodecim menses describit annum quem quia tricenos dies singulis mensibus Luna non explet desuntque dies solido anni qui solstitiali circumagitur orbe intercalares mensibus interponendo ita dispensavit ut vigesimo anno ad metam eandem solis unde orsi essent plenis annorum spatiis dies congruerent In all the Manuscripts that we have seen it is read vicesimo anno and not vigesimo quarto as in some printed Copies The period of 19 years of the Indians is therefore more exact than these periods of the Ancients and than our golden Cycle and it agrees to 3 minutes and 5 or 6 seconds with the period of 235 lunar months established by the moderns which do make it of 6939 days 16 hours 13 minutes 27 seconds This is the beginning of the current Indian period of 19 years and of the rest which follow for above an Age in the Gregorian Calendar at the Meridian of Siam with the hours after midnight    Days H. M.  1683 March 27 21 57  1702 March 28 14 26  1721 March 28 6 56 Biss 1740 March 27 23 25  1759 March 28 15 54  1778 March 28 8 24  1797 March 28 0 53 Biss 1816 March 28 17 22 Of the Indian Epacts THE Epact of the months is the difference of the time which is between the new Moon and the end of the solar month current and the annual Epact is the difference of the time which is between the end of the simple lunar or embolismic year and the end of the solar year which runs when the lunar year ends According to the exposition of the I Section 228 lunar months more 7 other lunar months are equal to 228 solar months Dividing the whole therefore by 228 1 lunar month more 7 22â— of a lunar month is equal to a solar month The Indian Epact of the first month is therefore 7 22â— of a lunar month The Epact of the second 14 228 and so of the rest and the Epact of 12 months which do make a simple lunar year is 84 228 the Epact of two years 168 228 the Epact of 3 years would be 252 22â— but because that 228 228 are a month a month is added to the third year which is Embolismic and the rest is the Epact 24 22â— Thus the Epact of six years is â—8 22â— The Epact of 18 years is 1â—4 22â— And adding thereunto the Epact of a year which is â—â—4 22â— The Epact of 19 years would be 22â— 228 which do make a lunar month To the nineteenth year is added a thirteenth month to make it Embolismic thus the Epact at the end of the nineteenth year is 0. If the lunisolar years are ordered after this manner they will always end before the synodical Equinox or in the Equinox it self But they may be so ordered that they end always after the synodical Equinox which will happen if when the Epact is 0 they begin them with the new Moon which happens a month after the synodical Equinox and after this manner the first month of the Astronomical year will commence at the beginning of the fifth month of the Civil year after the Embolisme whereas in the year of the first method the first month would end at the beginning of the fifth month of the Civil year after the Embolisme This Indian Epact is a great deal more exact than our vulgar Epact which augments 11 days by the year so that they deduct 30 days when it exceeds this number taking 30 days for a lunar month and the nineteenth year they substract 29 days to reduce the Epocha to nothing at the end of the nineteenth lunisolar year The Indian Epact of a month being reduced to hours consists of 21 hours 45′ 33″ 46‴ The Epact of a year consists of 10 days 21 hours 6′ 45″ The Epact of 3 years is 3 days 2 hours 36 minutes 13 seconds The Epact of 11 years which is the least of all in the Cycle of 19 years is 1 day 13 hours 18′ 7″ The Indian Epact may be consider'd in respect of the Julian and Gregorian years and it will serve to find the beginning of the Civil and Astronomical years of the Indians in our Calendar after they shall have established an Epocha and denoted the Terms From a Common or Bissextile year to the succeeding common Julian or Gregorian year the Indian Epact consists of 10 days 15 hours 11′ 32″ From a common year to the following Bissextile year the Indian Epact is 11 days 15 hours 11′ 32″ The annual Epact must be substracted from the first new Moon of a year to find the first new Moon of the following year But when after the Substraction the new Moon precedes the Term they add a month to the year to make it Embolismic Thus having supposed the first new Moon after the synodical Equinox of the year 1683 as in Chapter IX on the 25th of April 22 hours and 41 minutes after noon that is to say on the 26th of April at 10 a clock 41 minutes of the morning in the Meridian of Siam to have the first new Moon of the following year 1684 which is Bissextile they will substract from this time 11 days 15 hours 11 minutes 32 seconds and they will have the 14th of April at 19 hours 29 minutes 28 seconds of the year 1684 and to have the first new Moon of the solar synodical year of the year 1685 which is common they will substract from the preceding days 10 days 15 hours 11 minutes 32 seconds and they will have the 4th of April at 4 hours 17 minutes 56 seconds In fine to have the first new Moon of the solar synodical year of the following year 1686 which is common deducting likewise the same number of days they will have the 24th of March at 13 hours 6 minutes 24 seconds But because that this day precedes the term of the synodical years which for this Age hath been found the 27th of March it is necessary to add a lunar month of 29 days 12 hours 44 minutes 3 seconds thus the year will be Embolismic of 13 Moons and they will have the first new Moon of the synodical Indian year the 23d of April at 1 hour 50 minutes 27 seconds in the morning at Siam and continuing after the same manner they will have all the first new Moons of the following years In these Indian rules the name of an Embolismick or Attikamaat agrees to the year which immediately follows the Intercalation The lunisolar years may likewise be order'd in such a manner that the addition of the intercalary month may be made when the Epact exceeds 114 228 which do make the half of the month to the
found by the Rules of the II. Section that 7421 lunar months do comprehend 219146 days 11 hours 57 minutes 52 seconds if therefore we compose this period of whole days it must consist of 219146 days 600 Gregorian years are alternatively of 219145 days and 219146 days they agree then to half a day with a lunisolar period of 600 years calculated according to the Indian Rules The second lunisolar period composed of Ages is that of 2300 years which being joyned to one of 600 makes a more exact period of 2900 years And two periods of 2300 years joyned to a period of 600 years do make a lunisolar period of 5200 years which is the Interval of the time which is reckoned according to Eusebius his Chronology from the Creation of the World to the vulgar Epocha of the years of J. Christ XXIII An Astronomical Epocha of the years of Jesus Christ THese lunisolar periods and the two Epocha's of the Indians which we have examin'd do point unto us as with the finger the admirable Epocha of the years of J. Christ which is removed from the first of these two Indian Epocha's a period of 600 years wanting a period of 19 years and which precedes the second by a period of 600 years and two of nineteen years Thus the year of Jesus Christ which is that of his Incarnation and Birth according to the Tradition of the Church and as Father Grandamy justifies it in his Christian Chronology and Father Ricciolus in his reformed Astronomy is also an Astronomical Epocha in which according to the modern Tables the middle conjunction of the Moon with the Sun happened the 24 of March according to the Julian form re-established a little after by Augustus at one a clock and a half in the morning at the Meridian of Jerusalem the very day of the middle Equinox a Wednesday which is the day of the Creation of these two Planets De Trin. l. 4. c. 5. The day following March 25th which according to the ancient tradition of the Church reported by St. Augustine was the day of our Lords Incarnation was likewise the day of the first Phasis of the Moon and consequently it was the first day of the month according to the usage of the Hebrews and the first day of the sacred year which by the Divine institution must begin with the first month of the Spring and the first day of a great year the natural Epocha of which is the concourse of the middle Equinox and of the middle Conjunction of the Moon with the Sun This concourse terminates therefore the lunisolar periods of the preceding Ages and was an Epocha from whence began a new order of Ages Eclog. 4. according to the Oracle of the Sybil related by Virgil in these words Magnus ab integro Saeclorum nascitur ordo Jam nova progenies Coelo dimittitur alto This Oracle seems to answer the Prophecy of Isaiah Parvulus natus est nobis c. 9. v. 6. 7. where this new-born is called God and Father of future Ages Deus fortis Pater futuri Saeculi The Interpreters do remark in this Prophecy as a thing mysterious the extraordinary situation of a Mem final which is the Numerical Character of 600 in this word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 ad multiplicandum where this Mem final is in the second place there being no other example in the whole Text of the Holy Scripture where ever a final Letter is placed only at the end of the words This Numerical Character of 600 in this situation might allude to the periods of 600 years of the Patriarchs which were to terminate at the accomplishment of the Prophecy which is the Epocha from whence we do at present compute the years of Jesus Christ XXIV The Epocha of the Ecclesiastical Equinoxes and of the vulgar Cycle of the Golden number THe Christians of the first Ages having remarked that the Jews of this time had forgot the antient Rules of the Hebrew years so that they celebrated Easter twice in one year as Constantine the Great attests in the Letter to the Churches do borrow the form of the Julian years re-established by Augustus Euseb de vlta Constantini lib. 3. c. 9. which are destributed by periods of 4 years three of which are common of 365 days and a Bissextile of 366 days and do surpass the lunar years by 11 days They denote therefore in the Julian Calender the day of the Equinox and the days of the Moon with their variation and they regulate it some by the Cycle of 8 years others by the Cycle of 19 years as it appears by the regulation of the Council of Caesarea in the year of Christ 196 and by the Canon of St. Hyppolytus and by that of St. Anatolius But afterwards the Council of Nice held in the year 325 having charged the Bishops of Alexandria as the most experienced in Astronomy to determine the time of Easter these Prelates made use of their Alexandrian Calendar where the year began with the 29th of August and for Epocha they took the lunar Cycles of 19 years the first Egyptian year of the Empire of Dioclesian because that the last day of the preceding year which was the 28th of August of the 284th year of Jesus Christ the new Moon happened near Noon at the Meridian of Alexandria By reckoning from this Epocha backward the Cycles of 19 years they come to the 28th of August in the year preceding the Epocha of Jesus Christ so that the first year of Jesus Christ is the second year of one of these Cycles 'T is thus that these Cycles are still computed at present since that Dionysius the Less transported the Cycles of the Moon from the Alexandrian Calendar to the Roman and that he began to compute the years from the Epocha of Jesus Christ instead of computing them from the Epocha of Dioclesian denoting the Equinox of the Spring on the 21st of March as it had been set down in the Egyptian Epocha For the Epocha of the lunar Cycles they might have taken the Equinoxial conjunction of the same year of Jesus Christ rather than the conjunction of the 28th of August of the former year and renew it after 616 years which reduce the new Moons to the same day of the Julian year and to the same day of the week which is what they demanded of the Victorian period but they thought only to confirm themselves to the rule of the Alexandrians which was the sole method to reconcile the Eastern and Western Church Thus these Rules have been followed to the past Age altho it has been long perceived that the new Moons thus regulated according to the Cycle of 19 years anticipated almost a day in 312 Julian years and that the Equinoxes anticipated about 3 days in 400 of these years XXV The solar Gregorian Period of 400 years ABout the end of the past Age the Anticipation of the Equinoxes since the Epocha chosen by the Alexandrians was
This is thus practised in all the Courts of Asia but it is not true neither at Siam nor perhaps in any part of the East that the Queen has any Province to govern 'T is easie also to comprehend that if the King loves any of his Ladies more than the rest he causes her to remove from the Jealousie and harsh Usage of the Queen At Siam they continually take Ladies for the service of the Vang The King of Siam takes the Daughters of his Subjects for his Palace when he pleases or to be Concubines to the King if this Prince makes use thereof But the Siameses deliver up their Daughters only by force because it is never to see them again and they redeem them so long as they can for Money So that this becomes a kind of Extortion for they designedly take a great many Virgins meerly to restore them to their Parents who redeem them The King of Siam has few Mistresses that is to say eight or ten in all He has few Ministresses not out of Continency but Parsimony I have already declared that to have a great many Wives is in this Country rather Magnificence than Debauchery Wherefore they are very much surprized to hear that so great a King as ours has no more than one Wife that he had no Elephants and that his Lands bear no Rice as we might be when it was told us that the King of Siam has no Horses nor standing Forces and that his Country bears no Corn nor Grapes altho' all the Relations do so highly extol the Riches and Power of the Kingdom of Siam The Queen hath her Elephants and her Balons The Queen's House and some Officers to take care of her and accompany her when she goes abroad but none but her Women and Eunuchs do see her She is conceal'd from all the rest of the People and when she goes out either on an Elephant or in a Balon it is in a Chair made up with Curtains which permit her to see what she pleases and do prevent her being seen And Respect commands that if they cannot avoid her they should turn their back to her by prostrating themselves when she passes along Besides this she has her Magazine her Ships and her Treasures Her Magazine and her Ships She exercises Commerce and when we arrived in this Country the Princess whom I have reported to be treated like a Queen was exceedingly embroiled with the King her Father because that he reserved to himself alone almost all the Foreign Trade and that thereby she found herself deprived thereof contrary to the ancient Custom of the Kingdom Daughters succeed not to the Crown they are hardly look'd upon as free Of the Succession to the Crown and the Causes which render it uncertain 'T is the eldest Son of the Queen that ought always to succeed by the Law Nevertheless because that the Siameses can hardly conceive that amongst Princes of near the same Rank the most aged should prostrate himself before the younger it frequently happens that amongst Brethren tho' they be not all Sons of the Queen and that amongst Uncles and Nephews the most advanced in Age is preferred or rather it is Force which always decides it The Kings themselves contribute to render the Royal Succession uncertain because that instead of chusing for their Successor the eldest Son of the Queen they most frequently follow the Inclination which they have for the Son of some one of their Concubines with whom they were enamour'd The occasion which tendred the Hollanders Masters of Bantam 'T is upon this account that the King of Bantam for example has lost his Crown and his Liberty He endeavoured to get one of his Sons whom he had by one of his Concubines to be acknowledged for his Successor before his Death and the eldest Son which he had by the Queen put himself into the hands of the Hollanders They set him upon the Throne after having vanquished his Father whom they still keep in Prison if he is not dead but for the reward of this Service they remain Masters of the Port and of the whole Commerce of Bantam Of the Succession to the Kingdom of China The Succession is not better regulated at China though there be an express and very ancient Law in favour of the eldest Son of the Queen But what Rule can there be in a thing how important soever it be when the Passions of the Kings do always seek to imbroil it All the Orientals in the choice of a Governor adhere most to the Royal Family and not to a certain Prince of the Royal Family uncertain in the sole thing wherein all the Europeans are not In all the rest we vary every day and they never do Always the same Manners amongst them always the same Laws the same Religion the same Worship as may be judged by comparing what the Ancients have writ concerning the Indians with what we do now see Of the King of Siams Wardrobe I have said that 't is the Women of the Palace which dress the King of Siam but they have no charge of his Wardrobe he has Officers on purpose The most considerable of all is he that touches his Bonnet altho he be not permitted to put it upon the Head of the King his Master 'T is a Prince of the Royal blood of Camboya by reason that the King of Siam boasts in being thence descended not being able to vaunt in being of the race of the Kings his Predecessors The Title of this Master of the Wardrobe is Oc-ya Out haya tanne which sufficiently evinces that the Title of Pa-ya does not signifie Prince seeing that this Prince wears it not Under him Oc-Pra Rayja Vounsa has the charge of the cloaths Rayja or Raja or Ragi or Ratcha are only an Indian term variously pronounced which signifies King or Royal and which enters into the composition of several Names amongst the Indians CHAP. XIV Of the Customs of the Court of Siam and of the Policy of its Kings The Hours of Council THe common usage of the Court of Siam is to hold a Council twice a day about Ten a clock in the Morning and about Ten in the Evening reckoning the hours after our fashion The division of the day and night according to the Siameses As for them they divide the day into Twelve hours from the Morning to the Night The Hours they call Mong they reckon them like us and give them not a particular name to each as the Chineses do As for the Night they divide it into four Watches which they call Tgiam and it is always broad Day at the end of the Fourth The Latins Greeks Jews and other people have divided the Day and Night after the same manner Their Clock The People of Siam have no Clock but as the Days are almost equal there all the Year it is easie for them to know what Hour it is by
die about the Temple and they eat them only when they die of themselves Near certain Temples there is also a Pond for the living Fish which is offer'd to the Temple and besides these Festival days common to all the Temples The People love to adorn themselves to go to the Temples and their Charity to Animals every Temple has a particular one appointed to receive the Alms as if it was the Feast of its Dedication for I could not learn what it is The People voluntarily assist at these Festivals and make a show with their new Cloaths One of their greatest Charities is to give Liberty to some Animals which they buy of those that have taken them in the Fields What they give to the Idol they offer not immediately to the Idol but to the Talapoins and they present it to the Idol either by holding it in their hand before the Idol or by laying it upon the Altar and in a little time after they take it away and convert it to their own uses Sometimes the People offer up lighted Tapers which the Talapoins do fasten to the knees of the Statue and this is the reason why one of the knees of a great many Idols is ungilt As for bloody Sacrifices they never offer up any on the contrary they are prohibited from killing any thing At the Full Moon of the fifth Month The Siameses do wash their Idols their Talapoins and their Parents the Talapoins do wash the Idol with perfumed waters but respect permits them not to wash its head They afterwards wash the Sancrat And the People go also to wash the Sancrats and the other Talapoins And then in particular Families the Children do wash their Parents without having regard to the Sex for the Son and the Daughter do equally wash the Father and the Mother the Grandfather and the Grandmother This Custom is observed also in the Country of Laos with this Singularity that the King himself is washed in the River The Talapoins have no Clock The hour on which the Talapoins do wash themselves and they wash themselves only when it is light enough to be able to discern the veins of their hands for fear lest if they should wash themselves earlier in the morning they should in walking kill any Insect without perceiving it This is the reason why they wash later in the shortest days tho' their Bell fails not to wake them before day Being raised they go with their Superior to the Temple for two hours They go to the Temples in the morning There they sing or repeat out of the Balie and what they sing is written on the Leass of a Tree somewhat longish and fasten'd at one of the ends as I have said in discoursing of the Tree which bears them The People have not any Prayer-Book The posture of the Talapoins whilst they sing is to sit cross-leg'd and continually to toss their Talipat or Fan as if they would continually fan themselves so that their Fan goes or comes at each Syllable which they pronounce and they pronounce them all at equal times and after the same tone In entering in and going out of the Temple they prostrate themselves three times before the Statue and the Seculars do observe the same but the one and the other do remain in the Temple sitting cross-leg'd and not always prostrate In going from Prayer the Talapoins go into the City to beg Alms for an hour Then to begging on which alone they do not always live but they never go out of the Convent and never re-enter without going to salute their Superior before whom they prostrated themselves to touch the ground with their Forehead and because that the Superior sits generally cross-leg'd they take one of his Feet with both their hands and put it on their head To crave Alms they stand at the Gates without saying any thing and they pass on after a little time if nothing is given them It is rare that the People sends them away without giving them and besides this their Parents never fail them The Convents have likewise some Gardens and cultivated Lands and Slaves to plough them All their Lands are free from Taxes and the Prince touches them not altho' he has the real property thereof if he divests not himself by writing which he almost never does At their return from begging the Talapoins do breakfast if they will How they fill up the day and are not always regular in presenting to the Idol what they eat tho' they do it sometimes after the manner that I have related Till Dinner-time they study or employ themselves as to them seems meet and at Noon they dine After Dinner they read a Lecture to the little Talapoins and sleep and at the declining of the day they sweep the Temple and do there sing as in the morning for two hours after which they lie down If they eat in the evening it is only Fruit and tho' their day's work seems full by what I have said they cease not to walk in the City after Dinner for their pleasure Besides the Slaves which the Convents may have The secular Servants of the Talapoins they have each one or two Servants which they call Tapacaou and which are really Seculars tho' they be habited like the Talapoins excepting that their Habit is white and not yellow They receive the money which is given to the Talapoins because the Talapoins cannot touch it without sinning they have the care of the Gardens and Lands which the Convent may have and in a word they act in the Convents for the Talapoins whatever the Talapoins conceive cannot be done by themselves as we shall see in the Sequel CHAP. XVIII Of the Election of the Superior and of the Reception of the Talapoins and Talapoinesses The Election of the Superior WHen the Superior is dead be he Sancrat or not the Convent elects another and ordinarily it chuses the oldest Talapoin of the House or at least the most learned How a Secular does who builds a Temple and begins a Convent How a Talapoin is admitted If a particular person builds a Temple he agrees with some old Talapoin at his own choice to be the Superior of the Convent which is built round this Temple as other Talapoins come thither to inhabit for he builds no Talapoins Lodging before-hand If any one would make himself a Talapoin he begins with agreeing with some Superior that would receive him into his Convent and because there is none but a Sancrat as I have said can give him the Habit he goes to demand it of some Sancrat if the Superior with whom he would remain is not himself a Sancrat and the Sancrat appoints him an hour some few days after and for the Afternoon Whoever should oppose him would sin and as this Profession is gainful and it lasts not necessarily the whole life the Parents are always very glad to see their Children
end that the term might be as a medium between the several beginnings of the years some of which commence sooner and others later as it is practised in our Ecclesiastical years which began before the Vernal Equinox when the Equinox arrives before the 15th of the Moon and which begin after the Equinox when the Equinox happens after the 14th of the Moon But it is more commodious for the Astronomical Calculations to begin the year always before or always after the Equinox as it is practised in the Astronomical Indian year according to our Explication Nevertheless it is necessary to remark that the point of the Zodiack which the Indians do take for the beginning of the signs according to the Rules of the IV. and following Sections and which they consider in some sort as the Aequinoxial point of the Spring is in this Age removed 13 degrees from the Astronomical Term of the years discoursed of in the I. Section so that the Sun arrives there the fourteenth day after the synodical Aequinox Wherefore a part of the Astronomical lunisolar years which begin after the Term established by the Rules of the I. Section will begin in this Age before this sort of Aequinox and the other part will begin after so that this sort of Aequinox is as it were in the middle of the several beginnings of the lunisolar years which begin in the fifth and sixth month of the Civil year XII A Correction of the lunar Months and of the solar Synodical years of the Indians IT is very easy to accommodate the lunar months of the Indians and their solar synodical years to the modern Hypotheses After having made the calculations according to the Indian Rules it is necessary to divide the number of the years elapsed since the Astronomical Epocha by 6 and by 4. The first Quotient will give a number of seconds to substract from the time of the new Moons calculated according to these Rules EXAMPLE In the year of Jesus Christ 1688 the number of the years elapsed from the Astronomical Epocha of the Indians is 1050. This number being divided by 6 the Quotient which is 175 gives 175 minutes that is to say 2 hours 55 minutes to add This same number being divided by 4 the quotient is 262 which gives 262 seconds that is to say 6 minutes 22 seconds to substract and the Equation will be 2 hours 48 minutes 38 seconds Having added this Equation to the first Conjunction of the solar Synodical year 1051 which according to these rules happen'd the 31st of March in the year 1688 at 19 hours 28 minutes 24 seconds after midnight the middle Conjunction will be the 31st of March at 22 hours 17 minutes 12 seconds at the Meridian of Siam The same Equation serves to the Synodical years which result from the time of 235 lunar months divided into 19 years The first division by 6 will suffice if they take once and a half as many seconds to substract as there are found minutes to add XIII The difference between the solar Synodical and the Tropical years of the Indians IF the Indians take for a Tropical year the time which the Sun employs in returning to the beginning of the Signs of the Zodiack according to the fourth and following Sections the difference between these years and the Synodical is considerable as we have already remark'd According to the Western Astronomy the beginning of the Signs is the point of the Vernal Equinox where the ascending demicircle of the Zodiack terminated by the Tropicks is intersected by the Equinoxial for they hold no more to the Hypothesis of the Ancients who plac'd the Equinoxes at the eighth parts of the Signs and the Tropical year is the time that the Sun employs in returning to the same point whether Equinoxial or Tropical The Conjunctions of the Moon with the Sun which happen in the points of the Equinoxes return not precisely at the end of the nineteenth Tropical year for this nineteenth year ends about two hours before the end of the 235th lunar month which terminates the nineteenth Synodical year I say about two hours for in this the modern Astronomers agree not among themselves to 9 or 10 minutes because that the time of the Equinoxes being very difficult to determine exactly they agree not in the exactness of the Tropical year but to near half a minute tho they be almost unanimously agreed even to the thirds in the greatness of the lunar month Those that do make the greatness of the Tropical year of 365 days 5 hours 49 minutes 4 seconds and 36 thirds will have the period of 19 solar Synodical years above two exact hours longer than the period of 19 Tropical years They that make the Tropical year longer will have a lesser difference and they that make the Tropical year shorter as most of the Astronomers do at present will have it greater It may here be supposed that this difference would be 2 hours wantting 3 minutes seeing that the defect of the lunar Indian months in 19 years is 3 minutes and that the Tropical year would consist of 365 days 5 hours 48 minutes 55 seconds Thus if at every 19th year from the Astronomical Epocha of the Indians they deduct 2 hours from the Equinoxial Term calculated by the Indian rules without the correction and if they deduct also 14 hours 46 minutes for the time by which it may be supposed that the middle Equinox precedes the Epocha of the new Moons according to the modern Hypotheses they will have the middle Equinox of the Spring of the year proposed since the Epocha conformable to the modern Hypotheses EXAMPLE In the year 1686 the number of the years since the Astronomical Epocha of the Indians is 1048. This number being divided by 19 the Quotient is 55 3 19 which being doubled gives 110 hours 19 minutes that is to say 4 days 14 hours 19 minutes to which having added for the Epocha 14 hours 4 minutes the summ is 5 days 5 hours 5 minutes and this summ being deducted from the term of the same Synodical year 1048 which has before been found on the 27th of March 1686 at 15 hours 42 minutes of the evening there remains the 22d of March 10 hours 37 minutes of the Evening at the Meridian of Siam for the middle Equinox of the Spring of the year 1686. XIV An Examination of the great lunisolar period of the Indians IN the VII Chapter of these Reflexions we have found that the Period of 13357 years is composed of 165205 entire lunar months which do make 4878600 whole days according to the Rules of the II. Section This Period according to the Hypothesis of these Rules brings back the new Moons which terminate the Indian synodical years to the same hour and to the same minute under the same Meridian But having examined it by the method of the XII Chapter of these Reflexions it will be found that it is shorter than a period of a like
opinion to yield two Crops in a year as some have related concerning some other Cantons of India if the Inundation did not last so long They have Turky-Wheat only in their Gardens They do boil or parch the whole Ear thereof without unhusking or breaking off the Grains and they eat the inside CHAP. VIII Of the Husbandry and the difference of the Seasons Oxen and Buffalo's employ'd in Husbandry THey equally employ Oxen and Buffalo's in Husbandry They guide them with a Rope put through a hole which they make in the Cartilage that separates the Nostrils And to the end that the Rope may not slip when they draw it they do tie a knot on each side This same Cord runs also through a hole which is at the end of the draught Tree of their Plough The Siamese Plough The Plough of the Siameses is plain and without Wheels It consists in a long Beam which is the Rudder in another crooked piece which is the Handle and in another shorter and stronger piece fastned almost at Right Angles underneath at the end of the Handle and 't is this Third which bears the share They fasten not these four pieces with Nails but with leather Thongs How they cleanse the Rice from the Chaff To unhusk the Rice they employ large Beasts when it is trodden out they let it fall by little and little from a very high place to the end that the wind may carry away the Chaff And because the Rice has an hard Skin like Spelt a sort of Corn very common in Flanders and other places they bruise it in a great wooden Mortar with a Pestle of the same or in a Hand-mill all the pieces of which are also of Wood. They knew not how to describe them to me Three Seasons only and two sorts of years They know only three Seasons the Winter which they call Nanaou the Beginning of Cold the Little Summer which they call Naron the Beginning of Heat and the Great Summer which they call Naron-yai the Beginning of Great Heat and which strips the Trees of their Leaves as the Cold does ours They have two years together consisting of twelve months and a third of thirteen The names of their days from the Planets They have no word to express Week but like us they call the seven days by the Planets and their days correspond to ours I mean that when it is Monday here it is Monday there and so of the rest but the day begins about six hours sooner there than here Amongst the Names they have given to the Planets that of Mercury is Pout a Persian word which signifies an Idol from whence comes Pout-Gheda a Temple of false Gods and Pagode comes from Pout-Gheda From whence they begin their years They begin their year on the first day of the Moon in November or December according to certain Rules and they do not always denote the years by their number but by the names they give them for they make use of a Cycle of sixty years like the other Eastern Nations The Cycle of 60 years A Sexagenary Cycle is a Revolution of sixty years as a week is a Revolution of seven days and they have names for the years of the Cycle as we have for the days of the week 'T is true I have not been able to discover that they have more than twelve different names which they repeat five times in every Cycle to arrive at the number of sixty and in my opinion with some additions which do make the differences thereof They will date therefore for instance from the year of the Pigg or of the Great Serpent which amongst them are the names of the year and they will not always denote what year of their Aera this shall be as we sometimes date a Letter upon one of the days of the week to which we set down the name without noting what number it is in the month At the end of this Relation I will give you the twelve names of the years in Siamese with those of the seven days of the week Their months Their months are vulgarly esteem'd to consist of thirty days I say vulgarly because that in Astronomical exactness there may be some month longer or shorter but the Siameses do observe it otherwise than we in that we give names to the months and they do not They call them by their order the first month second month c. The distinction of their Seasons The two first Months which answer almost to our Months of December and January do make their whole Winter the third fourth and fifth do belong to their little Summer the seven others to their great Summer Thus they have Winter at the same time as we by reason they lye to the North line like us But their greatest Winter is at least as hot as our greatest Summer After the time of the Inundation they cover the Plants in their Gardens from the heats of the Sun as we do sometimes cover ours from the cold of the Night or Winter But as to their Persons the diminution of the heat appears unto them a very incommodious cold The little Summer is their Spring and they utterly ignore the Autumn They only reckon a great Summer although it seems that they might reckon two after the manner of the Ancients who have written of India seeing that they have the Sun perpendicularly over their heads twice a year once when it comes from the Line to the Tropick of Cancer and another time when it returns from the Tropick of Cancer towards the Line Their Winter is dry and their Summer rainy Of the Monsoons The Torrid Zone would doubtless be uninhabitable as the Ancients have held were it not for that marvellous Providence which makes the Sun continually to draw the Clouds and Rains after it and the Wind incessantly to blow there from one of the Poles when the Sun is toward the other Thus at Siam in Winter the Sun being in the middle of the Line or towards the Antarctick Pole the North-winds do constantly prevail and temper the Air very sensibly to refresh it In Summer when the Sun is on the North of the Line and perpendicularly over the head of the Siameses the South-winds which continually blow there do cause continual Rains or at least do make the weather always inclined to Rain leaving most People in doubt whether this Season of Rains ought not to be called the Winter of Siam 'T is this constant Rule of the Winds which the Portuguese have called Monçaos and we after them Monsoons Motiones aëris according to Ozorius and Maffeus And this is the reason that the Ships can hardly arrive at the Bar of Siam during the six Months of the North-winds and that they can hardly depart thence during the six Months of the South-winds At the end of this work I will give the order of the Winds and Tides in the Gulph of Siam in
the History of Illustrious Men even of those that were more Antient than the Deluge Moses cites certain places thereof wherein is remarked the Poetick Stile I conceive therefore that Men being wearied with singing always the same things and losing by little and little the sense of the old Songs How the Talapoins and their Brethren might have succeeded the Antient Poetry and Musick have ceased to sing them and have sought some commentaries on the Verses which they they sung no more for lack of understanding them That then the Magistrates left the care of these Commentaries to other Men and that they by little and little imposing on the belief of the People have inserted in their Lectures many things to their particular advantage which are the Source of the Superstitious Veneration which the Indians do still retain for the Talapoins and their Fellow-Brethren However it be their Habit their Convents and their Temples are inviolable though the Revolutions of this Country may have showed some examples of the contrary Vâ—iet whom I have often quoted relates that when the present King's Father seized on the Crown he thought it impossible securely to make an attempt upon the Person of one of the Princes of the Royal Family till he had cunningly made him first to quit the Talapoins Pagne which he wore After the same manner when this Usurper was dead his Son who now Reigns seeing his Uncle by the Father's side seize on the Throne turned Talapoin to secure his Life as I have reported at the biginning of this Relation CHAP. XXIV Of the Fabulous Stories which the Talapoins and their Brethren have framed on their Doctrine THE Talapoins are therefore obliged to supply the ancient Musick Fables common to all the Indians and to explain their Balie Books unto the People with an audible Voice These Books are filled with extravagant stories grafted on the Doctrine which I have explained and these Fables are almost the same throughout India as the ground of the Doctrine is every where the same or very near They every where believe the Metempsychosis and that it is only a way to punish the Souls for their faults and to carry them gradually unto Perfection They believe Spirits every where diffused good and bad capable of aiding and of hurting but which are no other than the Souls of the dead and they admit the Worship of these Spirits though they raise no Altars to them but only to the Manes of the men whom they conceive to be arrived at the highest degree of Vertue as far as they think Vertue possible They all have some Quadruped which they prefer before all others some favourite Bird and some Tree which they principally adore They all believe the same thing of the pretended Dragon which causes the Eclipses and of the pretended Mountain round which the whole Heaven turns to make the Days and the Nights They have almost the same five Precepts of Morality they reckon near the same number of Hells and Paradice They all expect other men who ought to merit Altars like those to whom they have already consecrated some to the end that every one may have the Field free to pretend to the supream Vertue They all suppose that the Planets the Mountains the Rivers and particularly the Ganges may think speak marry and have Children They all relate the ridiculous Metempsychoses of the men whom they adore in Pigs Apes and other Beasts Abraham Roger in his Book of the Religion of the Bramins relates that the Pagans of Paliacata on the Coast of Coromandel do believe that their Brama whom they adore was born almost as some Balie Books do say Sommona-Codom was born viz. of a Flower which was sprung from the Navel of an Infant which they say was a leaf a Tree in the form of an Infant biting its Toe and swimming on the Water which alone subsisted with God They take no notice that the Leaf-Infant subsisted too and according to Abraham Roger they in this Country believe in God but in a God which is not adored and without doubt he has with as little ground advanced that others have writ that the Siameses believe a God The Fables which the Siameses relate of their Sommona-Codom 'T is no fault of mine that they gave me not the life of Sommona-Codom translated from their Books but not being able to obtain it I will here relate what was told me thereof How marvellous soever they pretend his Birth has been they cease not to give him a Father and a Mother His Mother whose Name is found in some of their Balie Books was called as they say Maha Maria which seems to signifie the great Mary for Maha signifies great But it is found written Mania as often as Maria which proves almost that these are two words Man-ya because that the Siameses do confound the n with the r only at the end of the words or at the end of the Syllables which are followed with a Consonant However it be this ceases not to give attention to the Missionaries and has perhaps given occasion to the Siameses to believe that Jesus being the Son of Mary was Brother to Sommona-Codom and that having been crucified he was that wicked Brother whom they give to Sommona-Codom under the Name of Thevetat and whom they report to be punished in Hell with a Punishment which participates something of the Cross The Father of Sommona Codom was according to this same Balie Book a King of Teve Lanca that is to say a King of the famous Ceylon But the Balie Books being without Date and without the Author's Name have no more Authority than all the Traditions whose Origin is unkown This now is what they relate of Sommona-Codom 'T is said that he bestowed all his Estate in Alms and that his Charity not being yet satisfied he pluck'd out his Eyes and slew his Wife and Children to give them to the Talapoins of his Age to eat A strange contrariety of Idea's in this People who prohibit nothing so much as to kill and who relate the most execrable Parricides as the most meritorious works of Sommona-Codom Perhaps they think that under the Title of Property a Man has as much Power over the Lives of his Wife and Children as to them it seems he has over his own For it matters not if otherwise the Royal Authority prohibits particular Siameses from making use of this pretended Right of Life and Death over their Wives Children and Slaves whereas it alone exerts it equally over all its Subjects it may upon this Maxim of the despotic Government that the Life of the Subjects properly belong to the King The Siameses expect another Sommona Codom I mean another miraculous man like him whom they already name Pra Narotte and whom they suppose to have been foretold by Sommona-Codom And they before-hand report of him that he shall kill two Children which he shall have that he will give them to the Talapoins to
eat and that it will be by this pious Charity that he will consummate his Vertue This expectation of a new God to make use of this Term renders them careful and credulous as often as any one is proposed to them as an extraordinary Person especially if he that is proposed to them is entirely stupid because that the entire Stupidity resembles what they represent by the Inactivity and Impassibility of the Nireupan As for example there appeared some years since at Siam a young Boy born dumb and so stupid that he seemed to have nothing humane but the Shape yet the Report spread it self through the whole Kingdom that he was of the first men which inhabited this Country and that he would one day become a God that is to say arrive at the Nireupan The People flocked to him from all parts to adore him and make him Presents till that the King fearing the consequences of this Folly caused it to cease by the Chastisement of some of those that suffered themselves to be seduced I have read some such thing in Tosi's India Orientale Tom. I. pag. 203. He reports that the Bonzees of Cochinchina having taken away from them a stupid Infant show'd him to the People as a God and that after having inrich'd themselves with the Presents which the People made him they published that this pretended God would burn himself and he adds that they indeed burnt him publickly after having stupified his Senses by some Drink and calling the insensible state wherein they had put him Extasie This last History is given as a crafty Trick of the Bonzees but it demonstrates as well as the first the Belief which these People have that there may daily spring up some new God and the Inclination which they have to take extream Stupidity for a beginning of the Nireupan Sommona-Codom being disingaged by the Alms-deeds which I have mentioned from all the Bands of Life devoted himself to Fasting to Prayer and to the other Exercises of the perfect Life But as these Practises are possible only to the Talapoins he embraced the Profession of a Talapoin and when he had heaped up his good works he immediately acquired all the Priviledges thereof He found himself endowed with so great a Strength that in a Duel he vanquished another man of a consummated Vertue whom they call Pra Souane and who doubting of the Perfection whereunto Sommona-Codom was arrived challenged him to try his Strength and was vanquisht This Pra Souane is not the sole God or rather the sole perfect Man which they pretend to have been contemporary with Sommona-Codom They name several others as Pra Ariaseria of whom they report that he was Forty Fadoms high that his Eyes were three and a half broad and two and a half round that is to say less in Circumference than Diameter if there is no fault in the Writing from whence I have taken this Remark The Siameses have a time of Wonders as had the Aegyptians and the Greeks and as the Chineses have For Instance their principal Book which they believe to be the work of Sommona-Codom relates that a certain Elephant had Three and thirty Heads that each of its Heads had seven Teeth every Tooth seven Pools every Pool seven Flowers every Flower seven Leafs every Leaf seven Towers and every Tower seven other things which had each seven others and these likewise others and always by seven for the numbers have always been a great Subject of Superstition Thus in the Alcoran if my Memory deceives me not there is an Angel with a very great number of Heads each of which hath as many Mouths and every Mouth as many Tongues which do praise God as many times every day Besides corporal strength Sommona-Codom had the power of doing all sorts of Miracles For example he could make himself as big and as great as he pleas'd and on the contrary he could render himself so little that he could steal out of sight and stand on the head of another man without being felt either by his weight or perceived by the Eyes of another Then he could annihilate himself and place some other man in his stead that is to say that then he could enjoy the repose of the Nireupan He suddenly and perfectly understood all the things of the World He equally penetrated things past and to come and having given to his body an entire Agility he easily transported himself from one place to another to preach Vertue to all Nations He had two principal Disciples the one on the right Hand and the other on the left they were both plac'd behind him and by each other's side on the Altars but their Statues are less than his He that is plac'd on his right Hand is called Pra Mogla and he that is on his left Hand is called Pra Scaribout Behind these three Statues and on the same Altar they only represent the Officers within the Palace of Sommona-Codom I know not whether they have Names Along the Galleries or Cloysters which are sometimes round the Temples are the Statues of the other Officers without the Palace of Sommona-Codom Of Pra Mogla they report that at the request of the damned he overturned the Earth and took the whole Fire of Hell into the hollow of his Hand but that designing to extinguish it he could not effect it because that this Fire dried up the Rivers instead of extinguishing and that it consumed all that whereon Pra Mogla placed it Pra Mogla therefore went to beseech Pra Pouti Tchaou or Sommona-Codom to extinguish Hell Fire but though Pra Pouti Tchaou could do it he thought it not convenient because he said that men would grow too wicked if he should destroy the Fear of this Punishment But after that Pra Pouti Tchaou was arrived at this high Vertue he ceased not to kill a Mar or a Man for they write Mar and Man though they pronounce always Man and as a Punishment for this great fault his Life exceeded not Eighty years after which he died by disappearing on a sudden like a Spark which is lost in the Air. The Man were a People Enemies to Sommona-Codom whom they called Paya Man and because they suppose that this People was an Enemy to so holy a Man they do represent them as a monstrous People with a very large Visage with Teeth horrible for their Size and with Serpents on their Head instead of Hair One day then as Pra Pouti Tchaou eat Pig 's flesh he had a Chollick fit which killed him An admirable end for a man so abstemious but it was necessary that he died by a Pig because they suppose that the Soul of the Man whom he slew was not then in the Body of a Man but in the Body of a Pig as if a Soul could be esteemed even according to their Opinion the Soul of a Man when it is in the Body of a Pig But all these inventers of Stories are not so attentive
before the Consonant they have chosen those which in the pronunciation of the Dipthongs are first pronounced In this Alphabet there is also some Syllables which are not Dipthongs Of a fourth Siamese Alphabet which I have not graved THis Alphabet is of the Syllables which begin and which end with Consonants and it teaches two things First there are two Vowels an a and an o which must never begin the Syllable nor end it but be always between two Consonants They have a particular Accent The a is marked with a sharp accent ′ oftentimes very much lengthned and always placed over the first Consonant of the Syllable and the o is marked with a double Accent sharp ″ which they put likewise over the first Consonant of the Syllable When in the pronunciation the Syllable ends not with a Consonant they put the o mute in the place of the second Consonant as may be seen in the Syllable Ko in the Alphabet of the Siamese Dipthongs yet they sometimes dispense therewith after the accent ′ which marks the a but never after the two accents ″ which mark the o. Sometimes also instead of the double accent which marks the o they put a little o over the first Consonant and sometimes they put nothing and as often as two Consonants make a Syllable it is the o that must be understood The second thing which this Alphabet teaches are the final Consonants viz. the first ko the ngo the do the no the mo and the bo As often as they end a Syllable with any other Consonant it is a fault against their Orthography They pronounce these only at the end of the Syllables and they never show their Children any Syllable to read which ends with any other Consonant than with those I have mentioned It is true that they pronounce the do like a to and the bo like a po at the end of some Syllables and Words Of the Balie Alphabets THey are not difficult to understand after what I have related of the Siamese The stroke shows that the two Letters between which it is found do make a halt in the pronunciation The five which follow the twentieth are not now of different value from the five which immediately precede them but perhaps this was otherwise when this Tongue flourished Of the Siamese Cyphers I Have nothing to say of the Siamese Characters save that an experienc'd man inform'd me that they resembled those which he had found on some Arabian Medals between four and five hundred years old The Siamese names of the Powers of the number Ten are these Noee which they pronounce Noai signifies Number Sib which they pronounce Sip signifies Ten and Tenth Roi which they pronounce Roe signifies a Hundred and Hundredth Pan a Thousand Meuing Ten Thousand Seen or Sen an Hundred Thousand or Hundredth of Thousand Abraham Roger p. 104. Of the Manners of the Bramines says that at Paliacata Lac signifies an Hundred Thousand and Bernier says Laque in his Relation of the Gentiles of Indostan pag. 221. Cot a Million Abraham Roger in the before-quoted place saith that at Paliacata Coti signifies Ten Millions Lan Ten Millions The numbers are plac'd before the Substantive as in our Tongue but these numbers are put after the Substantive to signifie the names of Orders Thus Sam Deuan signifies Three Months and Deuan Sam the Third Month. Of the Pronouns of the First Person COu ca raou atamapap ca Tchaou Ca-ppa tchaou atanou are eight ways of expressing I or we for there is no difference between Singular and Plural Cou is of the Master speaking to his Slave Ca is a respectful term from the Inferior to the Superior and in civility amongst equals the Talapoins never use it by reason that they believe themselves above other men Raou denotes some superiority or dignity as when we say We in Proclamations Roub properly signifies body 't is as if one should say my body to say me 't is only the Talapoins that use it sometimes Atamapapp is a Balie term more affected by the Talapoins than any other Ca Tchaou is composed of ca which signifies me and Tchaou which signifies Lord as who should say me of the Lord or me who belong to you my Lord that is to say who am your Slave The Slaves do use it to their Masters the common people to the Nobles and every one in speaking to the Talapoins Ca-ppa Tchaou has likewise something more submissive Atanou is a Balie word introduced within three or four years into the Siamese Tongue to be able to speak of himself with an intire indifference that is to say without Pride and without Submission Of the Pronouns of the Second and Third Persons TEV Tan Eng Man Otchaou do serve equally to the Second and Third Persons for the Singular and Plural Numbers but oftentimes they make use of the Name or Quality of the person to whom they speak Teu is a very honourable term but is used only for the third person or for the Talapoins in the second that is to say in speaking to them Tan is a term of Civility amongst equals The French have translated it by the word Monsieur Sir Eng to an inferior person Man with contempt Otchaou to a mean person unknown Of the Particles which supply the place of Conjugations THe Present Tense is without Particle As for example pen signifies to be and raou pen signifies I am eng pen thou art and he is And again raou pen signifies we are Tan tang-lai pen ye be Kon tang-lai pen they are Tang lai signifies all or a great many and it is the mark of the Plural Kon signifies People as who should say the People are to say in general they are or he is The Imperfect is verbatim at this time I being or time this or when I being to say I was moua nan rao pen. Moua signifies time or when nan signifies this The Perfect is denoted by dai or by leou and sometimes by both But dai is plac'd always before the Verb and leou after Thus dai pen or rao dai pen I have been or rather raou pen leou or rather yet Raou dai pen leou Dai signifies to find leou signifies end The Pluperfect is composed of the Particles of the Imperfect and the Perfect Thus to say when you came I had already eaten they will say moua tan ma raou dai kin sam-red leou that is to say word for word time or when you come I already to eat end Ma signifies to come and with other Accents and another Orthography it signifies Horse and Dog Kin signifies to eat sam-red signifies to end and this term is added to the Perfect to form the Pluperfect Tcha is the sign of the Future raou chapen I shall or will be this Particle always precedes the Verb. Hai denotes the Imperative and is put before the Verb. Teut also denotes it and is placed always at the end of the Phrase haikin eat
2 multiply it by 2 you will have the Kanne 6. If the Kenne is 3 4 or 5 you shall substract the figure from this figure 5 29 60 which is called Attathiat and amounts to 6 Signs 7. If the Kenne is 6 7 8 substract 6 from the Raasi the remainder will be the Kanne 8. If the Kenne is 9 10 11 substract the figure from this figure 11 29 60 which is called Touataasamounetonne and amounts to 12 Signs the remainder in the Raasi will be the Kanne 9. If you can deduct 15 from the Ongsaa add 1 to the Kanne if you cannot add nothing 10. Multiply the Ongsaa by 60. 11. Add thereunto the Libedaa this will be the Pouchalit which you shall keep 12. Consider the Kanne If the Kanne is 0 take the first number of the Chaajaa of the Sun which is 35 and multiply it by the Pouchalit 13. If the Kanne is some other number take according to the number the number of the Chajaa aattit and substract it from the number underneath Then what shall remain in the lower number multiply by it the Pouchalit As for example if the Kanne is 1 substract 35 from 67 and by the rest multiply If the Kanne is 2 substract 67 from 94 and by the rest multiply the Pouchalit 14. Divide the Sum of the Pouchalit multiplied by 900. 15. Add the Quotient to the superior number of the Chajaa which you have made use of 16. Divide the Sum by 60. 17. The Quotient will be Ongsaa the Fraction will be the Libedaa Put an 0 in the place of the Raasi 18. Set the figure found by the preceding Article over against the Mattejomme of the Sun 19. Consider the Ken aforesaid If the Ken is 0 1 2 3 4 5 It is called Ken substracting Thus you shall substract the figure found in the 17 Article from the Mattejomme of the Sun 20. If the Ken is 6 7 8 9 10 11 it is called Ken additional So you shall joyn the said figure to the Mattejomme of the Sun which will give out at last the Sommepont of the Sun which you shall precisely keep Explication It appeareth by these Rules that the Kanne is the number of the half-signs of the distance of the Apogaeum or Perigaeum taken according to the succession of the Signs according as the Sun is nearer one term than the other So that in the 5th Article is taken the distance of the Apogaeum according to the succession of the Signs in Article 6th the distance of the Perigaeum against the succession of the Signs in Article 7th the distance of the Perigaeum according to the succession of the Signs and in Article 8th the distance of the Apogaeum contrary to the succession of the Signs In the 6th 7th and 8th Articles it seems that it must always be understood Multiply the Raasi by 2 as it appears in the sequel In the 6th Article when the degrees of the Anomalia exceed 15 they add 1 to the Kanne because that the Kanne which is a half Sign amounts to 15 degrees The degrees and minutes of the Kanne are here reduced into minutes the number of which is called the Pouchalit It appears by these Operations that the Chaajaa is the Aequation of the Sun calculated from 15 to 15 degrees the first number of which is 35 the second 67 the third 94 and that they are minutes which are to one another as the Sinus of 15 30 and 45 degrees from whence It follows that the Equation of 60 75 and 90 degrees are 116 129 134. 35 67 94 116 129 134 which are set apart in this form and do answer in order to the number of the Kanne 1 2 3 4 5 6. As for the other degrees they take the proportional part of the difference of one number to the other which answers to 15 degrees which do make 900 minutes making as 900 to the difference of two Equations so the minutes which are in the overplus of the Kanne to the proportional part of the Equation which it is necessary to add to the minutes which answer to the Kanne to make the total Equation They reduce these minutes of the Equation into degrees and minutes dividing them by 60. The greatest Equation of the Sun is here of 2 degrees 12 min. The Alphonsine Tables do make it 2 degrees 10 minutes We find it of 1 degree 57 minutes They apply the Equation to the middle place of the Sun to have its true place which is called Sommepont 19. This Equation conformably to the rule of our Astronomers in the first demi-circle of the Anomalia is substractive and in the second demi-circle additional Here they perform the Arithmetical operations placing one under the other what we place side-ways and on the contrary placing side-ways what we place one under the other As for Example  The Mattejomme The Chayaa The Sommepont  Raasi 8 0 8 Signs Ongsaa 25 2 27 Degrees Libedaa 40 4 44 Minutes  Middle Place Equation True Place  IX 1. Set down the Sommepont of the Sun 2. Multiply by 30 what is in the Raagi 3. Add thereto what is in the Ongsaa 4. Multiply the whole by 60. 5. Add thereunto what is in the Libedaa 6. Divide the whole by 800 the Quotient will be the Reuc of the Sun 7. Divide the remaining Fraction by 13 the Quotient will be the Naati reuc which you shall keep underneath the Reuc Explication It appears by these Operations that the Indians divide the Zodiac into 27 equal parts which are each of 13 degrees 40 minutes For by the six first Operations the signs are reduced into degrees and the minutes of the true place of the Sun into minutes and in dividing them afterwards by 800 they are reduced into 27 parts of a Circle for 800 minutes are the 27th part of 21600 minutes which are in the Circle the number of the 27 parts of the Zodiack are therefore called Reuc each of which consists of 800 minutes that is to say of 13 degrees 40 minutes This division is grounded upon the diurnal motion of the Moon which is about 13 Degrees 40 Minutes as the division of the Zodiack unto 360 Degrees has for foundation the diurnal motion of the Sun in the Zodiack which is near a Degree The 60 of these parts is 13 ⅓ as it appears in dividing 800 by 60 wherefore they divide the Remainder by 13 neglecting the fraction to have what is here called Nati-reuc which are the Minutes or 60 parts of a Reuc X. For the Moon To find the Mattejomme of the Moon 1. Set down the Anamaan 2. Divide it by 25. 3. Neglect the Fraction and joyn the Quotient with the Anamaan 4. Divide the whole by 60 the Quotient will be Ongsaa the Fraction will be Libedaa and you shall put an 0 to the Raasi Explication According to the 7th Article of the III Section the Anamaan is the number of the 703 parts of the day which remain from the end
of the Artificial day to the end of the Natural day Altho according to this rule the Anamaan can never amount to 703 yet if 703 be set down for the Anamaan and it be divided by 25 according to the 2d Article they have 28 3 25 for the Quotient Adding 28 to 703 according to the third Article the sum 731 will be a number of minutes of a degree Dividing 731 by 60 according to the fourth Article the Quotient which is 12d. 11′ is the middle diurnal motion by which the Moon removes from the Sun From what has been said in the II Section it results that in 30 days the Anamaan augments 330. Dividing 330 by 25 there is in the Quotient 13 ⅓ Adding this Quotient to the Anamaan the summ is 343 that is to say 5d. 43′ which the Moon removes from the Sun in 30 days besides the entire Circle The European Tables do make the diurnal motion of 12d. 11′ and middle motion in 30 days of 5d. 43′ 21″ besides the entire Circle 5. Set down as many days as you have before put to the month current Sect. II. n. 3. 6. Multiply this number by 12. 7. Divide the whole by 30 the Quotient put it to the Raasi of the preceding figure which has an 0 at the Raasi and joyn the fraction to the Ongsaa of the figure 8. Joyn this whole figure to the Mattejomme of the Sun 9. Substract 40 from the Libedaa But if this cannot be you may deduct 1 from the Ongsaa which will be 60 Libedaa 10. What shall remain in the figure is the Mattejomme of the Moon sought Explication After having found out the degrees and the minutes which agree to the Anamaan they seek the signs and degrees which agree to the Artificial days of the current month For to multiply them by 12 and to divide them by 30 is the same thing as to say If thirty Artificial days do give 12 Signs what will the Artificial days of the current month give they will have the Signs in the Quotient The Fractions are the 30ths of a Sign that is to say of the degrees They joyn them therefore to the degrees found by the Anamaan which is the surplusage of the Natural days above the Artificial The Figure here treated of is the Moons distance from the Sun after they have deducted 40 minutes which is either a Correction made to the Epocha or the reduction of one Meridian to another as shall be explain'd in the sequel This distance of the Moon from the Sun being added to the middle place of the Sun gives the middle-place of the Moon XI 1. Set down the Outhiapponne 2. Multiply by 3. 3. Divide by 808. 4. Put the Quotient to the Raasi 5. Multiply the fraction by 30. 6. Divide it by 808 the Quotient will be Ongsaa 7. Take the remaining fraction and multiply it by 60. 8. Divide the summ by 808 the Quotient will be Libedaa 9. Add 2 to the Libedaa the Raasi the Ongsaa and the Libedaa will be the Mattejomme of Louthia which you shall keep Explication Upon the VI. Section it is remarked that the Outhiapponne is the number of the Days after the return of the Moon 's Apogaeum which is performed in 3232 Days 808 Days are therefore the fourth part of the time of the Revolution of the Moon 's Apogaeum during which it makes 3 Signs which are the fourth part of the Circle By these Operations therefore they find the motion of the Moon 's Apogaeum making as 808 Days are to 3 Signs so the time passed from the return of the Moon 's Apogaeum is to the motion of the same Apogaeum during this time It appears by the following Operation that this motion is taken from the same Principle of the Zodiack from whence the motion of the Sun is taken The Mattejomme of Louthia is the Place of the Moon 's Apogaeum XII For the Sommepont of the Moon 1. Set down the Mattejomme of the Moon 2. Over against it set the Mattejomme of Louthia 3. Substract the Mattejomme of Louthia from the Mattejomme of the Moon 4. What remains in the Raasi will be the Kenne 5. If the Kenne is 0 1 2 multiply it by 2 and it will be the Kanne 6. If the Ken is 3 4 5 substract it from this figure 5 29 60 7. If the Ken is 6 7 8 substract from it 6. 8. If the Ken is 9 10 11 substract it from this figure 11 29 60 9. If the Kenne is 1 or 2 multiply it by 2 this will be the Kanne 10. Deduct 15 from the Ongsaa if possible you shall add 1 to the Raasi if not you shall not do it 11. Multiply the Ongsaa by 60 and add thereunto the Libedaa and it will be the Pouchalit that you shall keep 12. Take into the Moons Chajaa the number conformable to the Kanne as it has been said of the Sun substract the upper number from the lower 13. Take the remainder and therewith multiply the Pouchalit 14. Divide this by 900. 15. Add this Quotient to the upper number of the Moons Chajaa 16. Divide this by 60 the Quotient will be Ongsaa the Fraction Libedaa and an 0 for the Raasi 17. Opposite to this figure set the Mattejomme of the Moon 18. Consider the Ken. If the Ken is 0 1 2 3 4 5 substract the figure of the Moons Mattejomme if the Ken is 6 7 8 9 10 11 joyn the two figures together and you will have the Sommepont of the Moon which you shall keep Explication All these Rules are conformable to those of the VIII Section to find the place of the Sun and are sufficiently illustrated by the explication made of that Section The difference in the Chajaa of the Moon discoursed of in the 14th and 15th Article This Chajaa consists in these numbers 77 148 209 256 286 296 The greatest Equation of the Moon is therefore of 4 degrees 56 minutes as some Modern Astronomers do make it though the generality do make it of 5 degrees in the Conjunctions and Oppositions XIII Set down the Sommepont of the Moon and operating as you have done in the Sommepont of the Sun you will find the Reuc and Nattireuc of the Moon Explication This Operation has been made for the Sun in the IX Section It is to find the position of the Moon in her Stations which are the 27 parts of the Zodiac XIV 1. Set down the Sommepont of the Moon 2. Over against it set the Sommepont of the Sun 3. Substract the Sommepont of the Sun from the Sommepont of the Moon and the Pianne will remain which you shall keep Explication The Pianne is therefore the Moon 's distance from the Sun XV. 1. Take the Pianne and set it down 2. Multiply the Raasi by 30 add the Ongsaa thereunto 3. Multiply the whole by 60 and thereunto add the Libedaa 4. Divide the whole by 720 the Quotient is called Itti which you shall keep 5. Divide the Fraction
the 28th of March is so near the Vernal Aequinox that it might be stiled the Aequinoxial Term and might be thought the beginning of a Solar Astronomical Year 'T is not possible to reconcile together the Rules of divers Sections which speak of the number of the years elapsed from the Epocha under the name of Aera without supposing divers sorts of Indian years The Aera is spoken of in the I. Section where we have said that the Aera is the number of the years elapsed from the Astronomical Epocha In the same Section it is resolved into solar and lunar months and in the 2d Section the lunar months are resolved into artificial days of 30 for every lunar month and into natural days such as are of common use The Aera is likewise spoken of in the IV. Section wherein it appears that it is composed of a number of those very days which are found in the II. Section so that it would seem at first that this was the Synthesis of the same Aera the Analysis of which is made in the I. and II. Section But having calculated by the Rules of the I. and II. Section and by the Supplement of which we shall speak the number of the days that ought to be in 800 years which number in the IV. Section is supposed to be 292207 we have there found only the number of 292197 days 8 hours and 27 minutes which is less by 9 days 15 hours 33 minutes than that of 292207 days which are supposed in the IV. Section ought to be found in that very number of years This difference is greater than that which is found between 800 Julian years which consist of 292200 days and 800 Gregorian years which consist only of 292194 days the difference of which is 6 days and in 800 of these years which result from the Rules of the two first Sections there is a surplusage above the Gregorian years of 13 days 8 hours 24 minutes whereas 800 years of the IV. Section do 7 days exceed 800 Julian years and 13 days the like number of Gregorian As the Gregorian is a Tropical year which consists in the time that the Sun employs in returning to the same degree of the Zodiack which degree is always equally distant from the points of the Aequinoxes and Solstices there is no doubt that the year drawn from the Rules of the I. and II. Section does nearer approach the Tropick than the year drawn from the Rules of the IV. Section which as we have remarked approaches the Astral year determined by the return of the Sun to a fixed Star and the Anomalistick determined by the Sun's return to its Apogaeum which several ancient and modern Astronomers distinguish not from the Astral no more than the Indians supposing that the Sun 's Apogaeum is fixed amongst the fixed Stars tho' most of the moderns do attribute a little motion to it Nevertheless it appears that the Indians make use of the Solar year of the IV. Section as we make use of the Tropick when according to the Rules of the VII VIII X and XI Sections they calculated the place of the Sun and his Apogaeum and of the Moon and her Apogaeum For the time elapsed from the end of this year called Krommethiapponne serves them to find the Signs Degrees and Minutes of the middle motion of the Sun They suppose then that this year consists in the Sun's return to the beginning of the Signs of the Zodiack like our Tropical year 'T is true that at present the Signs of the Zodiack are taken amongst us in two ways which were not formerly distinguished When the Ancients had observed the tract of the Sun's motion thro' the Zodiack which they had divided into four equal parts by the points of the Aequinoxes and Solstices and that they had subdivided every fourth part into three equal parts which in all do make the 12 Signs they observed the Constellations formed of a great number of fixed Stars which fell in every one of these Signs and they gave to the Signs the name of the Constellations which are there found not supposing then that the same fixed Stars would ever quit their Signs But in the succession of Ages it is found that the same fixed Stars were no more in the same degrees of the Signs whether that the Stars were advanced towards the East in regard of the points of the Aequinoxes and Solstices or that these very points were removed from the same fixed Stars towards the West and it is now found that a fixed Star passes from the beginning of one Sign to the beginning of another in about 2200 years Therefore seeing that Ptolomy in the second Age of Jesus Christ confirmed this as yet doubtful discovery which had been made three Ages before by Hipparchus there is a distinction made between the Zodiack which may be called local which begins from the Aequinoxial point of the Spring and is divided into 12 Signs and the Astral Zodiack composed of 12 Constellations which do still retain the same name tho' at present the Constellation of Aries has passed into the Sign of Taurus and that the same thing has happen'd to the other Constellations which have passed into the following Signs Yet the Astronomers do ordinarily refer the places and motions of the Planets to the local Zodiack because it is important to know how they refer to the Aequinoxes and Solstices on which depends their distance from the Aequinoxial and Poles the various magnitude of the Days and Nights the diversity of the Seasons and some other Circumstances the knowledg of which is of great use Copernicus is almost the sole person amongst our Astronomers who refers the places and motions of the Planets to the Astral Zodiack by reason that he supposes that the fixed Stars are immoveable and that the Anticipation of the Aequinoxes and Solstices is only an appearance caused by a certain motion of the Axis of the Earth But they who follow his Hypothesis cease not to denote the places of the Planets in regard of the points of the Aequinoxes in the local Zodiack by reason of the Consequences of this Situation which we have remarked 'T would be an admirable thing that the Indians who follow the Dogmata of the Pythagoraeans should herein conform to the method of Copernicus who is the restorer of the Hypothesis of the Pythagoraeans Yet there is no appearance that they designed to refer the places of the Planets rather to any fixed Star than to the Aequinoxial point of the Spring For it seems that they would have chosen for this purpose some principal fixed Star as Copernicus has done who for the Principle of his Zodiack has chosen the Point to which refers the Longitude of the first Star of Aries which was found in the first degree of Aries where was the Aequinoxial Point of the Spring when the Astronomers began to place the fix'd Stars in regard of the Points of the Aequinoxes and Solstices But at
mounted to 10 days and that of the new Moons in the same years of the lunar Cycle continued without interruption was mounted to 4 days wherefore in several Councils there was discourse concerning the manner of correcting these defects and in fine Pope Gregory XIII after having communicated his design to the Christian Princes and to the most famous Universities and having understood their Advice deducted 10 days from the year 1582 and reduced the Equinox to the day of the year wherein it had been at the time of the Epocha chosen by the Deputies of the Council of Nice He established also a period of 400 years shorter by 3 days than 400 Julian years making common the hundred years for the reserve of each 400 to compute from the year 1600 or which amounts to the same thing to reckon from the Epocha of Jesus Christ These periods of 400 Gregorian years reduce the Sun to the same points of the Zodiac to the same days of the month and of the week and to the same hours under the same Meridian the greatness of the year being supposed 365 days 5 hours 49′ 12″ According to the modern Observations in the hundred Bissextiles the middle Equinox happens the 21st of March at 20 hours after noon at the Meridian of Rome and the 96th after the hundredth Bissextile it happens the 21st of March 2 hours 43 minutes after noon which is the Equinox that happens the soonest But the 303d year after the hundredth Bissextile the middle Equinox happens the 23d of March at 7 hours 12 minutes after noon which is the slowest of all the rest By these Epocha's and by his greatness of the year it is easie perpetually to find the middle Equinoxes of the Gregorian Calendar XXVI The Rule of the Gregorian Epacts IN the Gregorian correction they interrupt not the succession of the Cycles of 19 years drawn from the ancient Alexandrian Epocha as they might have done but they observe on what day of the Moon the Gregorian year ends at every year of the Alexandrian Cycle This number of the days of the Moon at the end of a year is the Epact of the following year 'T is found that after the correction of the first year of the Cycle the Epact is 1. Every year it is augmented by 11 days but after the 19th year it is augmented by 12 always deducting 30 when it surpasses this number and taking the rest for the Epact which is done in this Age. They observe also the Variation which the Epacts do make from Age to Age in the very years of the Ancient lunar Cycle and they find that in 2500 Julian years they augment 8 days which supposes the lunar month of 29 days 12 hours 44′ 3″ 10‴ 41″″ Greg. Calend. c. 2. Explic. Calend. Greg. c. 11. n. 10. But to find the Gregorian Epacts from Age to Age they made three different Tables of which it was judged the Construction could not be clearly explained but in a Book apart which was not finished till twenty years after the correction 'T was thought at first that the whole Variation of the Gregorian Epacts was included in a period of 300000 years But this not being found conformable to the project of the correction they were forc'd to have recourse to some difficult equations of which there is not found any determin'd period XXVII A new lunisolar and Paschal Period TO supply this defect and to find the Gregorian Epacts for future Ages without Tables we do make use of a lunisolar period of 1600 years which has for Epocha the Equinoxial Conjunction of the year of Jesus Christ and which reduces the new Moons since the correction to the same day of the Gregorian year to the same day of the week and almost to the same hour of the day under the same Meridian According to this period we give to each period of 400 years since Jesus Christ 9 days of Equinoxial Epact by deducting 29 when it surpasses this number and we add 8 days to the Equinoxial Epact since the correction to have the Civil Gregorian Epact by deducting 30 when the summ surpasses this number At every hundredth year not Bissextile we diminish the Equinoxial Epact 5 days in respect of the hundredth preceding and we take every hundreth year for Epocha of 5 periods of 19 years to find the Augmentation of the Epacts for an Age at every year of the Cycle after the accustomed manner Thus to have the Equinoxial Epact of the year 1600 which is distant from the Epocha of Jesus Christ 4 periods of 400 years multiplying 4 by 9 there is 36 from whence having deducted 29 there remains 7 the Equinoxial Epact of the year 1600 which shews that the middle Equinox of the year 1600 happen'd 7 days after the middle Conjunction of the Moon with the Sun adding thereunto 8 days there are 15 which is the Civil Gregorian Epact of the year 1600 Expl. Cal. p. 420. as it is set down in the Table of the Moveable Gregorian Feasts It is evident that the Equinoxial Epact of the year 11600 which terminates this period must be 0. But to find it by the same method since that the year 11600 is removed from the Epocha of Jesus Christ 29 periods of 400 years multiplying 29 by 9 and dividing the product by 29 the quotient is 9 and the remainder 0 for the Equinoxial period Adding 8 there is the Civil Gregorian Epact of the year 11600 which will be 8 as Clavius had found it by the Gregorian Tables in the 168th page of the Explication of the Calendar which demonstrates the conformity of the Epacts of the future Ages found by the means of this period after a method so easie with the Gregorian Epacts found by the means of three Tables of the Gregorian Calendar If the hours and minutes of these Equinoxial Epacts in the 400 years are also demanded thereunto shall be always added 8 hours and besides ⅓ and 1 1 10 of as many hours as there are whole days in the Epact and a third of as many minutes Thus for the year 1600 whose Equinoxial Epact is 7 days one third of 7 hours is 2 h 20′ a tenth is 0 h 42′ a third of 7 minutes is 2′ the summ added to 7 days 8 hours makes 7 days 11 h 4′ the Equinoxial Epact of the year 1600. Deducting this Epact from the time of the middle Equinox which in 1600 happened the 21 of March at 20 hours after noon at Rome the middle conjunction preceding will be on the 14th of March at 8 h 56′ adding thereunto half a lunar month which is 14 days 18 h 22′ the middle opposition will be found on the 29th of March at 3 h 18′ In the Table of the moveable Feasts Expl. Cal. p. 420. where the minutes are neglected it is set down on the 29th of March at 3 hours To have by hours and minutes the Equinoxial Epact in the hundreds not Bissextiles from the Epact
found in the preceding hundredth Bissextile shall be deducted 5 days 2 h 12′ for the first double for the second triple for the third borrowing a month of 29 days 12 h 44′ if it is required and you will have the Epact in the hundred proposed which shall be made use of in the preceding example comparing it with the middle Equinox of the same year By this method will be found the middle oppositions in the hundred years not Bissextile a day before that they are set down Expl. Cal. p. 484. ad 561. p. 201. 284. from the year 1700 to the year 5000 in the Table of the Movable Feasts which is in the Book of the explication of the Calendar where they are set down a day later than the Gregorian Hypotheses require Ap. 596. ad p. 609. p. 634. Which has happened also in the precepts and in the examples of finding the progresses of the new and full Moons and in the Epocha's of the hundred years not Bissextile and in all the Calculations which are deduced thence as is found by comparing together the new Moons calculated in the same Table the Anticipation whereof which from one common year to another must always be 10 days 15 hours is found sometimes 9 days 15 hours as from the year 1699 to the year 1700 sometimes 11 days 15 hours as from the year 1700 to 1701 and so likewise in the other hundreds not Bissextile Upon this account there were some differences which gave occasion carefully to examine the progress of the new Moon from one Gregorian hundredth to the other Expl. Cal. p. 595. and yet these disputes were not capable of unfolding at that time the real differences that there is between several hundred Common and Bissextile years But as these Calculations of the full Moons have been made only to examine the Epacts which were regulated otherwise the differences fell only under examination which being rectified demonstrates the exactness of these Gregorian Epacts much greater than the very Authors of the Correction supposed it 'T is a thing worthy of remark that the Astronomical Hypotheses of the Gregorian Calendar are found at present more conformable to the Coelestial motions than they were supposed at the time of the correction for as it appears by the project which Pope Gregory XIII sent to the Christian Princes in the year 1577 he proposed in the regulation of the years to follow the Alphonsine Tables which were judged to be preferable to the others but to retrench three days in 400 Julian years he was obliged to suppose the solar year shorter by some seconds than the Alphonsine and to prefer this conveniency to a greater exactness and yet all the Astronomers which have since compared the modern observations with the ancient have found that the Tropical year is indeed somewhat shorter than the Alphonsine altho they be not agreed in the precise difference The greatness of the lunar month which results from the Gregorian Hypothesis of the Equation of the Epacts which is 8 days in 2500 Julian years is also more conformable to the modern Astronomers than the lunar month of the Alphonsine and the disposition of the Gregorian Epacts and the new and full Moons which result therefrom are also oftentimes more precise than they which finished the correction pretended In fine the whole system of the Gregorian Calendar has some Beauties which have not been known by those who were the Authors thereof as is that of giving the Epacts conformable to those which are found by the great lunisolar period which has for Epocha the same year of Jesus Christ and the very day which according to the antient tradition immediately precedes the day of the Incarnation from whence may be drawn the Equinoxes and new Moons with more facility than from the Aegyptian Epocha of the Golden number of which they would in some manner keep the relation 'T were to be wish'd that seeing that in the project sent to the Christian Princes and to the Universities Expl. Cal. p. 4. it was proposed to retrench 10 or 12 days from the Julian year about the end of the past Age they had retrenched 12 which is the difference between 1600 Julian years and 1600 Gregorian years to place the Equinoxes on the same days of the Gregorian year as they were in the Julian year according to the form re-established by Augustus in the Epocha of Jesus Christ rather than to restore them to the days whereon they were at the time of the strange Epocha chosen by the Alexandrians for their particular conveniency and that instead of regulating the Epacts by the defective Cycle of the Alexandrians and of seeking Equations and Corrections for the Epacts born by this Cycle they had also taken heed to the great lunisolar period of 11600 years that we have proposed which immediately gives the true days of the Epacts which reduces the new Moons to the same day of the year and of the week and which has the most august and most memorable Epocha amongst the Christians that can be imagined I doubt not that if from this time they had found this period which we have proposed they would have employ'd it not only for the Excellency of its Epocha but also because the greatness of the month which it supposes is as conformable to the Alphonsine Tables as the greatness of the year which they establish to conform themselves to these Tables the most that the conveniency of the calculation did permit For this period is composed of 143472 lunar months and of 4236813 natural days and consequently it supposes the lunar month 29 days 12 h 44′ 3″ 5‴ 28″″ 48‴″ 20‴‴ and the Alphonsine Tables do suppose it 29 days 12 h 44′ 3″ 2‴ 58″″ 51‴″ which is shorter by 2‴ than that of our period According to Tycho Brahe the lunar month is 29 days 12 h 44′ 3″ 8‴ 29″″ 46‴″ 48‴‴ which exceeds ours by three thus this month is a mean between that of Alphonsus and that of Tycho Brahe Therefore this great period composed of a number of these whole months and of a number of Gregorian periods of 400 years and consequently of entire weeks and entire days might be proposed to serve as a Rule to compare all the other periods together and to relate the times before and after the Epocha of Jesus Christ which would be the end of the first of our periods and the beginning of the second and as this great period has been invented in the exercises which are perform'd in the Royal Academy of Sciences and in the Observatory Royal under the Protection and by the Orders of the King it seems that if the Julian period has taken its name from Julius Caesar and the Gregorian from Gregory XIII this might also justly be named the lunisolar period of LOVIS LE GRAND Note That what is said at the beginning of Page 189 that in this extract the numbers are written from the top to the bottom
after the manner of the Chineses must be understood that they place the sum of the minutes under that of the degrees that of the seconds under that of the minutes that of the thirds under that of the seconds and so successively as we place the sums one under the other when we would make the Addition thereof but in every particular sum whether of degrees or minutes seconds thirds or others the Cyphers are ranged in this extract according to our manner of ranging them Note Also that the word Souriat which is found Page 193 and elsewhere is the name of the Sun in the learned Language of Paliacata and that the word aatit which is found Page 195 is likewise the name of the Sun but in the Balie Tongue and also in the vulgar Language of Paliacata as it has been before remarked in the Chapter of the Names of the days of the months and of the years The End The Problem of the Magical Squares according to the Indians THis Problem is thus A square being divided into as many little equal squares as shall be desired it is necessary to fill the little squares with as many numbers given in Arithmetical progression in such a manner that the numbers of the little squares of each rank whether from top to bottom or from right to left and those of the Diagonals do always make the same sum Now to the end that a square might be divided into little equal squares it is necessary that there are as many ranks of little squares as there shall be little squares to each rank The little squares I will call the cases and the rows from top to bottom upright and those from right to left transverse and the word rank shall equally denote the upright and transverse I have said that the Cases must be filled with numbers in Arithmetical progression and because that all Arithmetical Progression is indifferent for this Problem I will take the natural for example and will take the Unite for the first number of the progression Behold then the two first examples viz. the square of nine Cases and that of 16 filled the one with the nine first numbers from the unite to nine and the other with the sixteen first numbers from the unite to 16 So that in the square of 9 Cases the summ of every upright and that of every Transverse is 15 and that of each Diagonal 15 also and that in that of 16 Cases the summ of every upright and that of every Transverse is 34 and that of each Diagonal 34 also 4 9 2 3 5 7 8 1 6 1 15 14 4 12 6 7 9 8 10 11 5 13 3 2 16 This Problem is called Magical Squares because that Agrippa in his second Book De Occulta Philosophia cap. 22. informs us that they were used as Talismans after having engraved them on plates of diverse metals the cunning that there is in ranging the numbers after this manner having appear'd so marvellous to the ignorant as to attribute the Invention thereof to Spirits superior to man Agrippa has not only given the two preceding Squares but five successively which are those of 25 36 49 64 and 81 Cases and he reports that these seven squares were consecrated to the seven Planets The Arithmeticians of these times have looked upon them as an Arithmetical sport and not as mystery of Magic And they have sought out general methods to range them The first that I know who laboured therein was Gaspar Bachet de Meziriac a Mathematician famous for his learned Commentaries on Diophantus He found out an ingenious method for the unequal squares that is to say for those that have a number of unequal cases but for the equal squares he could find none 'T is in a Book in Octavo which he has entituled Pleasant Problems by numbers Mr. Vincent whom I have so often mentioned in my Relation seeing me one day in the Ship during our return studiously to range the Magical squares after the manner of Bachet informed me that the Indians of Suratte ranged them with much more facility and taught me their method for the unequal squares only having he said forgot that of the equal The first square which is that of 9 cases return'd to the square of Agrippa it was only subverted but the other unequal squares were essentially different from those of Agrippa He ranged the numbers in the cases immediately and without hesitation and I hope that it will not be unacceptable that I give the Rules and the demonstration of this method which is surprizing for its extream facility to execute a thing which has appeared difficult to all our Mathematicians 1. After having divided the total square into its little squares they place the numbers according to their natural order I would say by beginning with the unite and continuing with 2 3 4 and all the other numbers successively and they place the unite or the first number of the Arithmetical Progression given in the middle case of the upper transverse 2. When they have put a number into the highest case of an upright they place the following number in the lowest case of the upright which follows towards the right that is to say that from the upper transverse they descend immediately to that below 3. When they have placed a number in the last case of a transverse the following is put in the first case of the transverse immediately superior that is to say that from the last upright they return immediately to the first upright on the left 4. In every other occurrence after having placed a number they place the following in the cases which follow diametrically or slantingly from the bottom to the top and from the left to the right until they come to one of the cases of the upper transverse or of the last upright to the right 5. When they find the way stopp'd by any case already filled with any number then they take the case immediately under that which they have filled and they continue it as before diametrically from the bottom to the top and from the left to the right These few Rules easie to retain are sufficient to range all the unequal squares in general An example renders them more intelligible 17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9 This square is essentially different from that of Agrippa and the method of Bachet is not easily accommodated thereto and on the contrary the Indian method may easily give the squares of Agrippa by changing it in something 1. They place the unite in the Case which is immediately under that of the Center and they pursue it diametrically from top to bottom and from the left to the right 2. From the lowest case of an upright they pass to the highest case of the upright which follows on the right and from the last case of a Transverse they return to the left to the first case
4 1 ♈ Quei ♃  15 32  15 32 ♈ Leu ♀  28 46  26 46 ♈      corrige 28 46 ♈ Cuey ♃  41 46  11 46 ♉ Mao ☉  53 37  23 37 ♉ Pie ☽  63 16  3 16 ♊ Sang ♂  77 14  17 14 ♊ Cu ☿  78 35  18 35 ♊ Cing ♃  90 8  0 8 ♋ Qu'ei ♀  120 33  0 33 ♌ Lieu ♄  125 9  5 9 ♌ Sing ☉  142 9  22 9 ♌ Chang ☽  150 32  0 32 ♠Ye ♂  168 36  18 36 ♠Chin ☿  185 36  5 39 ♎ Fixae ad initia Constellationum Sinensium ex comparatione Tabulae praecedentis cum Tychonica deductae Longitudines Tychonicae ad annum 1628. Nomina Fixae Grad Min. Kio Spica Virginis ♎ 18 39 Kang Austrina in fimbria Virginis ♎ 29 14 Ti. Lucida lancis australis ♠9 54 Fang Austr trium in fronte Scorp ♠27 49 Sing Praeced lucent in corp Scorp ♠2 34 Vi. Dexter humerus Ophiuci ♠20 8 Ki. Cuspis Sagittarij ♠25 43 Teu Antecedens in jaculo Sagitt ♑ 5 3 Nieu Austr in cornu praeced Capr. ♑ 28 54 Niu Antecedens in manu Aquarij ♒ 6 35 Hiu In humero sinistro Aquarij ♒ 18 14 Guei Dexter humerus Aquarij ♒ 28 12 Xe. Prima alae Pegasi ♓ 18 20 Pi. Extrema alae Pegasi ♈ 4 1 Quei In sinistro brachio Andromed ♈ 15 32 Leu. Sequens in cornu austr Ariet. ♈ 28 46 Guey In femore Arietis ♉ 11 46 Mao Occid trium lucid in Pleiad ♉ 23 37 Pie Oculus Tauri Barcus ♊ 3 16 Sang. Recedens Balthei Orientis ♊ 17 14 Cu. In extremo cornu austr Tauri ♊ 19 35 Cing Pes sequens praeced Gemin ♋ 0 7 Qu'ei Borea praec in quad lat Canc. ♌ 0 33 Lieu. Septentrion in rostro Canc. ♌ 5 30 Sing Cor Hydrae ♌ 22 9 Chang. In medio corpore Virginis ♠0 37 Ye In basi Crateris ♠18 36 Chin. Tertia in ala austrina Virg. ♎ 4 59 This agreement of the numbers of these Tables with those of Tycho almost in the same minute gave me ground to imagine that these Tables have been calculated by the Jesuites who went about an Age since to China and not by the Chineses For what probability is there that without being drawn from Tycho's Tables they should be so conformable thereto Our Astronomers of this Age find difficulty to agree in the same minute in the place of the fixed Stars and it is known that between the Catalogues of Tycho ane that of the Landgrave of Hesse made at the same time by excellent Astronomers there is a difference of several minutes Wherefore it is not very probable that the Observations of the Chineses should agree almost always with the Observations of Tycho in the same minute V. The Method of terminating the Chinese Constellations at any time FAther Martinius remarks that the Chineses do determine the Longitude in the Heaven by the Poles of the World that is to say by great Circles drawn through the Poles perpendicular to the Equinoxial where we denote the right ascensions of the Stars Therefore the stars which are between two Circles that do pass through the Poles and through the two fixed Stars which terminate a constellation relate to that very constellation But it appears by the comparison of the two preceding Tables that the longitudes are not set down differently in the Table of Father Martinius from what they are noted in Tycho's Table which reduces the Stars to the Ecliptick and not to the Equinoxial They are not therefore set down after the Chinese manner but to reduce them after the Chinese method it is necessary to refer the Stars which are at the beginning of every constellation to the Equinoxial and to find their right ascensions and the points of the Zodiack which shall have the same right ascensions will be at the beginning of these constellations When a Star falls in the Colure of the Solstices as the foot of Gemini in that Table where begins the constellation Cing there is no difference between its longitude after our manner and its right ascension which is the longitude after the Chinese but as the Stars remove from the Colure of the Solstices the difference of their longitudes and of their right ascensions augments so much more as the latitudes or declinations of the Stars are greater And because that the fixed Stars remove continually from one Colure and approach the other by a motion parallel to the Ecliptick and oblique to the Equinoxial this difference varies continually and otherwise more constellation than in another whence it happens that from one Age to the other the same Chinese constellation determined by two fixed Stars enlarges or contracts and comprehends not always the same number of fixed Stars Therefore to know in what Chinese constellation a Planet falls at a certain time it is necessary to find for this time the right ascension of the Planet and the right ascension of the fixed Stars adjoyning which determine the beginning and end of the Constellations which we should not have known without the reflexion which we have made that every Constellation begins with a certain fixed Star and without the advice which Father Martinius gives us that the Chinese longitudes are taken from the Poles of the world that is to say differently from what they are set down in this Table It appears by this Table that the Constellation Xe here treated of begins with the first of the Wing of Pegasus and ends with the last of the same Wing seeing that according to the second Column of this very Table this Constellation began in the year 1628 at 18 degrees and 20 minutes of Pisces where we find at the same year the first of the Wing by Tycho's Table reduced to the same time tho the first Column of the Chinese Table gives two degrees less which is doubtless an error of the impression or calculation which has crept into the two works of Father Martinius The Originals of the Tables of Tycho and Longimontanus do likewise give the last of the Wing at 4 degrees and a minute of Aries where ends the Constellation Xe and where begins the following Constellation Pi though the Rodolphine and Philolaick Tables with those of Father Ricciolus do show the same Star at 4 degrees of Pisces which certainly is an error of the Transcribers which is slipt into the works of these Astronomers As these two Stars have a great Northern longitude the first being 19 degrees and 26 minutes the second 12 degrees and 35 minutes the difference between their longitude and their right ascension which the Chineses take for longitude is considerable at present forasmuch as these Stars are near the Colure of the Equinoxes where this difference is greater than elsewhere But it was
they congratulated for that an Eclipse which they had predicted had not hapned the Heaven they said having spared him this misfortune and this Father has left to Mr. Thevenot a Manuscript of the same Eclipses which he has printed in his Chronology entituled Eclipses verae falsae without distinguishing the one from the other But without accusing the Chineses of falshood it may be said that it may be that the Eclipses set down in the Chinese Chronology might happen and that the contradiction which appears therein may proceed from the Irregularity of their Calendar on which no Foundation can be laid XXI A Composition of the lunisolar Periods THE Interval between the two Epocha's of the Indians which is 1181 years is a lunisolar period which reduces the new Moons near the Equinox and to the same day of the week This period is composed of 61 periods of 29 years which are longer than 1159 tropical years and of two periods of 11 years which are shorter than 22 tropical the defect of the one partly recompencing the excess of the others As the mixture of the lunisolar years some longer others shorter than the tropical does more or less recompence the defect of the one by the excess of the other as far as the Incommensurability which may be between the motions of the Sun and Moon permits it It makes the lunisolar periods so much the more precise as they reduce the new Moons nearer the places of the Zodiack where they arrived at the beginning The Antients have first made the tryal of the little periods the most famous of which has been that of 8 years which has been in use not only amongst the ancient Greeks but also amongst the first Christians as it appears by the Cycle of St. Hippolytus published at the beginning of the third Age. This period composed of five ordinary and three Embolismick years being found too long by a day and half which in 20 periods do make above a month they were obliged to retrench a month in the twentieth period But afterwards the period of 8 years was joyned to another of eleven years composed of seven ordinary and four Embolismick which is too short about a day and a half and thereof was made the period of 19 years which was supposed at first to be exact tho it has since had occasion of amendment in the number of the days and hours which it comprehends The correction of this period was the origine of the period of 76 years composed of 4 periods of 19 years corrected by Callippus and of the period of 304 years composed of 16 periods of 19 years corrected by Hipparchus The Jews had a period of 84 years composed of four periods of 19 years and one of 8 years which reduces the new Moons near the Aequinox on the same day of the week But the most famous period of those which have been invented to reduce the new Moons to the same place of the Zodiack and to the same day of the week is the Victorian of 532 years composed of 28 periods of 19 years Yet the new Moon which should terminate this period happen'd not till two days after the Sun's return to the same point of the Zodiack and two other days before the same day of the week to which the conjunction was arrived at the beginning of the period and these defects are multiplied in the succession of the times according to the number of these periods Nevertheless after that the defects of this period were known by every one several famous Chronologers have not ceased to make use thereof and they terminate it on the same day of the week and on the same day of the Julian year which in this interval of time exceeds the solar tropical year 4 whole days and the lunisolar year somewhat less than two days They do also multiply this period by the Cycle of 15 years which is that of the Indictions the origine of which is not more ancient than 13 Ages to form the Julian period of 7980 years of which they establish the Epocha 4713 years before the common Epocha of Jesus Christ. They prefer this imaginary period in which the errors of the Victorian period are multiplied 15 times to the true lunisolar periods and they do likewise prefer this Ideal Epocha which they suppose more antient than the World to the Astronomical and Historical Epocha's even so far that they refer thereto the Historical Acts of the antient times before Jesus Christ and before Julius Caesar tho the Indictions were not as yet in use that there was then no Calendar to which this period could serve to regulate the days of the week and that in fine the Cycle of 19 years extended to this time demonstrates not the state of the Sun nor of the Moon which are the three principal things for which these three Cycles which from the Julian period have been invented Wherefore it gives not so exact an Idea of the ancient times which were not regulated after this manner as of those of the thirteen last Ages which were regulated amongst us according to the Julian year But the lunisolar periods of 19 years which in regard of the tropical years are somewhat too long being joyned to the periods of 11 years which are too short do form other periods more precise than those which compose them Among these periods the first of the most precise are those of 334 353 and 372 years the last of which is terminated also on the same day of the week and might be placed in the stead of the Victorian XXII Lunisolar Periods composed of whole Ages THE first lunisolar period composed of whole Ages is that of 600 years which is also composed of 31 periods of 19 and one of 11 years Though the Chronologists speak not of this period yet it is one of the ancientest that have been invented Antiq. Jud. l. 1. c. 3. Josephus speaking of the Patriarchs that lived before the Deluge says that God prolonged their Life as well by reason of their Vertue as to afford them means to perfect the Sciences of Geometry and Astronomy which they had invented which they could not possibly do if they had lived less than 600 years because that it is not till after the Revolution of six Ages that the great year is accomplished This great year which is accomplished after six Ages whereof not any other Author makes mention can only be a period of lunisolar years like to that which the Jews always used and to that which the Indians do still make use of Wherefore we have thought necessary to examine what this great year must be according to the Indian Rules By the Rules of the I. Section it is found then that in 600 years there are 7200 solar months 7421 lunar months and 12 228. Here this little fraction must be neglected because that the lunisolar years do end with the lunar months being composed of intire lunar months It is