THE LIFE OF THEVETAT, Translated from the Balie.
AFter the birth of Pouti Sat This is one of the names of Sommona-Codom: Sat, in my Opinion signifies Lord in Baly, as Tchaou in Siamese, and so he is called Pouti Sat, and Pouti Tchaou; the word Pouti is Baly., who by his good works in process of time arrived at the Nireupan, his Father, King Taousoutout, consulted the Soothsayers to know what would betide him, and the fortune that a Son would have, at whose Nativity there had appeared so many Wonders. They all assur'd him that he had great reason to rejoyce, seeing that if his Son did continue in the World, he would be Emperor of the whole Earth; or that if he turned Talapoin, by abandoning the Pleasures of the Age, he would arrive at the Nireupan. It is necessary to know that this Emperor had seven sorts of things, which were so peculiar to him, that there was none besides him that had them. The first was a Glass-bowl, which he made use of to rid himself of his Enemies, by throwing it against those whom he would kill; which being let go, went to cut off the Enemies head, and then return'd of it self. The second were Elephants and Horses of an extraordinary goodness and beauty, which did fly with the same facility as they walked. The third was a piece of Glass, by the means of which he could have as much Gold and Silver as he pleased: for to this end he needed only to throw it into the Air, and of the heighth that it went, there would grow a Pillar of Gold or Silver. The fourth was a Lady, come from the North, of a marvellous Beauty, who had a great glass Pot sustained by three Columns of the same: then when she would boil any Rice, she needed only to put never so little Rice therein, and the Fire would kindle of it self, and extinguished also of it self when the Rice was boiled: the Rice multiplied so exceedingly in the boiling, that it would feed five hundred men and more. The fifth was a man, who took care of the House, and who had Eyes so penetrating, that he did see Gold, Silver, and Precious Stones in the Bowels of the Earth. The sixth was a great Mandarin of an extraordinary Strength and Valour. The last was, that he had a Thousand Children by one Queen, which indeed did not all come out of her Womb. One alone came out thence, and the rest were engendered of the Water, Blood, and whatever comes out at the Delivery. Every one of these Children in particular being grown up, was capable of subduing and vanquishing all the Enemies, which their Father could have. Now there was one of the Soothsayers, who taking the Father aside, told him, that assuredly his Son would abandon the World, would quit the Kingdom, and would consecrate himself to Repentance by turning Talapoin, to be able by his good works to arrive at the Nireupan.
[Page 146]His Relations, to the Number of Ten Thousand, understanding by the Answer of the Soothsayer, that the Universal Demesne of this whole World, or the Nireupan were ascertained to this young Prince, resolv'd amongst themselves every one to give him, when he should be a little advanced in years, one of their Sons to make up his Train; and so they did. When therefore this Prince, after the Repentance of some seven years, which he performed in the Woods, was become worthy of the Nireupan, a great many of these young men, whom we mentioned, which were of his Retinue, turn'd Talapoins with him; but amongst this great Company there were six, who though they were his Relations, and in his Train, would not yet follow him. We will recite the Names thereof, by reason that in the sequel we shall speak only of them. The first is called Pattia, the second Anourout, the third Aanon, the fourth Packou, the fifth Quamila, the sixthThe Siameses report that Thevetat was the Brother of Sommona-Codom, by this History he only is his Relation. Thevetat: and it is of this last that we wrire the History. One day the Fathers of these six young Princes being accidentally met together, after having discoursed a long time about several indifferent things, one of them observed to the rest that not any of their Sons had followed the Prince to turn Talapoin; and they said amongst themselves, is it because that not any of our Children will turn Talapoins, that we shall upon this account cease to be his Relations? Hereupon therefore the Father of Anourout, one of these six young Princes, who was the Successor of Taousoutout, said to his Son, that though he was of Royal Blood, yet if Sommona-Codom would receive him into his Company as a Talapoin, he would not hinder him, though some Persons of his Quality would not follow this Example.
Prince Anourout being accustomed to his Pleasures, and to have whatever he desired, understood not what this word of refusal, No, did mean. One day as these six young Princes diverted themselves at Bowls, and played for Confects for a Collation, Anourout having lost, sent a Man to his Mother, to intreat her to send him some Confects, which she did: having eaten them, they played for a second Collation, then a third and a fourth; and his Mother sent him some Confects, till all were gone: But as Anourout still sent to have more, his Mother then told the Servant: No, there are no more. Which being related to the Son, and the Son not understanding what these words, No there are no more, did signify, having never heard them spoken, thought that his Mother meant that she had yet others more excellent, the name of which must be these words, No there are no more. He therefore sent back his Servant to his Mother, desiring her to send him some of the Confects No there are no more; his Mother perceiving hereby that her Son understood not these words, No there are no more, resolved to explain them to him. She took a great empty Dish, covered it with another, and gave it to the Servant to carry to her Son. But then the Genij of the City Koubilepat reflecting on all that had passed between Prince Anourout and his Mother, and knowing that the Prince understood not these words, No there are no more, (because that formerly in another Generation he had Charitably given to the Talapoins his Portion of Rice, and had demanded and desired, that in process of time, when he should come to revive again in this World, he might not understand what these words, No there are no more, did mean; neither did he understand or know the place where the Rice did grow) they said that it was necessary speedily to assemble themselves with the other Genij, These Genij are not invulnerable, and their care is to recompence and punish. to consult what was proper to be done, because that if Anourout found the Plate empty, their head as a Punishment would be broke in seven pieces. It was therefore resolved that they would fill it with Confects brought from Heaven, which they did. The Servant who carried the Plate, having laid it at the place, where these young Princes were diverting themselves, Anourout, who only expected this to pay his Debt to his Companions, ran to the Plate and uncovered it, and found it as before, full of Confects, but so excellent that the whole City was perfumed with their Odor: The excellent taste which they found in these Confects, diffused it self through their whole Body. The Plate was soon empty, and hereupon Anourout reflecting on the goodness of these Confects said unto himself: It must needs be that my Mother has scarcely loved me till now, seeing that she never gave me the Confects, No there are no [Page 147] more. Returning home, he went to ask his Mother, whether she loved her Son. His Mother, who passionately loved him, was exceedingly surprized at this question, and answered him that she loved him as her own Heart, and Eyes. And why, if what you say is true, have you never given me the Confects, No there are no more. For the future I beseech you to give me no other: I am resolved to eat only of these. His Mother, astonished to hear her Son speak thus, addressed her self to the Servant, who had carried the Plate, and asked him secretly, whether he saw any thing therein, to whom he answered yes, that he saw the Dish filled with a kind of Confects, which he had never seen before: and then the Mother of Anourout comprehended the Mystery, and judged rightly that the Antient Merit of her Son had procured him these Confects, and that the Superior Genij had rendered him this good Office. Afterwards therefore when the Prince demanded these Confects of his Mother, she only took an empty Dish, covered it with another, and sent it him, and the Plate was always found full as I have said.
Anourout understood not likewise the meaning of these words, to assume the Pagne or Talapoins Habit, and having one day desired his elder Brother Pattia to explain them to him, Pattia informed him what he knew, that to assume the Talapoins Habit, was intirely to shave his Hair and Beard, to sleep on a Hurdle, and to cloath himself with a yellow Pagne. Which Anourout understanding, he told his Brother that being accustomed to live at his ease, and to have all things at pleasure, he should find much difficulty to lead this Life: And Pattia replyed, seeing then my Brother that you will not resolve to turn Talapoin, consider which is best: but also not to live Idly, learn to work and continue at my Father's House as long as you please. Anourout asked him what he meant by this word to Work, which he understood not: Pattia then said unto him, how can you know what it is to work, seeing that you neither know where nor how the Rice grows? One day indeed Quimila, Pattia, and Anourout discoursing together upon the Place where the Rice might grow, Quimila replyed that it growed in the Barn: Pattia, said no, and asserted that it grew in the Pot: And Anourout told them both that they understood nothing, and that it grew in the Dish. The first having one day observed that the Rice was taken out of the Barn, thought it was there that it grew. The second had seen it taken out of the Pot, and 'tis that which gave him occasion to think that it grew in the Pot: But the third who had never seen it otherwise than in the Dish, really believed that the Rice grew in the Dish, when one had a desire to eat: and thus all three knew nothing of the matter.
Anourout declared afterwards to the other two that he was not inclined to work, and that he chose rather to turn Talapoin: and he went to ask leave of his Mother. She refused him two or three times: but as he would not be denied, and as he continually pressed her more and more, she told him that if Pattia would turn Talapoin, she would permit him to follow him. Anourout went therefore to sollicit his five other Companions to make themselves Talapoins, and they resolved to do it seven days after. These seven days being elapsed they went out of the City, with a great Equipage, seeming to go to divert themselves in the Country. In their retinue they had a great many Mandarins mounted on Elephants, with a good number of Footmen. But principally they had in their Train a Barber by Profession, named Oubbali. Being atrived at the Confines of the Kingdom, they sent back all their retinue except Oubbali: then they stript themselves of their Cloaths, folded them up very neatly, and put them into the hands of Oubbali, to make him a present thereof, telling him that he should return into the City, and that he had wherewithal to live at his ease the remainder of his days. Oubbali, very much afflicted to separate himself from these six Princes, and yet not daring to contradict what they order'd him, after having taken his leave of them departed weeping, and took his road towards the Ciry, from whence they had set out together. But it presently came into his mind, that if he returned, and that the Parents of these young Princes should see the cloaths of their Children, they would have reason to suspect him of their death, and likewise to put him to death, not believing that these young [Page 148] Princes would have quitted such precious Habits to give them to him. Hereupon he hung up these Habits on a Tree, and returned to seek out these young Lords. So soon as they saw him, they demanded the reason of his return, and having declared it to them, he testified that he would continue with them, and assume the Habit of a Talapoin. These young Princes presented him then to Sommona-Codom, beseeching him to give the Habit to him, rather than to them: for finding themselves yet full of the Spirit of the World, and proud of heart, and willing to humble themselves, they desired that Oubbali, who was very inferior to them in the World, might be their Elder in Religion, to the end they might be obliged to respect him, and to yield to him in all things: theI suppose that this is a remark which the Translator has inserted into the Text, and we may therein remark some other. Rule, requiring that between two Talapoins the Eldest have all the Honours, though the youngest be much the more Learned. Sommona-Codom granted them their Request, and they assumed the Habit a little while after Oubbali. Being therefore entred into the time of Repentance, Pattia by his merit had a Caelestial Heart, Eyes, and Ears; that is to say he understood every thing, he knew the Hearts of others, he saw all things, and heard every thing, notwithstanding the distance and all obstacles. One day after Sommona-Codom had preached, Anourout was advanced to the degree of an Angel. At the same time Aanon a Talapoin, dear to Sommona-Codom, went to Sonda the first degree of Perfection. Packou and Quimila after having a long time exercised themselves in Prayer and Meditation, were advanced to be Angels. There was Thevetat alone that could obtain no other thing than a great strength, and the power of doing MiraclesThe Miracles of Jesus Christ perswade them that he is Thevetat: but it is necessary to evince to them that the Miracles which they attribute to Thevetat are to do Evil, and that those of Jesus Christ are for Good..
Sommona Codom being gone with his Talapoins to the City of Kousampi, the Inhabitants came daily to make them presents, sometimes to Sommona-Codom, sometimes to Mogla and to Saribout, his two principal Favourites, one of which sat on his Right hand, and the other on his Left: some to Kasop and Pattia, others to Quimila and Packon, or to Anourout; but what is remarkable, no body presented to Thevetat: and they spake no more of him than if he had never been in the world, whereat he was extreamly inraged. Is it, said he, that I am not a Talapoin as well as the others? Is it that I am not of the Royal Blood like them? Why has no one made any Present to me? He therefore resolved instantly to seek out some body that should present him, and to allure some Disciples. The King of the City Pimpisaan, was arrived to the first degree of Perfection, with One Hundred and Ten Thousand men, all Disciples of Sommona-Codom: and he had a Son as yet young, and who knew not what Evil was, Thevetat contriving to seduce this Son, to make use of him in his wicked designs, went from the City of Pinmesan, to go to Rhacacreu, and assumed by the power he had, the shape of a little Infant, with a Serpent round each Leg, another round his Neck, and another round his Head. Besides this he had one, who embracing him on the left Shoulder, descended underneath the right Shoulder before and behind. In this equipage he took wing, and went through the Air to the City of Rachacreu. He lights at the Feet of Achatasatrou, who was that young Prince the Son of the King of the City ofJust before he said Pimpisaan. Pimmepisan, and who seeing Thevetat after this manner, with his whole body twisted about with Serpents, conceived a great Terror thereat. Being affrighted at a thing so strange, he asked Thevetat who he was, and Thevetat having told him his Name, and entirely confirmed him, re-assumed his first shape, that is to say his Talapoins Habit, and his Serpents disappeared. Achatasatrou hereupon conceived a great esteem of Thevetat, and made him great Presents, an Honor which effected the ruine of Thevetat by the Pride he conceived thereat; for from that time he contrived the design of making himself Master and Chief of his Brethren. He went therefore to Sommona-Codom; he found him out who preached to the King, saluted him, approached him, and after some discourse told him, that being already in a very advanced Age, it was not fit that for the future he should take so much Pains, but that he ought to think of spending the rest of his days pleasantly and at his own Ease. I am, added he, ready to assist you to the utmost of my power, and as the care of so many Religious overwhelms you, you may for the future discharge it upon me. This is the Language, which the extream [Page 153] desire of seeing himself above all, did put into his Mouth. Sommona-Codom who knew him, refus'd and contemn'd his demand, whereat Thevetat was so enraged, that he only plotted ways to revenge himself. He returned to the City of Rachacreu to find out Achatasatrou his Disciple, and perswaded him to get rid of his Father, the sooner to get upon the Throne, and afterwards to afford him the means of putting Sommona-Codom to Death, and of setting up himself in his stead. Achatasatrou then caused his Father to be put into a Dungeon loaded with Irons, and seized on the Throne: Thevetat expressed unto him his Joy, and desired him to remember the Promise he had made him. The new King presently granted him 500 men armed with Arrows, to go and kill Sommona-Codom. They found him walking at the Foot of a Mountain; and his sight alone impressed in them so much Fear and Respect, that there was not any one who dared to let fly an Arrow; they all remained immoveable, every one with their Bow bent. Sommona-Codom intreated them to tell him the Author of their Enterprize; and when they had informed him, he preached a Sermon unto them, at the end of which they arrived at the first degree of Perfection, and returned home. So soon as Thevetat saw that they had missed their blow, he went himself on the Mountain, and applied himself to roul down Stones to the bottom, designedly to kill Sommona-Codom: and when he thought he had thrown down enough to kill him, he descended thence, and called him two or three times by his Name; Sommona-Codom who had ascended the Mountain at one side, when Thevetat descended at the other, answered that he was at top: Thevetat presently re-mounted, and at the same time Sommona-Codom, who knew him without seeing him, descended without being seen. Thevetat re-ascended again in vain, and he died with rage. Mean while Sommona-Codom seeing himself thus persecuted, said unto himself, what Crime, what Sin have I committed? Now that I am at the heighth of perfection, that I have performed so great a Penitence that I have preached so much and taught so holy a doctrine, yet they cease not to persecute me to kill me. And by thus examining himself he remember'd, that one day being drunk,Sommona-Codom sins and is punished in Hell. *he had hit a Talapoin with a little stone which he had flung, and which had drawn out a little blood, and he knew that he was to be punished in five hundred Generations successively; that he had already been punished in 499, and that this was the five hundredth: besides which, he had been a long time in Hell. Wherefore knowing moreover that if he permitted not Thevetat to do him some mischief, he should kill him with rage, and go into Hell after his death, he rather chose that a small shiver of a Flint which Thevetat threw at him, and which dash'd in pieces against another, should wound him in the foot to draw out a little blood. 'Twas he that stretch'd out his foot to receive the blow, and thereby he appeased the anger of Thevetat, who for some time forgot the Resolution of killing him.
One day as Sommona-Codom went to beg Alms in the City of Rachacreu, Thevetat being advertised thereof, procur'd the King to send his most mischievous Elephants to do him a mischief, if he did not retreat. Sommona-Codom ceased not to continue his road with his Talapoins: and as they came near the Elephants, Aanon went before his Master, to secure him from the fury of the Elephants, by exposing himself, but they hurt no body.
At his departure out of the City, Sommona-Codom retir'd into a Pagod, where the people brought him to eat. He eat, and preached afterwards to all this multitude, which was come out to the number of Ten Millions of persons, to hear him: and he converted fourscore and four Thousand, some of which went to the first degree, others to the second, others to the third, others to the fourth degree of Perfection. Several enlarged themselves on the Praises of Aanon, who loved his master so dearly, as to expose his life for him. Whereupon Sommona-Codom informed them, that this was not the first time Aanon had done it. Another time he said unto them, when I was King of the Ong ('tis a kind of Bird) Aanon being also an Ong, and my younger Brother, he saved my life by exposing his in my place. When the King Achatasatrou had heard Aanon thus commended, for having exposed his life for his Master, he recalled the 500 men, which he had given to Thevetat: and thus Thevetat saw himself abandon'd [Page 154] by every one. He had leave to beg, but no body gave him wherewith to live: being reduced to the extremity of seeking a livelihood himself, he returned to Sommona-Codom, and offered him five Propositions, which he intreated him to grant. The first was, that if there were some Talapoins who would oblige themselves to live in the Woods, and sequester'd from the World, he would permit them. The second, that those who would engage themselves to live only on Alms, might submit themselves thereto. The third, that he would grant the liberty of cloathing themselves poorly to such who would desire always to do it, and who would oblige themselves to be always contented with old Pagnes, patched and nasty. The fourth, that he would permit those which should desire it, to refuse all their life to have any other Convent or Lodging, than under a Tree; and in fine, that they who would never eat Meat or Fish, might deprive themselves thereof. Sommona-Codom answer'd him, that it was necessary to leave to every one his own will, and to oblige no person to more than he would, or even than he could. Thevetat rose up after Sommona-Codom's Answer, and cried aloud to all the Talapoins that were present; let all those that would be happy follow me: and immediately a Troop of ignorant persons, to the number of five hundred, deceived by the specious appearance of his false intentions, resolved to follow him, and exactly to keep the five things which he proposed. They had some devoto's which nourish'd them, and which supply'd all their wants: although they knew that Thevetat had kindled the War amongst the Talopoins, by separating himself from his Master. When Sommona-Codom saw that he took so wicked a Conduct, he endeavoured to reclaim him, by divers Sermons which he made to him, to convince him that there was not a greater Crime than this. Thevetat heard him very patiently, but without making any benefit thereby: for he briskly quitted Sommona-Codom. On the Road he met Aanon, who demanded Charity from door to door in the City of Rachacreu, and told him that he had just quitted his Master, to live for the future after his own humor. Aanon told it to Sommona-Codom, who repli'd, that he knew it very well, that he saw that Thevetat was an unhappy wretch, that he would go into Hell. This, adds he, is exactly as Sinners do; they commit great Crimes, and this they call doing Good, and what is Good they call Evil. Virtuous Men do good without trouble, whereas it is a punishment to the wicked; and on the contrary, Evil displeaseth the Good, and the wicked make a pleasure thereof. Knowing therefore the place and quarter where Thevetat was retir'd with his 500 Disciples, he sent Mogla and Saribout thither to bring them away. They found Thevetat preaching, and when he saw them, he thought that like him they had quitted their Master. Wherefore after his Sermon, he said unto them: I know that when you were with Sommona-Codom you were his two Favourites, and that he made you to sit one at his right hand, and the other at his left, I desire you to accept the same thing from me. Not to know him, and the better to cover their design, they told him that they kindly accepted it, and seated themselves indeed at his sides. Then he intreated them to preach in his stead whilst he went to repose. Saribout preached, and after his Sermon all those 500 Talapoins arrived at the perfection of an Angel, rose up into the Air and disappear'd. Conkali the Disciple of Thevetat ran to wake him and tell him, what had past. I had well advised you not to trust them, said he unto him: than he began to be vexed, and to such a degree, that he beat Conkali so as to make his Mouth to bleed. On the other hand, when the Talapoins, which were with Sommona-Codom, saw Mogla and Saribout return with their Company, they went immediately to acquaint their Master, and to express unto him the astonishment wherein they were to see Mogla and Saribout return so well accompanied, after having seen them depart alone. Mogla and Saribout came also to salute their Master, and the new come Talapoins told Sommona-Codom that Thevetat imitated him in all things. You very much deceive your selves, said he unto them, to think that he does what I do: formerly indeed he Counterfeited me, but now he practises the same. Then his Disciples said unto him, we know our dear Master that Thevetat Counterfeits you at present, but that he has Counterfeited you in times past we know nothing thereof, wherefore we desire you to explain it to us. He then open'd his mouth and [Page 155] said, you know that heretofore being a Bird, but a Bird which sought his living sometimes in the Water, sometimes on the Land, Thevetat at the same time was a Land-Fowl and had great Feet. After my example he would catch Fish, but he entangled his Neck in the Weeds, not being able to pluck it out, and died there. I remember also that I once was one of these little red Birds, which do eat the Worms of the Trees. Thevetat was a Bird of another sort, and he affected to nourish himself like me. I sought the Worms in the Trees, which have the heart included in the middle of the Trunck, and I sought out these Trees in a great and spacious Forest, he sought the Worms in Trees without heart, but which have an appearance thereof; and his head was bruised as a punishment. Another time I was born a Rachasi, and he was born a wild Dog. Now the Rachasi do live only on the Elephants which they kill in the Woods, and the Dog of the Woods would act like me, but he reapt the evil thereof: for the Elephants trampled him under their Feet and crushed him in pieces.
Another day Sommona-Codom preaching to his Disciples, spake to them of Thevetat, and said unto them. Once I was one of the Land-fowl with great Feet, and he was Rachasi. In eating of meat he would swallow a bone, which sticking in his Throat would strangle him. I had compassion on him, I drew the bone out of his Throat at the request he made me, confessing that what force soever he had used, yet he could not relieve himself. I entered therefore into his great Throat, which he open'd, and pluck'd out this bone with my Beak: and as he had promised me a recompence, I only demanded of him something to eat, but he answered me, that having permitted me to enter into his Throat, and to come out safe and sound, was the greatest Favour he could show me. Another time I was a Stag, and Thevetat a Hunter. Going one day a Hunting, he climb'd upon a Tree, which bore the little Fruits which Stags do eat, and there made himself as it were a little Hutt, to keep himself close and conceal'd in, expecting his Prey: and as the Stag'Tis one of the names of Sommona-Codom. Poutisat was come very near the Tree, Thevetat threw him some Fruits to entice him to approach nearer: but the Stag Poutisat seeing these Fruits fall on either side, doubted of the business, and observed the Hunter upon the Tree, to whom he said 'twas in vain to wait longer, that he would not approach him nearer. 'Tis thus that Thevetat desires much. Another time Thevetat was a Fisherman. Having one day thrown his Line, the Hook catch'd on a Tree fallen into the water, he thought that the hook held a great Fish, and considering already that he must share it among his Friends, he was troubled thereat, because that these presents would deprive him of the greatest part. To prevent this inconvenience he sent his Son whom he had with him, to carry unto his Wife the news of the prize he thought to catch, and orders to go immediately to quarrel with all her Neighbours. She then took her little dog, and repaired presently to the nearest, went into the house, and began to scold at him and his Wife: from thence she went to another, and at last to them all. In the mean time Thevetat was looking after his Line which he could not get out, so that to have it he stript himself, laid his Cloaths on the bank of the River, threw himself into the water, and gave such an unhappy blow against the Tree, that he beat out borh his Eyes. The Passengers stole away his Cloaths: and the quarrel of his Wife with his Neighbours, cost him all the little Money he had, by a Suit which they brought against him for this injury. After this Sommona-Codom departed out of the City of Rachacreu to go to Savati: he was there sick in a Convent where he lodged: and at the same time Thevetat was likewise sick of a distemper, which held him nine Months. He had an extream desire to see his Master Sommona-Codom, and he signified it to his disciples, desiring them to do him the kindness to carry him to him. They asked him how he dared to think thereof, and what Good and Succour he could expect from him, after having persecuted him so much. 'Tis true, said he unto them, that for the Good he has done me, I have only return'd him Evil; but that's no matter carry me to him, that sufficeth me. They obeyed him, and having laid him on an Hurdle, they set out on the road, to seek out Sommona-Codom. As they approach'd, the Disciples of Sommona-Codom ran to acquaint their Master, that Thevetat being sick came to visit him. I [Page 156] know it, answered he, I know that he comes, but he shall not see me. Since that you refused him, reply'd the Disciples, the favour he demanded of you, touching the five Articles which he desired to observe, we have not hitherto seen him. Upon these words Sommona-Codom said unto them: Thevetat is a miserable wretch, who has always followed his own capricious humour, and never took care to keep the Rule, which I have taken so much pains to teach him; wherefore, though he comes purposely to visit me, and how good a mind soever he has thereunto, yet he shall not see me; because he has endeavoured to oppose me, and raise a division among my Disciples. As Thevetat was within a Mile of the Place, where Sommona-Codom was, his Disciples went again to advertise him thereof; and he still told them, I know it very well, but yet Thevetat shall not see me. When Thevetat was within a half a mile of the City, the Disciples returned to acquaint Sommona-Codom: 'Tis true, said he, yet he shall not see me. When Thevetat was arrived at the Pool, which they call Bukoreni, near the place where Sommona-Codom was, the Talapoins went again to Sommona Codom to tell him that he was near at hand; to which he reply'd, how near soever he be yet he shall not see me. Thevetat being therefore come to this Pool, his Disciples set him on the ground on the bank of the water: and as he endeavoured to walk, his Feet sunk, and entred into the Earth, and by little and little he sunk up to the Neck, and then to the Chin. Seeing himself in this condition he began to recommend himself to Sommona-Codom, and offer himself to him, confessing that he was very perfect, very great: that he brought back Persons strayed out of the good way, as does a Groom, who takes care to beat his Horses, to correct them when they are mischievous: that he knew and understood every thing: that he was full of merit. He humbled himself, acknowledged the fault he had committed, and desired pardon. Mean while Sommona-Codom considering on this wretch, said unto himself, Why hast thou received him into thine house? Why hast thou given him the habit? Would it not be better to let him continue in the world? But no, reply'd he, for if he was setled there, he would have continued only to transgress the fiveBy this place it appears what the five Commandments of the Siameses are. Commandments, and to sin. He would destroy the life of an infinite number of Animals: He would seize on anothers estate, where-ever he could entrap it: He would be permitted to run into all sort of Impurity: He would have been a Lyar and Impostor: he would always be seen drunk, like a Beast: and in fine, he would never have done any good, and would never have meditated for the Future. This is the reason why I have received him. After this Sommona Codom prophesied that after an hundred ThousandPerhaps it must be Lan, that is to say Ten Millions, to say Ten Millions of years: as in other places of the Indies Lec is taken for an Hundred Thousand years, though Lec signifies simply an Hundred Thousand. It is seen by this place how they pretend that the Souls of the wicked may purify themselves by the force of Transmigrations. It appears also that the word Pout which signifies Mercury, enters into this name of God, and I doubt not that the Bali Adjective Pouti comes from Pout, though I have seen the Siameses write these two words with different Letters; but they are not exact in their Orthography. Kan, Thevetat should be a God and be named Attisaripothiequepout. Mean while Thevetat was buried in the Earth, and even to Hell where he is without possibility of removing, for want of having loved Sommona-Codom. His Body is the heighth of a Jod, that is to say, Eight Thousand Fadom: he is in the Hell Avethi, 650 Leagues in greatness: on his head he has a great Iron pot all red with fire, and which came to his Shoulders: he has his Feet sunk into the Earth up to the Ankles, and all inflamed. Moreover a great Iron Spit which reaches from the West to the East, pierces through his Shoulders and comes out at his Breast. Another pierces him through the sides, which comes from the South, and goes to the North, and crosses all Hell. And another enters through his Head, and pierces him to the Feet. Now all these Spits do stick at both ends, and are thrust a great way into the Earth. He is standing, without being able to stir, or lye down. The disciples of Sommona-Codom discoursed amongst themselves of the poor Thevetat, saying, that he was able to come only to the lake Bukoreni, and not to the Convent, which is near it: And Sommona-Codom taking up the discourse, told them, that this was not the first time that such a punishment had happen'd to Thevetat, to be swallow'd up and buried in Hell. I remember, pursued he, that Thevetat in one of his Generations was an Hunter, and that then I was an Elephant of the Woods. One day then as he was hunting, and as he wandered and was lost, not knowing where he was, I seeing him in so great an affliction had Compassion upon him, I took him upon my back, drew him out of the Woods, set him down near his House, and then returned. Going [Page 157] another time a hunting, as he saw me with very excellent Teeth, it came into his mind, that if he had such, he could sell them very well, and hereupon he cut off the two ends of mine. Having swallow'd the Silver that he had made thereof, he return'd to cut off as much more, and a third time he made an end of cutting what remain'd. I was extreamly afflicted thereat, and expressed all the resentments whereof I was capable: but he carry'd not his crime very far, for as he left me, the earth open'd and swallow'd him up, without giving him time to ask pardon. Upon these words of Sommona-Codom, every one rejoiced at Thevetat's death: And Sommona-Codom said likewise, I remember that anciently Thevetat was born King of the City of Paranasi. His name was Pingqueleracha. He so tormented his Subjects that not one of them loved him: on the contrary every one desired to see him dead: and his death happen'd when he least expected it. Every one made publick rejoycings, except the Porter of the City, who wept heartily: and being demanded the reason thereof: Ah! said he, I weep because that this wretch, wicked as he is, will torment the Devils, as he has tormented us, and the Devils not being able to bear him, will restore him to us, and we shall be as miserable as before. This is the cause of my Tears.
Sommona-Codom ceasing to speak, the Talapoins desired him to inform them where Thevetat was then, and in what place he was gone to revive: and he told them that he was gone to revive in the great Hell Avethi: but, said they to him, is it that after having suffered so much in this Life, he is gone likewise to suffer in Hell? yes, replyed Sommona-Codom, for you must know that all Sinners, whatever they are, and of what condition soever they may be, whether Talapoins, or Laicks, after all the sufferings of this World, will have others incomparably greater and more grevious.
This Life was given me at the Moment that I departed for my Return; and I received it without having time to peruse it. At the end I found the beginning of another Work, on which I could interrogate no Person. I give you what I have thereof.
An Explication of the Patimouc, or Text of the Vinac.
THere are four things, that we ought to do before we enter into the Explanation of the Patimouc, according to what Sommona-Codom has taught. 1. It is necessary to sweep the Hall where they assemble. 2. It is necessary to light the Lamps or Wax-candles. 3. They ought to prepare water in the Spout-pots, or in other Vessels designed to this purpose, for those that shall desire to drink. 4. They ought to spread Matts or Carpets to sit upon. After the disciples have swept it, they go to tell it to the Master, who answers them that they have done well: then they acquaint him that they have lighted the Lamps, and the Master replys that it was not necessary seeing that the Sun shines, and it is broad day. Afterwards the disciples inform him that they have brought the Water, and spread the Matts: Good, said the Master unto them, this is good. Behold then, said the disciples to the Master, these four things which Sommona-Codom has taught and ordain'd before they begin the reading of the Vinac. Yes, reply'd the Master. The Disciple. What are the four things which it is necessary to do after those which we have mentioned, and which Sommona-Codom has likewise prescribed; are they not these? 1. When there comes in any new Talapoins, after the explication begun, if they are fewer in number than the Auditors, they are obliged to declare that they believe and heartily receive what they have already explained: that if, on the contrary, those that come are more in number than the first, it is necessary to begin again what they have already read. 2. It is necessary to know and to tell in what Season of the Year it is. 3. To count the number of the Auditors. 4. To instruct. Begin then, if you please with the first of these four things.
The Principal Maxims of the Talapoins of Siam, translated from the Siamese.
KIll no Man. The Talapoins do not only not kill, but they never strike any Person.
Steal not.
Commit not the Sin of the Flesh.
Glorify not your self, saying, that you are arrived at Sanctity. Every Man, who is not a Talapoin, cannot become holy, that is to say he cannot arrive at a certain degree of Merit.
Dig not the Earth. 'Tis out of respect to this Element.
Cause not any Tree to die. They are prohibited to cut any branch thereof.
Kill not any Animal.
Drink not any intoxicating Liquor.
Eat not Rice after dinner. They may eat Fruit in the Evening, and chew Betel all the day long.
Regard not Songs, Dances, nor Players on Instruments.
Use no perfumes about you.
Neither Sit nor Sleep in a place so high as that of your Superior.
Keep neither Gold nor Silver. They are prohibited to touch it; but they ill observe this Rule, the Trade of a Talapoin is a Trade to grow Rich, and when they are Wealthy enough, they quit the Cloister and Marry.
Entertain not your self with things, which concern not Religion.
Do no work, which is not the work of Religion.
Give not Flowers unto Women.
Draw not water in a place, where Worms are engender'd.
A Talapoin that goes to do his Needs, and who has not first drawn water, to wash himself, Sins. Natural Impurities seem faults unto them.
Contract not Friendship with Seculars, in hopes of receiving Alms from them.
Borrow nothing of Seculars.
Lend not unto Usury, though it be only a single Cory.
Keep neither Lance, nor Sword, nor any Arms of War.
Eat not excessively.
Sleep not too much.
Sing not worldly Songs.
Play not on any Instrument, and eschew all sorts of Sports and Diversions.
Judge not your Neighbor; say not, He is good, this is wicked.
Shake not your Arms in walking. They little observe this Precept.
Climb not upon Trees. 'Tis for fear of breaking any Branch thereof.
Bake no Tile, nor burn any Wood. 'Tis out of Respect to the Earth and Wood. It is as bad to bake a Tile as Rice, and it is a wicked act to destroy the Wood.
Twinkle not with your Eyes in speaking, and look not with Contempt.
Labour not for Money. They ought to live on Charity, and not on the Work of their hands.
Give not strong Medicines to Women with Child. For fear of killing the Infant.
Look not upon Women to please your Eyes.
Make not any Incisions that may cause the blood to come out.
Neither sell nor buy any thing.
In eating make not the noise tchibe tchibe, tchiabe tchiabe, as do Dogs. 'Tis the unpleasant noise which certain Persons do make in chewing slowly and gently. The Siameses do take a great care of Decency.
Sleep not in a place exposed to view.
Give no Medicine wherein Poyson is put. By reason of the danger of killing. The Art of Physick is not prohibited them: they practise it very much. Wherefore the Siameses are so far from being scandalized, to see the Missionaries practise Physic, that it is principally upon this account that they suffer them, and love them. It is necessary that [Page 159] the Missionraies do freely cure the sick, either by the Art of Medicine, or by Miracle.
A Talapoin sins, if in walking along the Streets he has not his Senses composed.
A Talapoin who shaves not his Beard, his Hair, and his Eye-brows, and who puts not on his Nails, sins. I know not whether this has any other Foundation than an excess of Neatness.
A Talapoin who being seated, has his Feet extended or suspended, sins. Modesty, in their Opinion, requires that the Legs be crossed, and the Feet placed near the Knees.
After that you have eaten, gather not the remains for the next day. They give them to the Beasts.
Have not several Garments. The People frequently gives them some out of Charity, and they distribute them to their Family.
A Talapoin who loves the lesser Talapoins, and caresses them as if they were Women, sins.
A Talapoin who seems to be as austere as a Talapoin of the Woods, and to keep the Rule more exactly than another, who performs Meditation to be seen, and who being alone, observes nothing of all this, he sins.
A Talapoin who has received an Alms, and who goes presently to bestow it on another, sins.
A Talapoin who speaks to a Woman in a secret place, sins.
A Talapoin who concerns himself in the King's Affairs, which respect not Religion, sins.
A Talapoin who cultivates the Earth, or who breeds Ducks, Poultry, Cows, Buffalo's, Elephants, Horses, Pigs, Dogs, after the manner of Seculars, sins. Not to cultivate the Earth is a respect for this Element; the rest purely represents the Monastic Poverty.
A Talapoin who in Preaching speaks not Balie, sins. This Maxim is not well render'd by the Translator. Their way of preaching is to read out of the Balie, where they ought to change nothing, but they must begin in Siamese, and say nothing which is not in the Balie.
A Talapoin who speaks one thing, and thinks another, sins.
A Talapoin who speaks evil of another, sins.
A Talapoin who being waked rises not immediately, and turns himself on one side, and on the other, sins. It is necessary that it be the hour of rising, that is to say, that they may discern the Veins of their Hands.
A Talapoin who seats himself on the same Mat with a Woman, sins.
A Talapoin who embraces a Woman, sins.
A Talapoin who bakes Rice, sins, because it is to kill the Seed.
A Talapoin who eats any thing which has not been offer'd to him with joyned hands, sins. 'Tis a Vanity, for the respect in this Country, requires that every thing be given with both hands. The Talapoins believing themselves holy, are very vain in respect of the Seculars, whom they think loaded with Sin. They salute no Person, not the King himself, and when the Sancrat preaches, or speaks to the King, the King is behind a Vail to conceal his Majesty: but when this Prince cannot avoid a Talapoin, he salutes him, and the Talapoin salutes not the Prince.
A Talapoin who dreams in his sleep that he sees a Woman, so that the effect of the Dream wakes him, sins. Though all this be involuntary.
A Talapoin who covets another's Estate, sins.
A Talapoin who pisses on the Fire, on the Earth, or in the Water, sins. This would be to extinguish the Fire, and corrupt the two other Elements. Mandeslo reports, that the Banians are prohibited to piss upon the ground. He knew not the whole Precept; and he has been deceived, when he thought it grounded on the fear of killing some Insect. If this were so, the Banians would be prohibited to spill any Liquor, and moreover, they do not believe any Insect in the Fire. Pythagoras forbad pissing against the Sun.
A Talapoin who reviles the Earth, the Wind, the Fire, the Water, or any other thing whatever, sins.
A Talapoin who excites Persons to fall out, sins.
A Talapoin who goes upon an Horse, or an Elephant, or in a Palenquin, sins▪ He ought not to burden man, nor beast, nor tree.
[Page 160]A Talapoin who cloaths himself with rich Garments, sins.
A Talapoin who rubs his body against any thing, sins.
A Talapoin who puts Flowers in his Ears, sins.
A Talapoin who uses Shoes, which conceal his Heels, sins.
A Talapoin who plants Flowers, or Trees, sins. They think it not lawful to dig holes in the ground.
A Talapoin who receives any thing from the Hand of a Woman, sins. The Woman lays the Alms which she bestows on the Talapoin in some place, and the Talapoin [...]akes it where the Woman puts it.
A Talapoin who loves not every one equally, sins. That is not to say, that he must love another as well as himself.
A Talapoin who eats any thing that has Life, as for example, the Grains which may yet bear Fruit, sins. They forbid not to eat any thing that has had Life.
A Talapoin who cuts, or plucks up any thing, which has yet Life, sins.
A Talapoin who makes an Idol, sins. 'Tis, say they, because that the Idol is above the man, and that it is incongruous that the Idol should be the work of the man, forasmuch as in Justice the Work, is inferior to the Workman. The Secular therefore who makes the Idol, sins also, but according to them the Sin is inevitable to the Seculars. In a word, particular Persons have no Idol amongst them, and the Siameses do make and sell them only to set up in the Temples.
A Talapoin who fills not up a Ditch, which he has made, sins. He sins in making the Ditch, and he sins in not repairing the Evil which he has done.
A Talapoin who having no work to do, tucks up the Tail of his Pagne, sins.
A Talapoin who eats in Gold or Silver, sins.
A Talapoin who sleeps after having eaten, instead of performing the Service of Religion, sins.
A Talapoin who after having eaten what has been given him in Charity, pleases to say, this was good, or this was not good, sins. These Discourses do savor of sensuality, and not of Mortification.
A Talapoin who glorifies himself, saying, I am the Son of a Mandarin, my Mother is rich, sins.
A Talapoin who wears red, black, green, or white Pagnes, sins. Ʋnder these four Colors, and under the yellow, they comprehend all the other Colors, except the Colors of Animals, which have frequently some particular Names. The yellow and fevillemorte, for example, have one Name, blue and green the same; the blue they call little green.
A Talapoin who in Laughing raises his Voice, sins.
A Talapoin who in Preaching changes something in the Baly Text to please, sins.
A Talapoin who gives Charms to render invulnerable, sins. They believe it possible to render themselves invulnerable against the blows of the Executioners, in the Execution of Justice.
A Talapoin who boasts himself to be more learned than the rest, sins.
A Talapoin who covets Gold or Silver, saying: when I shall go out of the Convent I will Marry, and be at expence, sins.
A Talapoin who grieves to lose his Relations by death, sins, It is not Lawful for the Creng, that is to say, the Saints, to lament the Cahat, or the Seculars.
A Talapoin who goes out in the Evening to visit other than his Father, or his Mother, or his Sisters, or his Brethren, and who unawares contrives to quarrel in the way, sins.
A Talapoin who gives Pagnes of Gold or Silver, to other than his Father and Mother, Brethren and Sisters, sins.
A Talapoin who runs out of the Convent, to seize Pagnes, or Gold or Silver, which he supposes that some has stol'n, sins.
A Talapoin who sits upon a Carpet interwoven with Gold or Silver, which has not been given him, but which himself shall have caused to be made, sins.
A Talapoin who sits down, without taking a Pagne to sit upon, sins. This Pagne is called Santat, and serves to raise the Talapoin, when he is seated. Sometimes they make use of a Buffalo's skin folded in several doubles for this purpose.
[Page 161]A Talapoin who walking in the streets, has not buttoned a Button which they have in their habit, sins: and if going into a Balon, he has not unbuttoned this very Button, he sins also. 'Tis the Button of the Angsa. I know not the reason of the Precept.
A Talapoin who seeing a company of Maidens sitting, coughs, or makes a noise, to cause them to turn their head, sins.
A Talapoin who has not the under Pagne edg'd, sins: and if that which he has on the shoulder consists not of several pieces, he sins likewise.
A Talapoin who puts not his Cloaths on very early in the morning, sins.
A Talapoin who runs in the street, as pursued, sins.
A Talapoin who after having washed his Feet, makes a noise with his Feet, either on Wood or on Stone, then goes to the house of a Secular, sins. This noise is to make the cleanness of his Feet observed.
A Talapoin who has not learnt certain numbers, or calculations, sins. They are superstitious numbers. Father Martinius in his History of China, p. 16. informs us, that the Chineses are likewise extreamly superstitious on numbers; and that amongst other things, they think the number 9 the most perfect and most lucky of all, and that of 10 the most imperfect and most unlucky. For this reason, the King of China has for the service of his Palace 9999 Barks, and not 10000, and in one of his Provinces he has 999 Stues, or Fish-ponds, and not 1000. He prefers the lucky and odd number, before the even and unlucky. When the Chineses salute him, it is with nine Prostrations.
A Talapoin who going into any one's House makes a Noise with his Feet, and walks heavily, sins. In several of these Rules are discovered several things, wherein the Siameses do partly place politeness, for they require it extreamly in the Talapoins.
A Talapoin who raises his Pagne to pass the Water, sins.
A Talapoin who raises his Pagne in walking the streets, sins.
A Talapoin who judges of the persons that he sees, saying, This is handsome, that unhandsome, sins.
A Talapoin who boldly looks upon men, sins.
A Talapoin who derides any one, or who rails at him, sins.
A Talapoin who sleeps on something high, sins. They have no other Bedsted than a Hurdle.
A Talapoin cleaning his Teeth with a certain Wood common to this purpose, if the Wood is long, or if he cleanses them in discoursing with others, he sins.
A Talapoin who eats, and who at the same time wrangles with any one, sins.
A Talapoin who in eating, lets Rice fall on one side and on the other, sins.
A Talapoin who after having eaten, and washed his Feet, picks his Teeth, and then whistles with his Lips, in presence of the Seculars, sins.
A Talapoin who girds his Pagne under his Navel, sins.
A Talapoin who takes the Cloaths of a dead person, which are not yet pierced, sins. They willingly accept from a man that is a dying.
A Talapoin who threatens any one to bind him, or to have him put to the Cangue, or to be buffeted, or who threatens him with any other punishment, or to inform the King, or some great man against him; that Talapoin who does thus to make himself feared, sins.
A Talapoin who going any where, resolves not to keep the Commandments, sins.
A Talapoin who washes his body, and takes the current of the water above another Talapoin more ancient than him, sins.
A Talapoin who forges Iron, sins. This is not performed without extinguishing the Fire, with which the Iron is red.
A Talapoin who meditating upon the things of Religion, doubts of any thing, which he does not clearly understand; and who out of Vanity will not ask another, that might illustrate it, sins.
A Talapoin who knows not the three Seasons of the Year, and how he ought to make Conferences at every Season, sins. I have said in discoursing of the Seasons, that the Siameses have only three, the Winter, the Little Summer, and the Great Summer.
[Page 162]A Talapoin who knows that another Talapoin owes Money to any one, and who nevertheless enters into the Temple with this Talapoin, sins. We have before seen a Rule which prohibits them to borrow of Seculars.
A Talapoin who is at Enmity, or in a rage with another Talapoin, and who nevertheless comes with that Talapoin to the Conferences, which are made about the things of Religion, sins.
A Talapoin who terrifies any one, sins.
A Talapoin who causes any one to be seized, by whom he loses Money, if it is less than a Tical, sins; if more than a Tical, this Talapoin must be cashier'd.
A Talapoin who gives Medicines to a man, who is not sick, sins. They allow no preventing Medicines.
A Talapoin who whistles with his mouth to divert himself, sins. This Precept is general. The Talapoins are prohibited to whistle upon any account whatever, and to play on any Instrument: So that these words, with his Mouth to divert himself, which are in this Precept, are not to extenuate the signification, but only because the Siamese tongue loves to express the manner of the things which it expresses. The Hebrew tongue is of the same Nature, mulier si suscepto semine pepererit filium, &c. And this Remark may be applied to some other of these Maxims of the Talapoins.
A Talapoin who crys like Robbers, sins.
A Talapoin who uses to envy any one, sins. Some would say that, according to them, an Act of Envy is no Sin; but it may be that in this the Translation corresponds not exactly to the natural sense of the Precept.
A Talapoin who makes a Fire himself, or who covers it, sins. It is not lawful to kindle the Fire, because it is to destroy what is burnt; nor to cover the Fire for fear of extinguishing it. Pythagoras prohibited the striking a Sword into the Flame.
A Talapoin who eats Fruit out of the Season of this Fruit, sins. I am perswaded that these words, out of Season, must be understood before the Season, because that it is to kill the seed, which is in the Fruit, by not permitting it to ripen.
A Talapoin who eats one of these eight sorts of Flesh, viz. of a Man, of an Elephant, of an Horse, of a Serpent, of a Tyger, of a Crocodile, of a Dog, or of a Cat, sins.
A Talapoin who goes daily to beg Alms at the same place, sins.
A Talapoin who causes a Bason to be made of Gold or Silver, to receive Alms, sins. They receive Alms in an Iron Plate.
A Talapoin who sleeps in the same Bed with his Disciples, or any other Persons whatever, sins.
A Talapoin who puts his hand into the pot, sins. 'Tis for this reason that the affront of the Spoon in the Pot, is the greatest that can be given to a Siamese.
A Talapoin who pounds Rice himself, winnows it, and cleanses it, or who takes Water to boil it, sins. To be a Servant to Sin, is Sin.
A Talapoin who in eating besmears himself round the mouth, like a little Child, sins.
A Talapoin who begs Alms, and takes more than he can eat in one day, sins.
A Talapoin who goes to do his Needs in an open place, sins.
A Talapoin who takes Wood, or any thing else to make a Fire, in a place where some Animal uses to take his repose, sins. In the expression of this Precept there is something of the Genius of the Siamese tongue, for this Precept does not intimate that the Talapoin may for any reason whatever, take Wood in a place, where any Animal has used to take his repose, nor that he may kindle a Fire with any Wood whatever; but the meaning of the Precept is, that it is a double Fault to make the Fire, and take the Wood in a place, where some Animal has chosen his Lodging.
A Talapoin who going to beg Alms coughs, to the end that he may be seen, sins. He sins likewise as often as he coughs to attract the Eyes of others, though it be not in going to crave Alms.
A Talapoin who walking in the Streets, covers his Head with his Pagne, or puts on a Hat, as do sometimes the Seculars, sins. The Talapoins shelter themselves from the Sun with their Fan, in form of a Screen, which they call Talapat.
A Talapoin who takes off his Pagne, that his body may be seen, sins.
[Page 163]A Talapoin who goes to sing, or rather to rehearse, at a dead man's House, sins, if he reflects not upon Death, upon the Certainty of all Persons dying, upon the Instability of humane things, upon the Frailty of Man's Life. This is partly the matter of their Song over dead bodies.
A Talapoin who in eating has not his Legs crossed, sins. In general they cannot sit otherwise on any occasion.
A Talapoin who sleeps in a place where others have lain together, sins.
A Talapoin who being with other Seculars, and wrangling with them extends his Feet, sins. Modesty requires that they cross their Legs.
An Account of the Charges of Justice, translated out of the Siamese.
WHen the Judge receives the first Petition, for this 1 Livr.
The Judge, or Tchaou Meuang counts the Lines and the Cancellings, and affixes his Seal to the Petition, for this 3 Livres.
The Tchaou-Meuang sends the Petition to one of the Councellors, such as he pleases, but generally to the Nai of the Parties, to examine, and to show the habitation of both the securities of the Parties, 1 Livre.
For him that goes to summon the two Parties to come to the Hall of Justice, 3 Livres.
When he must lye a Night on the Road, 4 Livres.
To have the Liberty of giving each a Security, for the Judge 16 Livres, for the Clerk that writes 3 Livres; this is the receiving of the Bail.
For copying the reasons of the two Parties to present to the Judge, to the Clerk 3 Livres. to the Judge 3 Livres.
For the Clerk who goes to hear the Witnesses, 3 Livres. And if there is a day and a Night on the road, 4 Livres. In this Country they go to find the Witnesses at their Houses, to receive their Depositions, and for this purpose there is deputed only one Clerk. The Law prescribes neither a Re-examination nor confronting of Witnesses, though the Judges cease not sometimes to confront the Accuser with the Accused. Reproaches against the Witnesses are not here in use, and oftentimes the Accused knows not who are the Witnesses that depose against him.
If the Parties do examin several Witnesses, he takes one Livre for every Witness.
To copy the Evidences or Testimonies of the two Parties, and to make them fit to be presented to the Judge, to judge thereof, Four Livres, as well to the Councellor as to the Clerk.
For the Governour or Judge to sit in the Hall of Justice, five Livres. When there are Oc-Pra for Second or Belat, and for Councellors, to each five Livres. To the Oc-Louang three Livres.
When the Case is judged, for him that keeps it, three Livres.
A Collation or Entertainment for the Councellors, three Livres.
When it is order'd and judg'd to consult the Law of the Country, which they call, Pra Rayja cit di caa ajat caan; for the Councellor who reads it, whom they call Peng, three Livres. More a white Cloath of about four Ells, more about five pound weight of Rice, more a Taper of yellow Wax, more five mouthfuls of Arek and Betel, more a Hen, more two Pots of Arak, more some Flowers and a Mat to put under the Books. Of which the two Parties do pay as much one as the other.
Concerning the Measures, Weights and Moneys of Siam.
The Measures.THe Siamese Measures are formed or composed after this manner.
Peet met caou pleuac, that is to say, eight Grains of whole Rice, the first cover of which has not been bruised in the Mill, amount to a Fingers breadth, in Siamese niou.
Twelve Fingers breadth do make a Keub, that is to say, a Palm, or the opening of the Thumb and the middle Finger.
Two Keub do make a Sok, that is to say, from the Elbow to the ends of the Fingers.
Two Soks do make a Ken, that is to say a Cubit, from the ends of the Fingers to the middle of the Breast.
Two Kens make a Fadom, which they call Voua, and which is near an Inch less than our Toise; so that within a very little their eight Grains of Rice, which do make their Fingers bredth, do amount to 9 of our Lines, which we esteem equal to 9 Barly Corns.
Twenty Voua do make a Cord, which they call Sen.
And an hundred Sens, that is to say an hundred Cords, do make one of their Leagues, which amounts to two Thousand Fadom. They call their League roe neng, that is to say, a Hundred, roe signifies a Hundred, and neng signifies One. Thus the Italians do say a Thousand.
In a word, four of their Leagues, or 8000 Voua or Fadom, do make a Jod. And these are all their Measures of Lengths.
The Weights and Moneys.The Names and Values of the Weights and Moneys together are these. 'Tis true that some of these names do not signifie the Moneys, but the Values or the Sums; as in France, the word Livre signifies not a Money, but the value of a pound weight of Copper, which is a Sum of Twenty Sols.
The Pic is worth Fifty Catis.
The Cati is worth Twenty Teils.
The Teil four Ticals.
The Tical is a Silver Coin, and is worth four Mayons, and it is the weight of half an Ounce, by reason of which the Cati weighs two pounds and a half.
The Mayon is a Silver Coin, and is worth two Fouangs.
The Fouang is also a Silver Money, and is worth four Payes.
The Paye is not a Coin, and it is worth two Clams. But the Song-Paye, that is to say the two Payes, are a Silver Coin, which is worth half a Fouang.
The Clam likewise is not a Coin, but it is thought to weigh twelve Grains of Rice. This is what was told me, and upon this ground the Tical should weigh 768 grains of whole Rice, which I have not tryed.
All these names are not Siamese, but common amongst the Europeans which are at Siam. I know not of what Tongue the word Pic is. In the Levant it signifies a sort of Ell, nine of which do make five of Paris: At Siam it is the weight of One Hundred twenty five Pounds, of sixteen Ounces to the Pound.
The word Cati is Chinese, and is called Schang in Siamese, but the Chinese Cati is worth two Siamese Cati's.
Teil, or as others do write Tael, is also a Chinese word, which is called Tamling in Siamese, but the Siamese Cati is worth but eight Chinese Taels, whereas it is worth twenty Siamese, as I have said.
Tical and Mayon are words the Origine of which I am Ignorant of, and which the Siameses do call Baat and Seling. Fouang, Paye and Clam are of the Siamese Language.
As to the Agreement of this Money with ours, to take it vulgarly, and without this exactness, which is not necessary to Commerce, a Baat or Tical, although it weighs only half a Crown, yet it is worth Thirty seven Sols and a half of our Money, by reason of which a Cati is worth Fifty Crowns.
A List of the Moveables, Arms, and Habits of the Siameses, and of the Parts of their Houses.
PRa, a great Cleaver which serves them instead of a Hatcheth.Instruments common to all
Ciou, a Joyner's Chisel.
Leuai, a Saw.
Kob, a Joyner's Plane.
Kabila, a Wimble.
Quiob, a Spade.
Reuang, a House.
Saou the Bambou-Pillars which bear the House, being four or six in number,The parts of a House. planted at equal distances in two rows: They are twelve or thirteen foot above the ground.
Root, the two Transomes or Bambous laid a-cross, like Beams on Piles, along the front, and along the back part of the House.
Raneeng, the other Transomes or Bambous laid on the Piles, two or three in number, along both the sides of the House, and on the two middle Piles, when the House is set upon six Pillars.
Preuang, Hurdles serving to plank the lower, or first Floor.
Fak, Sticks flatted and joyned together at equal distances, to lay over the Floor, instead of a Carpet: They lay them also on the Hurdles, which serve the wall instead of Wainscot.
Mefa, the Mother wall, they are the Hurdles or Wainscoting, which serves as the outward wall.
Fa, the Hurdles which do make the principal inclosures.
Louk fa, the Son of the Inclosure, that is to say, the lesser Inclosures.
Paktou, the fore mouth or door of the House. Pak signifies a mouth.
Na-tang, a Visage-keeper or Window, they are kind of Penthouses which are raised, and supported with a stick, and which are let down again when they would shut the Window. There is no Glass. Na signifies a Visage, tang, to keep.
Keu, the Hurdle which serves for the upper Floor, or Cieling.
Dang, the two Bambou Pillars to bear the roof.
Okkai, the Transome or Bambou laid on these two Pillars, to make the Ridge of the Roof.
Cloon, the Hurdles of the Roof laid sloping on both sides the Okkai.
Kiak, Foliages which serve instead of Straw.
Krabouang, the Tiles: but the Houses of particular persons have none if they are not of Brick; on which account they belong to the Europeans, the Chineses or the Moors.
Pe, the Roof.
Hong, a Chamber.
Gadai, the Ladder of the House.
Tong, the two Bambou's which make the two sides of the Ladder.
Kan gadai, the Rounds.
Seua, a Matt of Bulrush.
Te-non, the place where the Bed is laid to lye upon,Their Moveables. when they have no Bedsted. Non signifies to Sleep. Ti signifies a Place.
Tiang-non, a Bedsted without Posts or Head, but with four or six feet, which are not joyned by overthwart Beams. The bottom of this Bedsted is a Lettice of Bulrush, like as have the Chairs which come to us from England, and the Wood of which the English do send to the Indies, to be there garnished with Bulrush.
Cre, such a sort of Bedsted, but without feet. All these Bedsteds are very narrow, because they only serve a single person. 'Tis only some of the meaner people, who lye in the same Bed with their Wives; and they have no Bedsted. Amongst the Rich every one has his Bed and his Chamber apart, but in little.
[Page 166] Fouk-rong-non, the Mattress, or rather the Bed of Capoc, a kind of Cottonwool, instead of Feathers. They are not quilted; rong signifies under, non to sleep.
Pa-pou-non, the under Sheet to sleep on. They have no upper Sheet, which is other than the Coverlet.
Pa-houm-non, the upper Sheet, that is to say the Coverlet. They are only single Cotton-sheets.
Mon, a longish Pillow, but when they lye together, every one has his own, as in Spain. Mon signifies also a Cushion to lean on, for they never sit thereon.
Man-can ti-non, a Curtain before the Sleeping-place. Man signifies a Curtain or Tapistry. Can signifies before. They put a Curtain before their Bed, to prevent being seen, because that from one Chamber to the other there is no Door which shuts.
Man-can-fak-reuan, a Linnen Curtain. Man a Curtain, can before, fak the flat sticks fasten'd at equal distances, to serve as Wainscot, reuan signifies a House.
Prom, a Carpet for the Feet.
Kiam, 'tis the same thing.
Tloum, Tables with a Border and without Feet, called otherwise bandeges, and by our Merchants flat and thin Tables. When they eat together, every one has his Table at Siam, as at China. They have neither Table-cloaths nor Napkins, but the varnish'd Wood of their Tables is very easily cleansed with hot water: and so they easily make a shift without a Table-cloath.
Hip, a Chest.
Hip chipoun, a Japan Chest.
Hip-lin, a Cabinet with Drawers.
Tad, a Copper Dish, they generally serve up their Fish therein.
Me-can, a Pot to put Water in; Can signifies a Pot, Me signifies Mother.
Can-nam, a bouli of Copper to boil Water for Tea; nam signifies Water.
Can-nam-noi, a little Cannam. 'Tis a Cup round at the bottom, and without Feet.
Kon thoo, a Drinking-pot.
Kon thii, an earthen bouli for Tea.
Tioc noy, a little Tea-Cup.
Tioc yai, a larger Cup.
Taboi-tong-kin-nam, a Copper Ladle to drink Water. They also have some of Coco for this use: They bore a Cup of Coco on both sides, and thrust a Stick into the two holes, which crosses the Coco, and serves as a handle. Tong equally signifies Gold and Brass, Tong di, good Gold; Tong Leuang, false Gold or Latten. Kin signifies equally to eat and drink, according as it is spoken of a thing solid or liquid. Thus the words, to take and to swallow are common in our language, to solid Aliments and to Liquors.
Touac, the Ladle in the Pot. 'Tis the greatest affront that can be spoken to any one, as if one should tax him to be such a Glutton, as with his own hand to take out of the Pot, and not to stay till the Pot be emptied into the Dish. None but Slaves take the Ladles out of the Pot, or use them.
Touas, a Porcelane Plate, or Dish.
Tcham, a Porcelane Bowl to put Rice in. They use a great deal of Porcelane, because they have some very course, and very cheap.
Tian, a little Saucer to put under the Tea-dish.
Mo-caou, a Skellet to boil the Rice; Mo a kind of Pot or Skellet, caou, Rice.
Quion, a Spoon. They use it only to take the Sweet-meats, which are always served in little Porcelane Saucers with the Tea. They have neither Fork nor Salt-seller. They use no Salt at Table.
Mid, a Knife. They have every one a little one to cut the Arek; they use it not like us, by holding what they would cut between the Thumb and the edge of the Knife, but they always place the Thumb on the back of the Knife, and they guide the edge with the fore-finger of the Right hand, which they keep extended.
Mid-coune, a Razor or Knife to shave. Their Razors are of Copper; coune signifies to shave.
[Page 167] Tin-quian, a Candlestick; quian is a Candle of yellow Wax. They know not how to whiten the Wax, which they have in abundance; and as they have no Butchers meat, they have no Tallow; and Tallow in this Country would be of a nasty use, it would melt too much by reason of the heat.
Pen, another sort of larger Knife, which they carry about them for their use, and which might serve them for Arms in case of need.
Mid-tok, a sort of Knife to cut the Wood, with which they fasten the foliage which serves them for Straw.
Krob, a Gold or Silver Box for the Arek and the Betel. The King gives them, but it is only to certain considerable Officers. They are large, and cover'd, and very light: They have them before them at the Kings Palace, and in all Ceremonies.
Tiab, another Box for the same use, but without a lid, and which lyes at the house. Tis like a great Cup, sometimes of Wood varnished; and the higher the family is, the more honourable he is. For ordinary use they wear a Purse about them, wherein they put their Arek and their Betel, their little Cup of Red Calx, and their little Knife. The Portuguese do call a Purse Bosseta, and they have given this name to Krob, which I have discoursed of, and after them we have call'd them Bossettes.
Ca-ton, a Spitting-pot, which they all use by reason of the Betel, which makes them to spit very much.
Reua, a Balon, or strait and long Boat for a single Officer.
Creu, a Balon for a whole Family.
Moung, a Fly-net. 'Tis a Testern and close Curtain of Tiffany, which the Talapoins alone do use, not to be incommoded with the Gnats, and to prevent being forced to kill them. The Seculars have none of these Fly-nets, but they kill the Gnats without scruple.
Kaou-i, a Chair of State. None but the King and Talapoins have thereof, to seat themselves higher than others. The Talapoins do think themselves very much above other men.
Monamout, a Chamber-pot. The Talapoins alone do use them, because they are prohibited to piss upon the ground, or in the water, or in the fire.
Lom-pok, a Bonnet of Ceremony. Lom signifies a Bonnet, pok high.Their Habits, It is commonly White, but in Hunting and in War it is Red.
Pa-noung, a Linnen Sash. 'Tis the Pagne which they wear round their Reins and Thighs. The King gives the finest, which are called Pasompac, and no person can wear them of this fineness, to whom he does not give them,
Seua-kaou, the Muslin Shirt, which is their true habit. The word Seua signifies also a Mat, but then it has another Accent, and the Siameses do write it with other Characters.
Tchet-na, a Handkerchief. The Lords have it carry'd by their Slaves, and do take it themselves only in entering into the Palace; but they dare not to wipe themselves before the King: the generality are without Handkerchiefs.
Pahoum, the upper Linnen. 'Tis that Linnen, which they wear like a Mantle against the cold, or like a Scarf on their Shoulders and round their Arms.
Rat-sa-you, a Belt into which they put their Dagger. They wear it also like a Scarf over the Coat of Mail.
Pasabai, a Womans Scarf.
Seua creuang, a Vest to put under the Muslin Shirt.
Seua houm, a close Coat of Mail, or Red Shirt for the War, and for Hunting.
Moak, a Hat. They love them of all colours, high, pointed, and the edge about a fingers breadth.
Peun-nok-sap, a Musket or Fusil. Peun signifies a Cannon,Their Arms.
Peun yai, a great Cannon.
Touan, a Lance after the Siamese fashion.
Stok, a Zagaye or Lance, after the Moors fashion; 'tis like the blade of a Sabre at the end of a Stick.
Dab, a Sabre. They have it carry'd by a Slave, who holds it respectfully on his Right Shoulder, as we carry the Musket on the Left.
[Page 168] Krid, a Dagger which the King gives to the Mandarins. They wear it thrust into a Girdle on the Left side, but very much before. The Europeans do corruptly call it Crist.
Kautar, a Bow.
Lo, a round Target.
Na-mai, a Cross-bow; mai signifies a Stick.
Lan, a Dart. 'Tis a Bambou arm'd with Iron.
Laou, a Dart of Bambou, harden'd in the fire, without Iron. Laou writ after another manner signifies all intoxicating Liquors.
Mai-taboug, a Battle-axe.
Mai-taou, a Trunchion.
The Names of the Days of the Months and of the Years of the Siameses.
The Dys. VAn in Siamese signifies a Day. The names of the Days are,
Van Athit, Sunday.
Van Tchan, Munday.
Van Angkaan, the days of Mars, or Tuesday.
Van Pout, the day of Mercury, or Wednesday.
Van Prahaat, the day of Jupiter, or Thursday.
Van Souc, the day of Venus, or Friday.
Van Saou, the day of Saturn, or Saturday.
The names of the Planets are therefore Athit, Tchan, Angkaan, &c. It is true they name not the Planets without the names of the Days, without giving them the Title of Pra, which, as I have several times declared, denotes a very great excellency. Thus Pra Athit signifies the Sun, Pra Tchan the Moon, Pra Pra Prahaat Jupiter: but the word Pra is written with a P. stronger than that which is in the first syllable of the word Prahaat: In short all these names are of the Baly Tongue, the Sun is called Tavan, and the Moon Doen, in Siamese. Abraham Roger in his History of the Manners of the Bramines has given us the names of the Days in Samscortam, which, saith he, is the learned Language of the Bramines of Paliacata on the Coast of Coromandel. They are taken also from the Planets. Suriawaram Sunday, Jendrawaram Munday, Angaracawaram Tuesday, Buttawaram Wednesday, Brahaspitawaram Thursday, Succrawaram Friday, Senniwaram Saturday. It is evident that Waram signifies Day, that Suria is the name of the Sun, perhaps with some inflection to denote the Genitive; and that Jendra is the name of the Moon, perhaps also with some inflection, which being taken away, would leave some resemblance between this word, and the Bali Tchan. As to the other names, Angaraca participates enough of Angkaan: Butta, which it is necessary to pronounce Boutta, is no other than Pout: Prahat agrees with the beginning of Brahaspita, and Succra and Souc are the same word. Senni and Saou appear more remote, and Suria and Athit have nothing common: but what the same Author adds, is remarkable, that Sunday is called Aditawaram in the vulgar Language of Paliacata: for it is there that we do again find the Baly word Athit.
The Chinese, according to Father Martinius in his Historia Sinica, p. 31. do not name the Days by the Planets, but by the sixty names, which they give to the sixty Years of every Cycle: so that their Week, so to explain my self, is a Revolution of sixty Days.
The Months.The Siameses do call the Months in their Order.
Deuan signifies a Month
Deuan ai, the first Month.
Deuan Tgij, the second Month.
Deuan Sam, the third Month.
[Page 169] Deuan Sii, the Fourth Month.
Deuan Haa, the Fifth Month.
Deuan Houk, the Sixth Month.
Deuan Ket, the Seventh Month.
Deuan Peet, the Eighth Month.
Deuan Caou, the Ninth Month.
Deuan Sib, the Tenth Month.
Deuan Sib &, the Eleventh Month.
Deuan Sib-Song, the Twelfth Month.
The Siamese People understand not the Words Ai and Tgii, which are the names of the two first Months; but it is probable that these are two old numerical Words, which signifie One and Two; and this is evident from the Word Tgii, because that the Siameses do say Tgii-Sib, to signifie Twenty, which verbatim is two Tens. All the other names of Months are still in use to signifie Numbers, with this difference, that when they are put before the Substantive, they signifie pure Numbers; and that when they are plac'd after, they become Names, which denote Order. Thus Sam Deuan signifies Three Months, and Deuan Sam, the Third Month.
Pii signifies a Year. The Twelve Names of the Year are:The Years.
Pii ma mia, the Year of the Little Mare.
Pii ma me, the Year of the Great Mare.
Pii Vok, the Year of the Ape.
Pii Rakaa, the Year of the Crow.
Pii Tchio, the Year of the Sheep.
Pii Counne, the Year of the Pig.
Pii Chouat, the Year of the Rabbet.
Pii Tchlou, the Year of the Lizard.
Pii Kan, the Year of the Hens.
Pii Tho, the Year of the Goat.
Pii ma Rong, the Year of the Sea-Gull.
Pii ma Seng, the Year of the Great Serpent.
Most of these Names are also of the Balie Tongue. Now as the Siameses do make use of the Cycle of Sixty Years, they ought to have Sixty Names to name the Sixty Years of every Cycle; and yet the Persons, whom I have consulted, could give me no more than Twelve, which are repeated five times in every Cycle, to arrive at the Number of Sixty: But I doubt not that it is with some additions, which do make the differences thereof; and I think to find the proof thereof in two dates of Siamese Letters, which I have carefully taken from the Originals. The first is thus: In the First Month, the Ninth Day after the Full Moon in the Aera 2229, the Year Tchlou Sapsoc. And the second is thus: The Eighth Month, and the First Day of the Moon's Decrease in the Year Pii Tho Sapsoc of the Aera 2231. The Word Aera in these two dates simply signifies Year, according to the Spanish language; so that it is all one to say the Aera 2229, and to say the Year Tchlou Sapsoc: to say the Aera 2231, and to say the Year Pii Tho Sapsoc. Besides, as the Word Pii signifies Year, they might put Tho Sapsoc instead of Pii Tho Sapsoc, as they have put Tchlou Sapsoc, and not Pii Tchlou Sapsoc. Now these two Years which are the Years 1685, and 1687 of Jesus Christ, are not called simply either by Tchlou and Tho, that is to say of the Lizard and Goat; but to the Words Tchlou and Tho, is added the Word Sapoc, which I understand not, and which was added to the Names of the Twelfth of the Years, which run then to distinguish it from the four other Twelfths of the Years of the same Cycle.
Of the Monsons and Tides of the Gulph of Siam.
WE find upon our Seas, that tho' the Winds be very variable, yet they change with this almost infallible Rule, of passing from the North to the South only by the East; or from the South to the North, only by the West; or from the East to the West, only by the South; or from the West to the East, only by the North. So that the Wind continually veers about the Heaven, passing from the North to the East, and from the East to the South; and from the South to the West, and from the West to the North; and almost never in the contrary manner: Yet in the temperate Zone, which is on the South of the Line, when we navigated those Seas which are on the East of Africk, we experimented in our return from Siam, that the Winds went always contrary to this Rule; but to assert whether this may be always so, requires more than one Proof. However it be, the Wind goes not so in the Gulph of Siam, but it only encompasses the Heaven in a year; whereas on our Seas it does it in a small number of days, and sometimes in one day. When in the Indies the Wind blows round the Compass in a day, it is stormy: This is what they properly call a Hurricane.
In the Months of March, April and May, the South-wind prevails at Siam, the Heaven is disorder'd, the Rains begin, and are very frequent in April. In June they are almost continual, and the Winds do turn to the West, that is to say, do blow from the West and the South. In July, August, and September, the Winds are in the West, or almost West, and always accompany'd with Rains, the Waters overflowing the Earth to the breadth of nine or ten Miles, and above One hundred and fifty to the North of the Gulph.
During this time, and especially towards the middle of July, the Tides are so strong, that they ascend up to Siam, and sometimes to Louvo; and they decrease in twenty four hours with that measure, that the Water becomes sweet again before Bancock in an hour; tho' Bancock be seven Miles from the mouth of the River, yet the Water is always somewhat brackish.
In October the Winds do blow from the West and the North, and the Rains do cease. In November and December the Winds are North, do clear the Heavens, and seem so exceedingly to lower the Sea, that in few days it receives all the Waters of the Inundation. Then the Tides are so insensible, that the Water is always sweet two or three Leagues in the River, and that at certain hours of the day, it is the same for a League in the Road. But at Siam there never is more than an Ebb and Floud in twenty four hours. In January the Winds have already turn'd to the East, and in February they blow from the East and the South.
'Tis a considerable Circumstance, that at the time when the Winds are in the West, or that they blow from the West, the Currents of the Gulph do rapidly carry the Ships on the Eastern Coast, which is that of Camboya, and do hinder them from coming back again; and that at the time when the Winds are to the East, or that they blow from the East, the Currents do run on the Western Coast, so that then in Sailing it is necessary to fear being bore away. Now this proves, in my opinion, that the Winds have a great share in the motions of the Sea, forasmuch as some have proved, that these Currents are only in the upper parts of the Waters, and that underneath they have a quite contrary Current, because that the upper Waters being continually rowled on the Shore, returns underneath towards the Coast from whence it came. After the same manner it seems that they are the South-winds, which drive on the Flux, and maintain it for six Months further up in the River, and that they are the North-winds which do hinder it the entrance of the River for the six other Months.
A Bunch of Banana's
Three Siamese Alphabets
- Ko [...]
- Khò [...]
- Khó [...]
- Khò [...]
- Khoo [...]
- Khoo-ngo [...]
- cho [...]
- chó [...]
- chò [...]
- Sò [...]
- choo [...]
- yo [...]
- do [...]
- to [...]
- thò [...]
- thó [...]
- thoo [...]
- no [...]
- [...]o [...]
- po [...]
- ppò [...]
- fo [...]
- ppo [...]
- mo [...]
- no [...]
- ro [...]
- lo [...]
- vo [...]
- So [...]
- Só [...]
- Só [...]
- hò [...]
- lo [...]
- Kâ [...]
- Kí [...]
- Ki [...]
- Keú [...]
- Keû [...]
- Koù [...]
- Kû [...]
- Ké [...]
- Kê [...]
- Ka [...]
- Kaái Ko [...]
- Kàon [...]
- Kam [...]
- Ka [...]
- Keúy [...]
- Kaái [...]
- Kâou [...]
- Kiou [...]
- Küon [...]
- Keuy [...]
- Keúï [...]
- Koú̈y [...]
- Koúi [...]
- Keòn [...]
- Keôu [...]
- Koú̈y [...]
- Kôï [...]
- Kouáï [...]
- Kiaóu [...]
- Kiá [...]
- The Sequel of this Alphabet is in the following Plate.
A Description of the principal Fruits of Siam.
THE Figs of India, which the Siameses do call Clouey-ngouan-tchang, Elephant's Trunks, have not the taste of our Figs, and, in my mind, they are not so good. Thus the Melons of Siam are not true Melons, but the Fruit of a Tree known in the Isles of America under the name of Papayer. I have not eaten of this Fruit. But to return to the Fig, it is of the size and shape of a Sausage. Its green Skin, which waxes yellow and spotted with black in its maturity, is easily separated from its soft and clammy pulp, and 'tis that which has given it the name of Fig; but in the midst of its pulp there is no vacuity, nor any of those kernels which do make as it were a little gravel in our Figs, when they are a little dry'd. Its taste is strong, and it has something of sharpness and sweetness both together.
The Bananas, which the Siameses do call Clouey-ngaa-tchang, or Elephant's Tooth, is almost the same thing as the Fig, save that it is greener and longer, and that it has Angles, and Faces or flat Sides, which are re-united point-wise at both ends. These Fruits do hang like Nosegays, or rather like great Bunches of Grapes, from the top of the Trunk of the Trees which bear them. The Figs grow hard in the Fire, the Bananas which are not altogether so delicate raw, do wax soft again, do there lose their sweetness, and do acquire the taste of our Pippins ripen'd on the Apple Tree.
The Goyaye (in Siamese Louc-Kiac, Louc signifies Son, Kiac is the name of the Goyavier) is about the size of a middling Apple. Its Skin is of a grayish green, like that of certain Pears: under this Skin is a pulp of the consistence of that of the Citron, but not so white. When it is put into the mouth, it savors the Strawberry; but this Strawberry taste soon loses itself, because it becomes too strong. This pulp, which exceeds not the thickness of a Crown-piece, contains a liquid substance like Broth, but grayish, and which would not be less pleasant to eat than the pulp, if it was not mix'd with an innumerable number of small kernels so hard, that it would be difficult to chew them.
The Jacques, in Siamese Ca-noun, are of the shape of a great Melon ill rounded. Under a grayish Skin fashioned like Chagrin, they have a very great number of kernels, or stones; stones, if we consider their magnitude, which is almost like a Pigeon's Egg: kernels, by the thin and smooth wood which incloses them. These stones therefore or kernels being broil'd or boil'd, differ not from our Chestnuts either in taste or consistence, excepting that they are, in my opinion, more delicate. At one end they stick to a pulp which invelops them all, and separates them one from the other. It is easily torn off, according to the course of its fibres; it is yellow, juicy, clammy, and glutinous, of a sweet taste, and strong smell. It is not possible to chew it, they only suck it.
They gave us a Fruit like to Plums, and we at the first appearance were deceived. It had the pulp and taste of a Medler, and sometimes two, sometimes three stones, but bigger, flatter, and smoother, than the Medler has them. This Fruit is called Moussida in Siamese.
The Ox-heart was so named by reason of its size and shape. The Skin thereof is thin, and this Fruit is soft, because that on the inside it is only a kind of white Cream, and of a very agreeable taste. The Siameses do call it Mancout.
The Durion, in Siamese Tourrion, which is a Fruit very much esteem'd in the Indies, appear'd insupportable to me for its ill smell. This Fruit is of the size of our Melons cover'd with a prickly Coat like our Chestnuts. It has also, like the Jacques, several stones, but as big as Eggs, in which is contained what they eat, in the inside of which there is also another stone. The fewer there is of these stones in a Durion, the more pleasant the Fruit is. There never is less than three.
The Mango, in Siamese Ma-mouan, participates at first of the taste of the Peach [Page 172] and the Apricot; toward the end this taste waxes stronger, and less agreeable. The Mango's are highly esteem'd, I have seen some as big as a Child's hand, they are flat and oval, but pointed at the two ends almost like our Almonds. Their Skin is of the consistence of that of our Peaches, of colour inclining to yellow; but their meat is only a pulp which must be suck'd, and which quits not a great flat stone which it envelops.
I have not seen the Mangoustan, which is said to be much better than the Mango's.
The Siameses have some sharp Fruits which quench the thirst, and which upon this account appear'd unto me the most agreeable of all. They are small as Plums, and have a stone encompast with a white pulp, which easily melts in the mouth.
The Tamarinde is also sharp. 'Tis a Fruit enclosed in a shell like an Almond, and then several of these Fruits are likewise included in a Cod. I preserved some, and found the Syrup thereof very pleasant during my return; but by little and little it lost its sharpness, and there remain'd only the taste of the Pimpernel. The Tree which bears it, and which is very large, has a Leaf resembling Pimpernel.
From this Country I brought several sorts of liquid Sweet-meats, which were come from China to Siam about two years, and they ceased not to keep very well to Paris. The Syrup especially was very good, and had nothing of Candy, notwithstanding the heat of the Climats through which it had passed. These Sweet-meats had perhaps been made with Sugar-candy, whith is the sole Purifier that the Orientals have. I refer my self to the Confectioners.
I speak not of the Sugar-canes wherewith Siam abounds, nor of the Pepper, because I saw none thereof. The King of Siam, they say, has caused an hundred thousand thereof to be planted. 'Tis a Plant which needs Props like the Vine, and the Pepper hangs thereon also by little Bunches, like to those of Currents.
The Ananas, in Siamese Saparot, has the meat white, and the taste of our Peaches. Its meat is mixed with a little wood, not a wood which separates, as there is in our Nuts, but with a wood that adheres thereto, and which is only the meat over-hardned; and it is at the Center that it begins to grow hard. The Ananas is believed unwholsom, because that its juice, they say, corrodes Iron. It is yellow when it is ripe, and then to smell it without opening it, it has the scent of a roasted Apple. Its Figure is like a great Pine Apple, it has little rindes curiously ranged, under which, to behold them, one would think that the kernels are. The Plant which produces it bears it at the top of its stalk, which is not three foot high. The Ananas keeps directly upon the little end; and at the great end there is a tuft of Leaves, like little Corn-flags, short, bent outwards, and toothed. Sometimes from the body of this Fruit, and at the sides, there grows like Wens, one or two other little Ananas, which have also their Tufts. Now every Tuft cut and put in the ground, may produce another Ananas, but every Plant bears only one, and bears no more than once.
The Coco, in Siamese Ma-praou, is a kind of Filbert, but much bigger indeed than a Filbert, as may be seen by those Cups of Coco which they sell us. 'Tis the wood thereof which is naturally cover'd like that of our Nuts, with a brou or green bark an inch thick, and full of fibres, whereof Cordages may be made. In the wood of the Coco is a very pleasant liquor, and the wood thereof is so full, that it spurts a great way when it is pierced. As this Fruit ripens, this liquor congeals at the extremities, that is to say near the wood, and there forms a Nut very white, and of a very good taste; the water which is not yet congealed remains still at the Center of the Fruit, and at length it all congeals.
Of the Siamese and Balie Languages.
THE Siamese Tongue has Thirty seven Letters, and the Baly Thirty three, but they are all Consonants. As to the Vowels and Dipthongs, of which there is a great number in the one and the other Language, they have indeed some particular Characters, whereof are made other Alphabets: but of these Characters some are placed always before the Consonant, some others always after, others above, others underneath: and yet all these Vowels, and all these Dipthongs thus variously disposed in respect of the Consonant, must only be pronounced after it.
But if in the Pronunciation the Syllable begins with a Vowel, or with a Dipthong, or if it is only a pure Vowel, or a pure Dipthong, then they have a mute Character, which supplys the place of a Consonant, and which must not be pronounced.
This mute Character is the last in the two Alphabets, the Siamese and Balie. In the Siamese it has the figure of our o, and indeed it countervails an o, when it must be pronounced, and not be a mute Consonant, that is to say, when it is preceeded with a Consonant or by it self. In the Balie Alphabet this last Character countervails ang, when it is not a mute Consonant; but its figure has no resemblance to any one of our Letters. Thus the first Letter of the Hebrew Alphabet, which is Aleph, serves as a mute Consonant, in relation to which they place the Points which are the Vowels; and it is probable that the Aleph was anciently pronounced like the Alpha of the Greeks, which has taken its name from the Aleph.
The Siamese Pronunciations are very difficult for us to imitate, and they correspond so ill to most of ours, that of ten Siamese words written in French Characters, and read by a Frenchman, there will not perhaps be one, that is known and understood by a natural Siamese, what care soever is taken to accommodate our Orthography to their Pronounciation.
They have the r, which the Chineses have not. They have our v Consonant, but they pronounce it frequently like the w of the High-Germans, and sometime like the w of the English. They have likewise the ng of the Germans, which we have not: For the Germans pronounce Engel, for example, after a manner that we hardly apprehend, and which is only a g pronounc'd before the e, and the i as before the a, but very softly and much through the Nose.
They have a middle Pronunciation between our two Pronunciations of yo and jo, and from hence it is that the Europeans do say sometimes Camboja, and sometimes Camboya, because they know not how to pronounce these sorts of words exactly after the Siamese.
'Tis the same as to the word Kiai, which signifies, Heart. It is not known whether they rather say Kiai than Ciai, pronounced after the Italian manner, because that indeed they do not exactly speak either the one or the other, but something which partakes of the one and the other.
They have our Aspiration, which yet they pronounce very softly, and when they put the Character thereof before a Consonant (which the French tongue never permits) they do it only to weaken the pronunciation of the Consonant: and in general they speak so softly, that it is not known often whether they pronounce an m or a b, tio or tchio.
They have not our u Vowel which the Chineses have, but they have our e, such as we pronounce it in our Monosyllables, ce, le, me, que, se, te: but this e suffers no elision in their Tongue as in ours. I dare even affirm that they have no other e than this, not in the Cries of the Pagayeurs, ho, he, he, which they pronounce as we would pronounce ho, heu, heu; nor in the Syllables which end with a Consonant, like this, Pet, which signifies a rough Diamond, and which they rather pronounce peut, than pet.
They have an a extreamly short, which they write with two points, thus:, and which they pronounce clearly at the end of the words, as in this Balie [Page 174] word Pra, which they give to whatever they honour most; but when this a is found in the middle of a word, it passes so quick that it is not discerned, and that it answers to our e mute. Hence it is that the word Pa-ya, which we have translated by that of Prince, and of which the first a written with the two points, is pronounced Pe-ya, or Pia, though in the Relations we find it written Peja and Puja, by the confusion of the e mute with the u, and of the y with the j consonant. This a marked with two points suffers no other Letter after it in the same Syllable.
'Tis a thing very singular that in the Syllables which end with a Consonant, they pronounce it not after our manner: but their tongue remains fix'd either to the palate of the Mouth, or to the Teeth, according to the nature of the Consonant; or rather their Lips remain shut: and it is thus that they terminate these sorts of pronunciations, I mean without unloosing the Tongue, and opening the Lips again. They cannot pronounce an Aspirate at the end of a Syllable, was it in the middle of a word. They pronounce Petpayatong, though they write Petchpayatong. The Convent of the Palace they call vat Si-Sarapet, though they write Sarapetch. Thus when they would say un oeuf they said un oeub, but they open'd not their Lips again to finish after our manner the pronunciation of the b. By the same reason they will pronounce an n for an r and for an l, at the end of a word, because that at the end of the words they unloose not the Tongue from the Palate, and it is necessary to unloose it in the pronunciation of the r or of the l: for in that of the l, the Tongue cleaves not to the Palate at sides. They will write Tahar and Mar, and they will say Tahan and Man.
They have a great deal of Accent, like the Chineses: they do almost sing in speaking: and the Siamese Alphabet begins with six different Characters, which do all countervail only a K, more or less strong, and variously accented. For though in the pronunciation the Accents be naturally upon Vowels, yet they do mark some by varying the Consonants, which otherwise are of the same weight. From whence it is perhaps permitted to conjecture that they writ at first without Vowels, like the Hebrews, and that at last they have marked them by some strokes foreign to their Alphabet: and which for the most part are placed out of the rank of the Letters, like the Points, which the modern Hebrews have added to their ancient manner of writing. Whoever therefore has learn'd to give the true Accent to the six first Characters of the Siamese Alphabet, easily pronounces the rest; because that they are all ranged with that art, that in their pronunciation it is necessary to repeat almost the same Accents. They read the Balie Alphabet after the same manner, save that they give it only five Accents, which they repeat five times in the twenty five first letters, the eight last having no accent. And as far as I can judge of the Hanscrit by the Alphabet, which Father Kirker has given us thereof in his China Illustrata, this Tongue, which is the learned Tongue of the Mogul's States, has five Accents like the Balie Tongue: for the Characters of its Alphabet are divided by fives.
Of the first Siamese Alphabet.
THe first Alphabet is of Consonants, which are thirty seven in number, and which I have plac'd in their natural order, with their value at the top, as far as to me has been possible. This double stroke (II) which is found six times, is to denote the places where they stop in saying their Alphabet by heart; for it is a kind of Song. They say seven Letters at first, and then the others six and six.
The little stroke which is between the names of two Letters, denotes that they pronounce the Letter which precedes the stroke very quick, and that it makes a shank with the following Letter, when they say their Alphabet by heart.
[Page 175]I have put an h after the K, 'tis to show that the K must be pronounced with an Aspiration after the German way, and not so simply as our c hard: and where I have put two pp, it is to denote a p harder than ours.
The Ngo is pronounced before all the Vowels, like our g before the a, the p and the u; with this difference, that it is pronounced a great deal more carelessly, and altogether from the Nose, which gives it something of n at the beginning of its pronunciation. At the end of the words, it is pronounced without loosing the Tongue from the roof of the Mouth: they will say Tong, and not Tongue.
The three first Letters of the second division are pronounced between the quio and cio of the Italians.
The ço is pronounced after the Castilian manner by lisping.
The do which is in the third division, is pronounced like a to at the end of words, and they have no other to final.
They have a double yo, the one at the second division and the other at the fifth: they pronounce them between our yo and our jo, and there is no other difference between these two Letters, save that the last yo which is that of the fifth division, is the true yo final: they place it after the Vowels to make Dipthongs, though they cease not sometimes to place the other there, but through ignorance: for this Orthography is not in their Alphabet, where all their Dipthongs are. Now these yo are however thought Consonants, as the i is thought a Consonant in German and Spanish in these Dipthongs ja, je, jo, ju, with which a Vowel which preceeds them in Verses, is not confounded, but makes its Syllable apart. And yet though the Siameses put the yo among the Consonants, they so clearly perceive that they sound like Vowels, that in writing the words, which begin with a yo in the Pronunciation, they place an o mute at the head, as they do at the head of the words, which begin with the Vowel: this is not regular, but they are all incapable of all these little attentions.
The No which is the last Letter of the third division is not pronounced at the end of words like our n, but like the n of the Gascons and Spaniards. I have writ it with an u simple, in writing the Siamese words with our Characters; and sometimes to avoid ill agreement, which these words caused with those of our Language, I have thereunto added an e feminine, although this be ill, in that the Siameses pronounce it not, seeing that they unloose not not the Tongue from the roof of the Mouth, in pronouncing their n at the end of words.
The Vo is pronounced indifferently like our v Consonant, or like the w of the High-Germans, which is a b pronounced softly, or without closing the Lips, or in fine like the w of the English, that is to say like our ou in the word oui. The Vo is likewise put after Vowels to form certain Dipthongs, in which case it is pronounced like our ou.
The three So of the last division, have the accent somewhat more sharp one than the other, the Voice ascending gradually to the last.
The ho is put sometimes before the Consonants, to mollifie the pronunciation thereof.
The o is a mute Consonant, as I have said, which serves to place the Vowels, as the Aleph serves to place the Points of the Hebrews, when the Syllable begins with a Vowel, or when it is only a Vowel: but the o becomes a Vowel, and is pronounced like our o when it is preceded by another Consonant, or by itself.
Of the second Siamese Alphabet.
THe second Siamese Alphabet is that of the Vowels placed in respect of the first Ko, as they are placed in respect of every other Consonant, and in respect of the o mute.
[Page 176] Eu, ou and ai are simple Pronunciations, though we write them each with two Letters.
Ai is a Dipthong and not a single Vowel, and is pronounced as in our exclamation of complaint, ai.
Aou is also a Dipthong, which must be pronounced as au in Italian and in Spanish; but the Siamese Orthography is altogether fantastical: for it answers to ea.
Am is a Syllable and not a Vowel. The a is there clearly marked after the Ko, and that little o which is at top, denotes the m final. They have put the m final amongst the Vowels, because they have marked it above the Consonants, after the manner of the Vowels. They do sometimes also place at the end of the Syllables and Words, the m which is in their Alphabet of Consonants.
The last a which is marked with two points is an a very short, which suffers no other Letter after it in the same Syllable, and which is pronounced only at the end of words: for in the middle it is frequently lost, and becomes our e mute, such as the first e of purete: wherefore in several Siamese words I have omitted this a, and sometimes I have written it with an e. Thus I have put Jocbat for Joccabat, Blat or Belat for Balat, by reason that this Orthography more nearly approaches their Pronunciation.
The Character of the first a is always joyned to the Consonant, and is always placed after it, 'tis an a long, which is as two, as we anciently write aage for age.
The four following Vowels are placed always over the Consonant, and the long are marked with a stroke also. The two Vowels after, viz. the sixth and the seventh are placed underneath, and the seventh is only the double stroke of the sixth. The five following are placed before the Consonant, and the e long is only the e short redoubled.
The aou consists in two Characters, which answers ea as I have said, and the e is always put before the Consonant, and the a after, according to their Nature.
The m final marked with a little o is placed always on the Consonant, and is pronounced without opening the Lips.
The a short and sharp, marked with two points, is always put after the Consonant, and suffers no Letter after it in the same Syllable.
All these Vowels thus disposed, sometimes above, sometimes below, sometimes before, sometimes after the Consonant, are always pronounced after it, as I have already declared. This would be a trouble to us, when the Syllable begins with a Mute and a Liquid, like pret, the Letters of which they would range thus eprt, so that we could not know if it were necessary to say pret or pert: but they always pronounce the Liquid before the Vowel, saying pret, and not pert. They cannot pronounce pert but pent: they will also say pent for pelt, and they will range the Letters in this manner, lept, or rept, or nept, The e pronouncing itself always after the Consonant, which follows it in the writing, leaves not any doubt to them in this Orthography. For pnet, or pent, pmet or pemt, they will always pronounce pent and pemt.
Of the third Siamese Alphabet.
THis Alphabet is of Dipthongs, most of which are truly orthographized and easie to read: but some of which are pronounc'd after a manner very different from their Orthography. We shall observe in these that the Vowels are pronounced according to their disposition; those which precede the Consonant pronounced first, altho they nevertheless are pronounced after the Consonant. Whence it appears, that designing to place certain Vowels before the Consonant, they have chosen those, which in the pronunciation of the Dipthongs [Page 177] 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.
[Page 178] 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, 'tis as if one should say my body: to say me, 'tis 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.
TEƲ, 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 [Page 179] 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, or rather kin teut, or rather hai kin teut. Hai properly signifies to give, and is used likewise to signifie to the end.
Reu is the Note of Interrogation. Kin le ou reu? Hath he eaten? or have you eaten? Leou, as we have said, is the sign of the Perfect, reu is plac'd always at the end of the Phrase.
To say I did eat, they say I would eat, tcha erai ken. Tcha is the sign of the future, crai signifies to will, and so tcha crai signifies I would, and kin signifies to eat.
To say if I was at Siam, I should be satisfied, they would say word for word, if me to be City Siam, my heart good much. Heart good signifies content, and the Verb I should be is there understood.
Of the Construction.
THey have Pronouns demonstrative, and not relative. They have Prepositions and Adverbs, or at least Nouns taken in this sense.
The Nominative always precedes the Verb, and the Verb precedes the governed.
The Preposition precedes also what it governs.
When two Substantives come together, the latter is taken in the Genitive. Van athit, day of the Sun, athit which signifies Sun is in the Genitive.
The Adjective is always after the Substantive, and the Adverb after the Adjective, or after the Verb to which it refers.
Their Construction is always shorter than ours, because it wants Articles, and a great many Particles which we have, and oftentimes a Verb; but the turn of their expressions seems long to us, if we translate them word for word. To say, How is this thing named? they say, ny scheu rai, that is to say verbatim, this thing name how? where they suppress the Verb. But to say, bring me that, they will say, go, take that, and come. To say, give some Rice to thy Child, they say, take Rice, give Child to eat: The Construction is always short, but the turn of the expression is long, because they express all the circumstances of the Action.
In naming particular things, they do almost always make use of the general word, to which they add another word for the difference. They say, Head of Diamond, to signifie a Diamond; and they have two words, the one for the Rough Diamond, pet, and the other for the Diamond set in work, Ven: houa pet, houa ven. Houa signifies Head.
To say a Man, they say pou tchay, to say a Woman, pou ying, which they pronounce almost pou-ging, and pou signifies person: to name the Beasts, they put the word body; body of an Ox, body of a Cow. Louk signifies Son, Louk Schaou, young Son, that is to say Daughter; Schaou in Siamese, signifies young, as nang in Balie. To denote the Female amongst the Animals, they use the word mia. They joyn the word ban, which signifies Village, to almost all their Names of their Villages. Ban-pac-tret yai, Village of the Mouth of the great Strait. Banc-pac-tretnoe, Village of the Mouth of the little Strait. Ban-vat Village of the Convent. Banc-pacnam, Village of the Mouth of the Water.
The Pater Noster, and Ave Maria in Siamese, with an Interlineary Translation.
PO raou Savang. Scheu Pra hai prakot touk heng kon tang-lai touai Pra pon. Meuang Pra co hai dai ke raou. Hai leou ning tchai pra Meuang Pendin semo savang. Ahan raou touk Van co hai dai ke raou Van ni, co prot bap raou, semo raou prot pou tam bap ke raou. Ya hai raou tok nai kouan bap: hai poun kiac anerai tang-poang. Amen.
The Ave Maria.
AVE Maria Ten anisong, Pra you hengNang is that Balie word, which signifies young, and which added to Nouns Masculine renders them Feminine. Nang. Nang soum-boui yingkoua Nang Tang-lai. Toui louk outong, heng nang Pra, Ongkio Yesu soum-boui ymgkoua Tanglai. Sancta Maria Me Pra thoui ving von Pra pro raou kon bap teit-bat-ni le moua raou'Tis the Latin Word. tcha tai. Amen.
A Smoaking Instrument made use of by the Moors, which are at Siam.
THey have a glass bottle of the figure of our Caraffas, excepting that it has a foot to be more firm, they fill it up half with water, and into the neck, which is all of a bigness and very long, they put a silver Pipe wound about with a Fillet, to the end that it close the better: but this Pipe enters only the length of two Fingers breadth, though it be more than half a Foot long. At the upper end is a little Cup, either of Silver or Porcelane, which has the bottom perforated to communicate with the Pipe; and in this Cup is the Tobacco, on which they put a live coal. From the side of the Pipe there proceeds another much less in form of a Spout, or rather it is the little one which enters into the great one at the side, and it descends within the great one, and as far as the great one it self, yet without filling the whole capacity thereof, but leaving a space through which the smoak of the Tobacco, which is consumed in the Porcelane Cup, may descend into the Bottle. In fine, to the inferior Orifice of the little Pipe, they put another little Pipe of Bambou, bound about also with a little Ribbon or black Silk, which descends into the water. Now he that would smoak, setting this glass bottle, or rather all this Machine which I have described upon the ground, puts into the superior orifice of the little silver pipe, the end of a Bambou-slip, which though of one single shoot is sometimes between seven and eight foot long. The two ends thereof are garnished with Gold or Silver, and besides this one of the two is garnished with a little Chrystal Pipe, which he that smoaks puts between his Lips. From this manner it seems that in smoaking, he would attract to his Mouth the Water of the Bottle, by reason of the Communication that there is from the Mouth of the Smoaker to the Water of the Bottle, viz. through the great Bambou slip, thro the little Silver Pipe to which it joyns, and thro the little Bambou Pipe which enters into the Water, and which unites at the lower end of the small silver Pipe: but instead of this, the exterior air not being able to enter into the Bottle, the Smoak of the Tobacco descends along the great silver Tube, not only into the Bottle, but even into the Water, to insinuate it self into the little tube of Bambou, from whence it ascends to the Mouth of the Smoaker. So that he who invented this Instrument, has very ingeniously apprehended that it would be more natural that the Smoak should be drawn into the water, and from the water to the Mouth of the Smoaker, then that the water, which is heavier than the smoak, should yield to the force of this Attraction.
[Page 181]Sometimes there are several small Tubes round the great one, to the end that several persons may smoak in company with the same Instrument, and the better to settle it, it is placed on a copper Bason, covered in that place with a little piece of cloth, which hinders the foot of the Bottle from slipping over the Bason.
The Chess-Play of the Chineses.
THeir Chess-board is composed like ours of 64 squares,A Description of their Chess-board, and the number of their Men. but which are not distinguished by white and black. Neither do they place their pieces in the Squares, but at the corners of the Squares, that is to say at the points where the lines of the Chess-board do intersect. Moreover the Chess-board is divided into two halves, thirty two Squares for each of the two Players, and these two halves are separated by a space, which they call the River. It is about the bigness of a row of Squares, and runs not from one Player to the other: but after the same manner wherewith the pieces are ranged on the Chess-board. 'Tis not therefore the Squares which are the Points of their game, but the corners of the Squares. And so they have nine Points on each line, and there are five times nine or forty five on each half of the Chess-board; I have marked them with circles.
They have thirty two Men like us, sixteen for each Gamester, the one white, the other black; but these Men are not all the same as ours, and they dispose them not altogether after the same manner. Every Gamester has a King and no Queen, two Guards, two Elephants, two Horsemen, two Waggons, two Cannons, and five Pawns. Each Gamester places nine Men on the first Line of the Chess-board, which is on his side, at the Points where this first Line is divided, and on those where it is terminated. These nine Men are, the King, whom they place in the middle; the two Guards which are next him, the one on the right and the other on the left; the two Elephants which are next the Guards, the one on the right and the other on the left; then the two Horsemen, the one on the right and the other on the left; and in fine the two Waggons which take up the two corners of the Chess-board. The two Cannons are placed in the second Point before the two Horsemen, and the Pawns in the first, third, fifth, seventh, and ninth Points of the fourth Line, that is to say on that which is our Chess-board, separates the first Points before the Men, from the second.
The King makes only one step as in our Game,The motion of their Men. but he cannot do it every way: he goes forward, or backward, or side ways, as do our Rooks, but he marches not bias-wise like our Bishops. Moreover he cannot stir out of a Square, which is his field of Battle or his Palace, and which contains four Squares, which on our Chess-board are those, where we place the King and Queen, and the Pawns of the King and Queen.
The two Guards do not move also out of the Square, and they never make more than one step, but bias-wise like our Bishops, and not otherwise.
The two Elephants do move after the manner of our Bishops, but they do always make two steps, and never more nor less, and they pass not the River: they enter not into the Enemy's Camp. I understood that the Elephant is called fil in Arabia, and that it is from this word fil that we have taken that of fol or Bishop for that of our Chess-men which answers to the Elephant.
The Horseman skips two points like our Knight, the one of which is according to the march of our Rooks, and the other is according to the walk of our Bishop. But their Horseman leaps not over the other Men: it is necessary that he have the way open, at least on one side. I explain my self. The walk of the Horseman is composed of two steps, as I have said, the one of which is according to the march of our Rook, and the other according to that of our Bishop. It is therefore necessary that the first step of the Horseman, be free [Page 182] in one sense, that is to say, either according to the march of the Rook, or according to that of the Bishop. Besides the Horseman may pass the River, and the breadth of the River is esteem'd one of the two steps that he must take, as if it was a Rank of Squares.
The Waggons march like our Rooks, and may pass the River. The Cannons have also the walk of our Rooks, and may pass the River.
The Pawns do only make one step as amongst us, and they never have the liberty of making two, not even the first time that they are used. They may pass the River which is always reckoned for one step, and when they have passed it, they may move not only forwards, but also sideways like the Rook, and never bias-ways like the Bishop, and like our Pawns when they take, nor also backward, not even when they have been at the end of the Game, which we call making a Queen.
The design of the Game.The design of the Game is to give Check-mate, as amongst us; and the King is obliged amongst them, as amongst us, to free himself from Check, either by removing place, or by covering himself from Check.
How their men do take.Every Man takes, by putting it self in the place of the Man which it takes, provided that the walk from the one to the other be free. There is only the Cannon which requires that there be a Man between it, and that which it takes, and it matters not whether this Man be Friend or Enemy. 'Tis said that it serves as a carriage. Thus it is necessary that there be a Man between the Cannon and the King, for that the Cannon gives Check to the King; and if the Man which is between both, is on the King's side, he whose King is in Check, may free him from Check by taking away this Man, and by exposing the King before the Cannon. In a word one Cannon may serve as a carriage to another Cannon.
Their Pawns take not bias-ways like ours, but in the natural sense of their walk, which is forward, when they have not passed the River: and forward or sideways according to the march of our Rook, when they have passed the River.
One cannot put nor leave his King opposite to the other King, when there is not a Man between both, he that should do it, or would take the Man that is between both, would himself put his own King in Check, which cannot be done, yet the King can take nothing but what is at a point near him, and according to the march of our Rook, and not according to the march of our Bishop.
The Abacus, or Counting-Table of the Chineses.
THe Counting-Table which the Chineses use, is a wooden frame of a square figure, but much longer than broad. It is divided into two long squares, with a flat stick of Lath parallel to the two great sides, and terminated at the two little ones. These three parallel sticks, (I mean the two great sides of the frame and the middle stick) are threaded at right Angles, by several small sticks of wood, or copper wires, which are all parallel to one another, and parallel to the two little sides of the Frame, and placed at equal distances for Decency. And in fine, on each of these sticks are put seven Beads or Balls, two on one side of the middle piece, and five on the other, which will slide, or come along the Sticks; that is to say, to approach to, and remove from the middle Lath, or Partition.
This Instrument, which is composed at most of Twenty, or Twenty five sticks, for the number thereof is uncertain, is laid flat, and not on the side, and one turns to him the ends of those sticks, which do each bear five Beads, or Balls. The way of using it is grounded, 1st. On this, that the Beads do signifie only when slid near the middle Lath or Partition. 2d. On this, that each of the five Beads stands for a point, and each of the two Beads five points, as [Page]
The Wind Mountain
The Table Mountain
The Lyon Mountain
The Lyon Mountain
The Table Mountain.
The Lyon Mountain at ye. East ¾ S.E.
The Table Mountain at E.S.E.
- A. The Road.
- B. The Fort.
- C. The Garden.
- D. The Houses of ye Town
- E. The Gardn: House
- F. Several Springs
- G. Island Robin
- H. The Cabanes of ye Hotantots.
- L. The Conduit where the Ships do take in fresh water.
- K. The Top of the Lyon Mountain.
- L. The Bottom of ye: same Mountain.
- M. The Table Mountain.
- N. The Wind Mountain.
- O. The Windmill.
- P. The Place where M. Volan was when he drew this Design.
The Whale Rock.
[Page] [Page 183] often as these Beads do stand for any thing, that is to say, as often as they approach them near the middle Partition. 3d. On this, that the sticks are reckoned, from the right to the left, and do stand for Number, or Ʋnites, Tens, Hundreds, and Thousands, and all the other powers of the number ten in their natural Order. In a word, one may at the same time denote several sums in divers places of this Instrument, by taking such sticks, as one will to denote Unites, and the next on the left to denote Tens and Hundreds, and so successively. And this is sufficient to illustrate the use of this Instrument to those, that know how to reckon with Counters. The Swiftness with which I have seen the Chineses, which are at Siam, make use thereof, is inconceivable; but they say that it is an effect of two years Apprenticeship. The Instrument may be more simple if one will, by putting only four Beads on one side, and one on the other, because that this is sufficient to mark to nine on each stick, which is all that is requir'd; and in this simplicity was the Roman Instrument, which in my Relation I have mentioned, that Pignorius has given us. From whence the Learned may, at their pleasure, draw their Conjectures, to decide which of these two Instruments is probably the Original, either the most compound, or the most simple. The Simple seems a Correction of the Compound, the Compound seems to have added to the Simple, for the more facility and exactness in practice.
Of the Cape of Good-Hope.
I Have given three different Prospects thereof, two of which are entirely new, and the third, which is that whose place of view is in the Road, is copied after a very good Dutch Map.
Every one knows that the Dutch have an important Establishment there, which secures their Navigation from the East-Indies. The Fort which defends it, would perhaps be no considerable thing in Europe; but it is sufficient in a Country, where there is no Neighbour to fear, and where there can go no considerable Enemy, but from a great distance, and consequently with a great deal of difficulty.
The Company's Garden, the Platform whereof is in one of these Prints, is very spacious, as may be judged by comparing it to the Fort: And tho' the Soil be not over-good, it plentifully produces Coleworts, Citruls, Oranges, Pomegranets, and, in a word, Pulse and Fruits, which keep at Sea, and of which the Mariners are desirous in long Voyages. In a corner, and under a shelter, I saw a Camphire-Tree, an European Fig-Tree, and a Shrub about two Foot high, which was said to be that which bears the Tea, and which I had taken for a young Pear-Tree. It had neither Flowers nor Fruit, and very few Leaves. Close by, and under another shelter, were two or three Foot of Ananas, and this was all the Rarity they show'd me for the Country. The Grape is not more rare, but there is only that which the Hollanders have planted there. The Wine thereof is white, and very good. Some of our Crew went to the top of the Table Mountain, to seek some extraordinary Plants, but they found none. Nevertheless, upon a strict Scrutiny, there is not any that has not something particular, which the Plants of these Countries have not. The shells there found are not the Remains of the Deluge, as some have conjectur'd. The Birds, the Apes, and the Hotantots, do bring them, and leave them there.
The Walks of the Garden do almost spontaneously maintain themselves, because that the Soil produces only Moss if it is not cultivated: Besides the neatness of the Garden has nothing, which savours not a wise oeconomy, nor any thing which savours a too great negligence, like a Kitchen Garden of Merchants, more wedded to the profit, which they reap thence, than to the Pleasures, which they could not enjoy.
[Page 184]The water which waters it through several little Channels, enters therein at the going out from a Mill which it turns, and underneath the Garden, it serves for blanching. They only divert a part thereof, which is conducted to a Cistern, which is on the bank of the Road, and where the Ships do go to take in their fresh water.
The Garden is divided into several great Squares, almost like the Plot of the place Royal. They are encompassed with Pales, to shelter them from the Winds, which are sometimes furious enough to wreck the Ships in the Road, if they have not good Anchors and good Cables. These Winds are formed of the thick Clouds, which do sometimes assemble between the Table-Mountain, and that which is called the Mountain of the Wind, by reason of these Storms. A walk of Citron-trees and Orange-trees planted in Earth, which go from one end of the Garden to the other, do altogether resent their fury. Next to this the situation of the Garden, and that of the Village which is a little nearer to the Road, are very good; for they are wholly exposed to the Sun, and sheltered from the South Winds, which are the cold Winds of this Country. The Hollanders which are setled there, do say, that if the South-west Wind blows not during their Summer, which is our Winter, the Distempers of the Lungs are frequent and dangerous.
The short stay that I made, permitted me not througly to instruct my self concerning the Manners of the Hotantots, the natural Inhabitants of the Cape, though in the extream Simplicity in which they live, this can be no long study. They are called Hotantots, because that when they dance, they always in singing say this word Hotantot. The Love of the Tobacco and Brandy, which the Strangers offer them, and which has made them to receive the Hollanders into their Country, makes them to dance so long as one will, that is to say, to stamp sometimes with one Foot, and sometimes with the other, as he that treads the Grapes, and incessantly, and vigorously to say, Hotantot, Hotantot, but with a very low voice, as if they were out of breath, or that they fear'd to awaken any one. This mute Song has no diversity of Tones, but of Measure: the two first Syllables of Hotantot are always two Blacks, or Crochets, and the last always a White or Minime.
They go all naked, as may be seen in the figure, which I have given. They have but one skin over their Shoulders, like a Cloak; yet do they quit it at every place: and then they have only a little Leather Purse, hung to their Neck by a string, and a piece of a Skin a little bigger than one's Hand, hung before, and fastned with another string round their body: but this little piece covers them not, either when they show themselves side-ways, or when they do make a brisk motion.
Their stature is acceptable, and their gate more easy, than can be expressed. They are born as white as the Spaniards, but they have their Hair very much frizled, and Features participating somewhat of those of the Negro's: and besides they are always very black; because that they grease their Body and Face. They do also grease their Head, and we smell them twenty Paces, when they have the Wind. Our men gave them Pots, and Cauldrons to bath in; and before all things, they took the Fat by hands-full, and herewith anointed their whole Body, from the Head to the Feet. The Grease defends them from the Air and the Sun, renders them sound and well disposed, and they prefer these natural Advantages before Sweet Scents and Pleasure. They are so active, that several among them do out-run Horses. There is no Brook which they swim not over. They are expert in drawing the Bow, and throwing the Dart; and they have Courage even to Undauntedness. They do sometimes worst a Lion, provided they have Skins enough, and Furniture enough to garnish their left Arm. They do thrust it thus into the Throat of this Animal, and they pierce it with a Dart or Knife, which they will have in their right hand. If they are two, the one kills the Lion, whilst the other amuses him. If they are several, and they have nothing to secure themselves from the Claws of the Lion, they fail not to expose themselves all at once: The one of them generally perishes, but the Lion perishes likewise by the Blows which [Page 185] the others give him. Sometimes they are all saved, and they kill the Lion.
Their Wives do likewise grease themselves, though they affect some Ornament; as to fasten little Bones and Shells to their short Cottony, and greasie Hair. They also have Necklaces with divers colors of Glass, Bone, or such other matter, according as the Foreigners do give them, or sell them to them. On each Leg they have fifty Rings of Leather, which do beat one upon the other, and make some Noise when they dance, and which defend them from the Briers, when they go to get Wood: for this care concerns them, and not their Husbands.
The Men and the Women did eat Guts, almost without cleansing them, when our men presented them therewith, and they did hardly put them a moment on the Coals. If we offer'd them Brandy, they would gather up the first Shell, they found on the ground to receive it, and after having blow'd therein, they used to drink in it. They eat their Lice, as well as the Cochinchinese: and when we thought it strange, they answer'd pleasantly, that 'tis because their Lice eat them.
They lodge under little Huts made of Branches, or great Bulrush Mats, the top of which hardly reach'd to my middle; and to me it seem'd that I could not lye therein, my whole length. Under these Mats they make a hole in the ground, and in this Hole, about two Foot deep, they make their Fire, not caring for the Smoak, whereof their Huts do not empty themselves. They live on Hunting, Fishing, Milk and the Flesh of their Flocks.
In this Poverty they are always merry, singing and dancing continually, living without Pains and Business: and caring for Gold and Silver, only as far as it is necessary for them to buy a little Tobacco and Brandy; a Corruption which the Foreign Commerce has introduced into their Customs.
As some amongst them were exercising themselves, in throwing the Dart before us, I offer'd them five or six Papers of Necklaces with Beads of coloured Glass; and they all so exactly seized my Hand, that I could not open it to let go the Necklaces, and I could not besides explain my self unto them. I was sometime in this perplexity, till they perceived that they must set me at Liberty to obtain what they desired. They love these Necklaces for their Wives, and when we had set sail again, I understood that a Laquais of ours had sold one for a Crown to one of them. The little Money they have, and of which they have little esteem, is the Wages for the Service which they render sometimes to the Hollanders, and to the other Foreigners, which land at the Cape: but they care but little to work.
Every one has but one Wife, their Chief only has three, and Adultery amongst them is punished with Death. They kill their Children, when they have too many: and as they marry those which they keep, exceeding young, there is seen amongst them a great many Grand-Daughters, already Widows; who want a Joynt in their little Finger: For when a Woman loses her Husband, she cuts off a Joynt of the little Finger, or of the fourth Finger, if she has so often been a Widow, as to have her whole little Finger cut off. Nevertheless she may dispence therewith, if she please: and there are some Husbands who dispence not therewith, when they have lost their Wife. Most of them do make themselves Ridgils, to be more fit for the Women; and when the Age of renouncing comes, they make themselves entirely Eunuchs, to deprive themselves wholly of their Commerce, and to enjoy a more vigorous old Age. The Hollanders had educated an Hotantot Infant after the European manner, and had sent him into Holland. Sometime after they caused him to return to the Cape, where he might be useful to them amongst those of his own Nation. But so soon as he found himself again amongst them, he continued there, and renounced the Dutch Habit, and Manner of living.
They commit no Robbery amongst themselves, nor in the Houses of the Hollanders, where they are received without Care: and if the thing happens, they punish it with Death. Nevertheless in the Country, when they can do it securely, and that they think not to be discovered, they do sometimes assassinate to rob; and do show that the Contempt of Riches is, amongst them, only the Hatred of work.
[Page 186]The Dutch do nominate their Chief, and this Chief is their Judge: but those who could not bear this Foreign Dependance, are gone further into the Country, to live with the other Caffres.
Some informed me at first, that they had no sence of Religion; but at last I understood, that tho they have neither Priests nor Temples, yet they make public rejoycing, which savor of Worship, at the New and Full Moons. I suspect that they have some Tincture of Manicheisme, because that they acknowledge a Principle of Good, and another of Evil, which they call the Captain above, and the Captain below. The Captain above, they say, is good, it is not necessary to pray to him, 'tis only needful to let him act freely, he always does good: But the Captain below is wicked, he must be prayed to, and intreated to divert him from mischief. 'Tis thus that they speak, but it appears not in their exterior Conduct, that they pray much. A Dutchman of Wit and Knowledge informed me, that amongst the Hotantots, he had found the Names of Asdrubal and of Bocchus.
Rules of the Siamese Astronomy, for calculating the Motions of the Sun and Moon, translated from the Siamese, and since examined and explained by M. Cassini, a Member of the Royal Academy of Sciences.
MOnsieur de la Loubere, the King's Ambassador extraordinary at Siam brought back a Siamese Manuscript, which comprehends the Rules for calculating the motions of the Sun and Moon, according to the method of that Country, the Translation thereof he likewise brought from Siam, and communicated unto me.
This method is extraordinary. They make no use of Tables; but only of the Addition, Substraction, Multiplication, and Division of certain numbers, of which we do not presently discern the Ground, nor to what these numbers refer.
Under these numbers are conceal'd divers Periods of Solar Years, of Lunar Months, and other Revolutions, and the Relation of the one with the other. Under these numbers are likewise conceal'd several sorts of Epoches which are not distinguished, as the Civil Epoche, the Epoche of the Lunar Months, that of the Equinoxes, Apogaea, and Solar Cycle. The numbers in which the difference between these Epoches consists, are not ordinarily at the head of the Operations to which they serve, as they ought to be according to the Natural Order: they are often mixed with certain numbers, and the Sums or differences are multiplied or divided by others, for they are not always simple numbers, but frequently they are Fractions, sometimes Simple, sometimes Compound, without being ranged after the manner of Fractions, the Numerator being sometimes in one Article, and the Denominator in another; as if they had had a contrived design to conceal the Nature and Use of these numbers. In the Calculation of the Sun, they intermix some things which appertain only to the Moon, and others which are not necessary, either to the one or to the other, without making any distinction. They confound together the Solar and the Lunisolar Years, the Months of the Moon, and the Months of the Sun, the Civil and the Astronomical Months, the Days Natural and the Days Artificial. The Zodiack is divided sometimes into twelve Signs, according to the number of the Month of the Year, sometimes into 27 parts, according to the number of the Days that the Moon runs through the Zodiack, and sometimes in 30 parts, according to the number of the Days, that the Moon returns to the Sun. In the Division of the Day there is no discourse of Hours; but therein is found the 11th the 703d and the 800th parts of the Day, which result from the Arithmetical Operations which are prescribed.
This Method is ingenious; and being illustrated, rectified, and purged from [Page 187] Superfluities, it will be of some use, being practicable without books, by the means of divers Cycles, and of the difference of their Epoches. Wherefore it is that I have endeavoured to decypher it, what difficulty soever I found at first, not only by reason of the confusion which every where appeared, and of the Names which are wanting in the supposed numbers; but likewise by reason of the extraordinary names, which are given to what results from the Operations, of which there are more than Twenty which have not been interpreted by the Translator, and of which I could never have found the Signification, if I had not first discover'd the method; which has likewise evinced to me, that the Interpretation, which the Translator has made of three or four other names, is not very exact.
In this research I have first distinguished, and separated from the other numbers, those which belong to the Epoches, having observed that these numbers, are those which were given to add or to substract, either simply, or by dividing or multiplying them by certain other numbers.
Secondly, I have considered the Analogies which result from the Multiplications and Divisions of the other numbers, separated from the Epoches; and it is in the Terms of these Analogies, that I have found the Periods of the Years, of the Months, and of the Days, and the differences of the one from the other, which the experience of things Astronomical, and the occasion of divers operations which I have made, has given me to understand.
I thought that the Missionaries, to whom Astronomy gives admittance amongst the great and learned throughout the East, might reap some advantage from this work, for the Understanding, and for the Explication of the Oriental Astronomy, which might easily be rectified and adapted to ours, with a little altering the Method, by correcting the numbers which it uses.
I thought also that it would not be useless to reduce the Astronomy of Europe to this form, to be able to supply the want of the Tables which greatly abridge the work. This method would be much more easie to practise in the form of the Julian and Gregorian year of which we make use, than in the form of the Lunisolar year, which the Orientals observe: for their principal difficulty consists in reducing the Lunisolar years and the Civil Lunary months to the years and months of the Sun, which the form of our Kalender immediately gives us; and what has given me the most trouble, has been to find out the method which they use to reduce them, in which the several sorts of Years, Months and Days, which are supposed and sought, are not distinguished. Wherefore the reason of the Explication which I give, and of the Determination of the Genus to the Species which I make in the beginning, will not presently be understood; but in the sequel it will be comprehended by the Connexion of things, and by what necessarily results therefrom.
Concerning the Astronomical Epocha of this Method.
I Have endeavoured to discover what is the Epocha, from whence they here begin to compute the Motions of the Sun and Moon; and to what year, what month, and what day of our Kalender it refers: for it is not treated of in this extract, which supposes it either known, or explained perhaps in the preceding Chapters from whence this extract has been taken, seeing that without the knowledge of the Epocha, it is absolutely impossible to practice this Method.
I have found that this Epocha is Astronomical, and that it is different from the Civil, which I have understood, because it is here prescribed to begin to compute the Months of the Year, current with the fifth Month in the Leap Year, which consists of 13 Months, and with the sixth Month in the common Year, which consists of 12 Months. For this would not be intelligible, if they supposed not two different Epoches of Years, the one whereof, which must be the [Page 188] Astronomical, begins sometimes in the fifth, and sometimes in the sixth Month of the other, which is the Civil. That which likewise evinc'd to me that the Astronomical Epoche, is different from the Civil Epocha, not only in the Months, but also in the Years, is the Operation which is here made to find the Year of ones Nativity, by substracting his Age from the number of the Years elaps'd since the Epocha; for this Operation would be useless, if they demand only the Year of the Birth after the Civil Epocha, which is immediately known, and which is compared to the Year current, to know the Age of a Person.
This being supposed, I have first searched out the Age to which this Astronomical Epocha may refer; and having found in the Calculation of the Sun, performed by this method, that two Signs and twenty Degrees which are therein employed, can only denote the place of the Zodiack, where was found the Apogaeum of the Sun in the Epocha, which Apogaeum must be in the twentieth Degree of Gemini; I judged that this Epocha must be about the seventh Age, where the Apogaeum of the Sun is found in the twentieth Degree of Gemini according to most Astronomical Tables.
Secondly, having found that the number 621, which is intermixed in the Calculation of the Sun, can only be the number of the days comprized, between the Astronomical Epocha, and the return of the Moon's Apogaeum, to the beginning of the Zodiack; and that the number 3232, which is afterwards employed therein, can be only the number of the Days, during which, this Apogaeum makes a Revolution; I have confirmed that the Apogaeum of the Moon, which in 621 Days makes two Signs and nine Degrees, was in this Epocha, in the 21 Degrees of Capricorn: And because that the Moon's Apogaeum by the Revolution it makes in eight Years three quarters, returns to the same degree of the Zodiack twelve times in one Age; I have distinguished the Years of the Age, in which the Moon's Apogaeum is found in this Degree, and I have excluded the other Year.
Thirdly, having found by the method here used for Calculating the place of the Sun, that this Astronomical Epocha is very near the vernal Aequinox, which in the seventh Age fell on the 20th or 21st of March; Amongst these select Years I have found one in which the Moon's Apogaeum, arrived at this Degree of Capricorn, about the 21st of March, which is found but once in 62 Years, wanting some Degrees; and I have found that in the 638th Year of Jesus Christ, the Apogaeum of the Moon was at the 21st Degree of Capricorn the 21st of March.
Fourthly, I have remarked that this Astronomical Epocha must have begun at a new Moon; because the Lunar Months are reduced into Days, to find the number of the Days from the Epocha, and the value of the whole Months being deducted from the Sum of the Days, the rest serves to find the Moon's distance from the Sun.
In the 638th Year of Jesus Christ, the Aequinoxial new Moon happened the 21st of March at three a Clock in the Morning at Siam, when the Sun by its middle Motion ran through the first degree of Aries, the Sun's Apogaeum being in the 20th Degree of Gemini, and the Moon's in the 21st Degree of Capricorn. This Day was likewise remarkable for a great Eclipse of the Sun, which happened the same day, but 14. Hours after the mean Conjunction.
Fifthly, By the manner of finding the day of the week, which is here observed, it appears that the day of the Epocha, was a Saturday; and the 21st of March, in the Year 638 was also a Saturday. This likewise confirms the certainty of this Epocha, and demonstrates the Knowledge and Judgment of those that have established it, who contented not themselves with a Civil Epocha, as other Astronomers have done: but who have chosen an Astronomical one, which was the Natural Principle of several Revolutions, which could not begin again, till after several Ages. This Epocha is 5 Years and 278 Days distant from the Persian Epocha of Jesdegerdes, the first year of which began on the 16th of June, in the Year of Jesus Christ, 632. Yet these Indian Rules are not taken from the Persian Tables related by Crisococa; for these Tables do make [Page 189] the Sun's Apogaeum two degrees more backward, and the Moon's Apogaeum above six degrees forwarder; which agrees not so exactly with our modern Tables. The Persian Tables do also make the Sun's Aequation 12 Minutes less, and that of the Moon 4 Minutes greater; which agrees better with the Moderns.
These Indian Rules are not drawn neither from the Tables of Ptolomy, where the Sun's Apogaeum is fixed to the 5th degree and a half of Gemini; nor from the other Tables since made, which have all this moveable Apogaeum. It seems therefore that they have been invented by the Indians; or that perhaps they have been taken from the Chinese Astronomy, as may be conjectured from this, that in this extract the Numbers are written from the top downwards, after the manner of the Chineses: but it may be that this way of writing the numbers might be common to these two Nations.
Having found the Astronomical Epocha of this method, and the Relation it has with the Julian years; we may rectifie the Epocha's of the motions of the Sun and Moon by the modern Tables, by adding about a Minute a Year to the Sun's Apogaeum, and by correcting the other Periods. Thus there will be no difficulty, to reduce the Years and Months since the Epocha into days; and if the Equations are likewise corrected conformably to the modern Tables, we shall by the same Method, find the place of the Sun and Moon with a great deal more exactness. We will give this Correction, with the Supplement of what is wanting in these Rules, after that we have explained them.
Rules to find the place of the Sun and Moon at the time of any Person's Birth.
I.
1st. SET down the Aera.
Explication. 1st. THE Aera in this place is the number of the years since the Astronomical Epocha from whence is taken the motion of the Planets to the current year; which will appear in the sequel.
2d. Substract the Age of the Person from the Aera, you will have the Age of the Birth.
Explication. 2d. The Age of the Person, is the number of the Years from his Birth to the Year current, which being deducted from the Aera, there remains the Age or Time of the Birth, that is to say, the Year from the Astronomical Epocha in which the Nativity happened.
3d. Multiply it by 12.
Explication. 3d. By multiplying the years by 12 they are reduced into Months. These Months will be solar, each consisting of 30 days, 10 hours and a half, a little more or less, according to the several Hypotheses, if the years are solar; or near upon if they are lunisolar, and in so great number, that the excess of the one recompences the defect of the others.
4th. Add hereunto the number of the Months of the year current: and for this purpose if the year current is Attikamaat, that is to say, if it has 13 Lunar months, you shall begin to compute with the 5th month; but if it is not Attikamaat, you shall begin to compute with the 6th month.
Explication. 4th. The form of the Year here mentioned, is lunisolar, seeing there are some common of 12 lunar months, and abundant or Embolismal, called Attikamaat, of 13 lunar months. For that they begin to compute the months, not with the first month of the year, but with the fifth, if it is Leap-year, and with the sixth if it is not: I have inferred that there are two Epocha's, and two forms of different [Page 190] Years, the one Astronomical and the other Civil: that the first Month of the Astronomical Year begins in the fifth Month of the Civil Leap-year, which would be the sixth Month without the intercalation of the Leap-month, which is not reckoned amongst the 12 Months, and which is supposed to be inserted before; and that in the other Years, all the Months of which are successively computed without Intercalation, the first Month of the Astronomical Year, is computed only from the sixth Month of the Civil Year.
But as it is not expresly determined here, whether one ought to begin to compute an entire month at the beginning or end of the 5th or 6th month, it may be that for the first month of the Astronomical Year they take, that which ends at the beginning of the months whereof it is discoursed in this Article. In this case, the Interval between the beginning of the Civil Year, and the beginning of the Astronomical Year, would be only of 3 or 4 entire months: whereas if an entire month is reckoned only at the end of the 5th or of the 6th month, and that the first month which is reckoned, according to this Rule, be the first of the Astronomical Year; the interval between the beginnings of these two sorts of years, will be 4 or 5 whole months. We shall see in sequel, that the Indians have diverse sorts of Astronomical Years, the beginnings of which are different, and are not much distant from the Vernal Aequinox; whereas the Civil Year must begin before the Winter Solstice, sometimes in the month of November, sometimes in the month of December of the Gregorian Year.
They add the number of the months of the current year, which are lunar months, to those that they have found by the third Article, which are solar months; and they suppose that the sum, as heterogeneous as it is, should be equal to the number of the solar months elapsed from the Astronomical Epocha. They neglect the difference that there may be, which in a year cannot amount to an entire month: but they might be deceived a month in the succession of the years, if they took not good heed to the Intercalations of the months, after which the number of the months which are computed in the Civil Year, is lesser than that which they would reckon without the precedent Intercalations.
5th. Multiply by 7 the number found Art. 4.
6th. Divide the sum by 228.
7th. Joyn the quotient of the division to the number found Art. 4. This will give you the Maasaken (that is to say, the number of the months) which you shall keep.
Explication. 5th. 6th. 7th. They here seek the number of the lunar months from the Astronomical Epocha, discoursed of in the 1st. Article, to the beginning of the current month: which is performed by reducing the solar months, which are supposed to have been found above, into lunar months, by the means of the difference, which is between the one and the other. In the operations which are made, is is supposed that as 228 is to 7, so the number of the solar months given, is to the difference which the number of the lunary months surpasses the number given of the solar months elapsed, during the same space of time; that thus in 228 solar months, which do make 19 years, there are 228 lunary months, and 7 months more, that is to say 235 lunary months. This therefore is a Period like to that of Numa and Meto, and to our Cycle of the golden number of 19 years, during which the Moon rejoyn'd it self 235 times to the Sun.
Yet in the sequel we shall see, that these Periods which accord together in the number of the lunar months and solar years, agree not in the number of the hours, by reason of the greatness of the solar year and of the lunar month, which is supposed various in these several Periods: and that the Indian is not subject to a fault so great, as the ancient Cycle of the Golden Number, which they have been obliged to expunge out of the Roman Kalender, in the Gregorian correction, because it gave the new Moons later than they are, almost a day in 312 years; whereas the New Moons determined by this Indian Period, agree with the true in this interval of time to near an hour, as will be found by comparing these Rules with the following.
II.
1. Set down the Maasaken.
2. Multiply it by 30.
3. Joyn thereunto the days of the current Month.
Explication. The months of the Moon are here reduced into days: but because they make all the months to consist of 30 days, there only will be some artificial months about 11 hours 16 minutes longer than the Astronomical, or some artificial days which begin at the New Moons, and are 22 minutes, 32 seconds shorter than the natural days of 24 hours, which begin always at the return of the Sun to the same Meridian.
4. Multiply the whole by 11.
5. Add thereunto also the number of 650.
Explication. They 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 [Page 192] 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 that in the third Art. the day of the Week is found by the Horoconne, after a very easie manner, it is needless to stay on this which is longer and more compounded.
VI.
1. Horoconne.
2. Substract from it 621.
3. Divide the remainder by 3232. The Fraction is called Outhiapponne, which you shall keep.
Explication. This Substraction of 621, which is always deducted from the Horoconne, what number soever the Horoconne contains, denotes an Epocha, which is 621 days after the Epocha of the Horoconne.
The number 3232 must be the number of Days, which the Moon's Apogaeum employs in running through the Circle of the Zodiack: 3232 Days do make 8 Julian Years and 310 Days. During that time this Apogaeum finishes a Revolution after the rate of 6′. 41″. which it performs in a Day, even according to the Astronomers of Europe. The Apogaeum of the Moon does consequently finish its Revolution 621 days after the Epocha of the Horoconne. 'Tis here performed then; as 3232 days are to a Revolution of the Apogaeum, so the number of the days is to the number of the Revolutions of the Apogaeum. They keep the remainder which is the number of the days called Outhiapponne. The Outhiapponne will therefore be the number of the days elapsed from the return of the Moon's Apogaeum to the beginning of the Zodiac; which will more evidently appear in the sequel.
If you would have the day of the Week by the Outhiapponne, take the Quotient of the aforesaid Division; multiply it by 5, then joyn it to the Outhiapponne, then substract thence two days, divide it by 7, the Fraction will show the day.
Whatever is before is called Poulasouriat, as if one should say the Force of the Sun.
Explication. Having already explained the true method of finding the day of the Week, it is needless to stay here. Leaving the care of examining it, and and searching the ground thereof, to those that shall have the curiosity.
Notwithstanding the name of the Sun's Force which is here given to the precedent Operations, it is certain that what has hitherto been explained, belongs not only to the Sun, but likewise to the Moon.
VII.
1. Set down the Krommethiapponne.
2. Divide it by 24350.
3. Keep the quotient, which will be the Raasi, that is to say, the Sign where the Sun will be.
Explication. To find what the number 24350 is, it is necessary to consider, that the Krommethiapponne are the 800 parts of the day which remains after the Sun's return to the same place of the Zodiac, and that the solar year contains 292207 of these parts, as has been declared in the explication of the fourth Section. The twelfth part of a year will therefore contain 24350 and 7/121 of these 800 parts: wherefore the number 24350 denotes the twelfth part of a solar year, during which the Sun by its middle motion makes a Sign.
Seeing then that 234 350/800 of a day do give a Sign, the Krommethiapponne divided by 24350 will give to the Quotient the Signs which the Sun has run since his return by his middle motion to the same place; The Raasi then is the number of the Signs, run through by the middle motion of the Sun. They here neglect [Page 194] the Fraction 7/12, so that the solar year remains here of 292 200/800, that is to say, of 365 days ¼, like the Julian year.
4. Lay down the Fractien of the aforesaid Division, and divide it by 811.
5. The Quotient of the Division will be the Ongsaa, that is to say, the degree wherein the Sun will be.
Explication. Seeing that by the preceding Article 24 350/800 of a day do give a Sign of the Sun's middle Motion, the 30th part of 24 [...]50/800 will give a degree which is the 30th part of a Sign. The 30th part of 24330 is 811 ⅔ which do make a degree: dividing then the remainder by 811 ⅔, they will have the degree of the Sun's middle motion. Here they neglect the ⅔ which can make no considerable difference.
6. Set down the Fraction of this last Division, and divide it by 14.
7. The Quotient will be the Libedaa, that is to say the Minute.
8. Substract 3 from the Libedaa.
9. Place what belongs to the Libedaa, underneath the Ongsaa, and the Ongsaa underneath the Raasi: This will make a Figure which shall be called the Mattejomme of the Sun, which you shall keep. I suppose it is locus medius Solis.
Explication. Seeing that in a degree there are 811/800 parts; in a minute, which is the 60th part of a degree, there will be 13 31/60 of these parts. Neglecting the Fraction, they take the number 14, which dividing the remainder, will give the minutes. The Substraction which is here made of three minutes is a reduction whereof we shall speak in the sequel.
It is here prescribed to put the Degrees under the Signs, and the Minutes under the Degrees in this manner.
- Raasi, Signs.
- Ongsaa, Degrees.
- Libedaa, Minutes.
This Disposition of the Signs, Degrees, and Minutes one under the other is called a Figure, and it here denotes the middle place of the Sun.
VIII.
To find the true place of the Sun.
1. Set down the Mattejomme of the Sun, that is to say, the figure which comprehends what is in the Raasi, Ongsaa, and Libedaa.
2. Substract 2 from the Raasi. But if this cannot be, add 12 to the Raasi, to be able to do it, then do it.
3. Substract 20 from the Ongsaa. But if this cannot be, deduct 1 from the Raasi, which will amount to 30 in the Ongsaa, then you shall deduct the aforesaid 20.
Explication. The number 2, which is substracted from the Raasi in the second Article, and the number 20 in the third Article, are 2 Signs and 20 degrees, which doubtless denotes the place of the Suns Apogaeum according to this Hypothesis; in which there is not seen any number which answers to the motion of the Apogaeum. It appears then that this Apogaeum is supposed fix'd to the 20th degree of Gemini, which precedes the true place of the Apogaeum, as it is at present 17 degrees, which this Apogaeum performs not in less than 1000 years, or thereabouts: From whence it may be judged that the Epocha of this method is about a thousand years before the present age. But as the greatness of the year agrees better here with the Suns return to the Apogaeum and the fixed Stars, than with the Suns return to the Equinoxes; it may be that the beginning of the Signs here used, is not at present in the Equinoxial point, but that it is advanced 17 or 18 degrees, and so it will be necessary to be corrected by the Anticipation of the Equinoxes. Here then they substract the Suns Apogaeum from its middle place called Mattejomme, to have the Suns Anomalia: and the number of the Signs of this Anomalia is that which they call Kenne.
4. What will afterwards remain, shall be called Kenne.
5. If the Kenne is 0, 1, or 2, multiply it by 2, you will have the Kanne.
6. If the Kenne is 3, 4, or 5; you [Page 195] 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 [Page 196] 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 [Page 195] 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 [Page 196] 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.
[Page 197] 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 [Page 197] 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 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, [Page 200] 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 1/11 [...], 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. 'Tis 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 of meridians, one might have reason to believe that the substraction of these 40 minutes has been made a long time after these first rules; because that it is perceived in process of time, that the motion of the Moon was not exactly so quick, as it results from the preceding Rules, which do make the lunar month about three quarters of a second shorter than the modern Tables; and this difference amounts to 1 hour and 13 minutes in 450 years, or thereabouts. Thus, if 450 years after the Epocha they had compared the first rules to the observations, one might have judged that the Moon retarded, in respect of these first rules, 1 hour and 13 minutes, or 40 minutes of a degree. But this difference, which is always the same, when attributed to the difference of the meridians, would not be always the same if it depended on the motion of [Page 201] the Moon, for it would augment one minute to 12 years; to which 'twould be necessary to have regard in the Correction of these Rules.
II. The Determination of the Astronomical Epocha of the Indian Method.
SEeing that these Indian Rules have been brought from Siam, and that the Civil year of the Siameses begins in the season that we think it ought to begin according to the Rules of the I. Section, as we shall show in the sequel, it is reasonable to suppose that the meridian to which these Rules have been reduced by the additions mentioned in the VII. and X. Sections, is the meridian of Siam: therefore by the calculation which we have made, the new Moon which they have taken for the Epocha, must happen at 3 a Clock in the Morning at Siam. As the lunar month of this method agrees to near a Second with the lunary month established by all the European Astronomers, it may be supposed that this hour of the new Moon of the Epocha is very precise, since it may have been deduced from the Observations of the Eclipses of the Moon, which are much more easie to determine than all the other Phaenomena of the Planets. We may therefore make use of the common Tables to seek the new Moons which happen'd about the seventh Age at three in the morning in the meridian of Siam, the difference of which from the meridian of Paris is very exactly known to us by several observations of the Eclipses of the Moon, and the Satellites of Jupiter, which the Jesuites sent by the King into the East in quality of his Majestie's Mathematicians have made at Siam, and by the Observations of the same Eclipses made at the same time at Paris in the Royal Observatory; by the Comparison of which Observations it is found that the difference of the meridians of these two Cities is 6 hours 34 minutes.
To this Character of time we might add the Circumstance of the middle Aequinox of the Spring, which according to the Hypothesis of the IV. Section, must happen at 11 hours 11 minutes after the midnight which followed the middle Conjunction of the Moon with the Sun taken for the Epocha, according to what has been said on the 5th Article of the IV. Section, where they deduct 373/800 of a day, that is to say, 11 hours and 11 minutes from the days elapsed since the Epocha, which distinguishes as much as the Krommethiapponne, which we have declared to be the time elapsed from the Suns return to the the point of the Zodiack, from whence is taken the motion of the Sun and Moon, which must be the Aequinoxial point of the Spring.
But it must not be pretended that the modern Tables do give the very hour of this Aequinox: for they do not exactly agree together in the Aequinoxes, by reason of the great difficulty which is found to determine them precisely. They agree not with the antient Tables of Ptolomy in the middle Aequinoxes, to near 3 or 4 days: wherefore it is sufficient that we found by the modern Tables a new Moon to happen at Siam at 3 a Clock in the morning, within a day or two of the middle Aequinox of the Spring found by the modern Tables.
The place of the Suns Apogaeum, which according to what we have drawn from the Rules of the 2d and 3d Articles of the VIII. Section, was at the time of the Astronomical Epocha in the 20th degree of the sign Gemini, denotes the Age wherein it is necessary to seek this new Aequinoxial Moon, which according to the modern Tables, was about the seventh after the Nativity of Jesus Christ.
It is true that as these Rules give not motion to the Sun's Apogaeum, it may be doubted, whether it was not in this degree at the time of the Epocha, or at the time of the Observations upon which these Rules have been made. But the Age of this Epocha is likewise determined by another Character joyned to the former: 'Tis the place of the Moon's Apogaeum, which according to what we have drawn from the 2d and 3d Articles of the VI. Section, was at the time of the Epocha in the 20th degree of Capricorn, and to which these Rules do give [Page 200] [...] [Page 201] [...] [Page 203] a motion conformable to that which our Tables do give it; altho they agree not together in the Epoches of the Apogaea, but to one or two degrees.
In fine, the day of the Week must be a Saturday in the Epocha, seeing that according to the 3d Section, the first day after the Epocha was a Sunday; and this circumstance joyned to what has been said, that the same day was near the Equinox, gives the last determination to the Epocha.
We have therefore sought a new Equinoxial Moon, to which all these Characters do agree; and we have found that they agree to the New Moon, which happened in the 638th year after the Birth of Jesus Christ, on the 21 of March, according to the Julian form, on Saturday at 3 a Clock in the morning, in the Meridian of Siam.
This middle conjunction of the Moon with the Sun, according to the Rudolphine Tables which are now most used, happen'd on this day at Siam on the very same hour, the reduction of the meridians being made according to our Observations: And according to these Tables 'twas 16 hours after the middle Aequinox of the Spring; the Sun's Apogaeum being at 19 degrees ¼ of Gemini; the Moon's Apogaeum 21 degrees ½ of Capricorn; and the Node descending from the Moon at 4 degrees of Aries: so that this Aequinoxial Conjunction had also this in particular, that it was Ecliptick, being arrived at so little distance from one of the Nodes of the Moon.
This Astronomical Epocha of the Indians being thus determined by so many Characters, which cannot agree to any other time, by these Indian Rules are found the middle Conjunctions of the Moon with the Sun about the time of this Epocha, with as much exactness as by the modern Tables, amongst which these are some which for this time do give the same middle distance between the Sun and the Moon, to one or two minutes, the Reduction being made to the same meridian.
But from this Epocha, as they remove from it, the middle distances from the Moon to the Sun found by these Rules, do by one minute in twelve years surpass those which the modern Tables do give, as we have before remarked: from whence it may be inferred that if these Indian Rules, at the time that they were made, gave the middle distances from the Moon to the Sun more exact than they have given them since, they have been made very near the time of the Epocha established by these Rules. Yet they might be established a long time after, on some Observations made very near the time of the Epocha, thus they would more exactly represent these Observations than those of the other times remote from the Epocha: as it ordinarily happens to all the Astronomical Tables, which do more exactly represent the Observations upon which they are founded, than the others made long before and after.
III. Of the Civil Epocha of the Siameses.
BY the Rules of the first Section I judged, that the Civil Epocha which is in use at the East Indies, is different from the Astronomical Epocha of the Indian method which we have explained-
I have at present new assurances by several dates of Siamese Letters, which have been communicated to me by Mr. De La Loubere, and by other dates of the Letters which Father Tachard published in his second Voyage, in the year 1687; by which it appears that the Year 1687, was the 2231st from the Siamese civil Epocha, which consequently refers to the 544th year before the Birth of Jesus Christ; whereas by the 2d and 3d Rules of the 8th Section, and by other Characters of this Indian method, it is evident that the Astronomical Epocha refers to the 7th Age after the Birth of Jesus Christ.
This Civil Siamese Epocha is in the time of Pythagoras, whose dogmata were conformable to those which the Indians have at present, and which these people had already in the time of Alexander the Great, as Onesicritus, sent by Alexander himself to treat with the Indian Philosophers, testified unto them, according to the report of Strabo lib. 15.
[Page 202]The Letters which the Ambassadors of Siam wrote the 24th of June 1687, were dated according to Mr. de la Loudere, in the eighth month, the first day of the decrease of the year Pitosapsec of the Aera 2231. And according to Father Tachard, the eighth month, the second full Moon of the year Ihoh napasoc of the Aera 2231. The full Moon happened not till the day following; and the lunary month which then ran, was the third after the Vernal Equinox; the first after this Equinox beginning the 12th of April in the same year, therefore the first month from the Equinox was the sixth month of the Civil year, which must begin the 15th of November, 1686.
It appears also that the same year was Leap-year of 13 months, and that there was one which is not put in the number of the others: for the 20th of October in the same year they reckon'd the fifteenth day of the eleventh Moon of the year 2231, and between the full Moon of June and that of October there were 4 lunar months. Nevertheless they reckoned only three, seeing that at the full Moon in June they reckon'd the eighth month, and at that of October they reckon'd only the eleventh; there was therefore in this interval of time a Leap-month which is not reckon'd. This Intercalation is likewise found by comparing the Letter from the Ambassadors with three of the King of Siam's Letters, of December 22 of the year 1687, recited by Father Tachardin, page 282, 287, and 407, which are dated the 3d of the decrease of the first Moon of the year 2231: and it appears that if the Moon of June was the eighth Moon of the Civil year 2231, that of December was the fourteenth of the same Civil year, which is reckon'd for the first Moon of the succeeding years, tho the year be yet named 2231, whereas according to the preceding dates, it ought to be named 2232.
Perhaps they chang'd not the name of the Civil year, till it was sufficiently advanced, and had attained the beginning of the Astronomical year: or rather unto this time they do name it after two ways, For another date which Mr. de la Loubere communicated unto me, is thus, the eighth of the encrease of the first Moon of the Year 223½. 2. which is the eleventh of December 1687. It seems that this manner of date denotes that the year may in this month be named either 2231, or 2232: which has relation to the form now used in the Northern Countries, where the dates are frequently set down in two ways, viz. according to the Julian, and according to the Gregorian Calendar; and to the ten first days of the Gregorian year, is set a Year more than in the Julian.
By comparing the date of October 20th which supposes that the first of the Moon was the 6th of this month (which day was also that of the new Moon) with the other date of December the eleventh, which supposes that the first of the Moon was the 4th of this month, there are found 59 days in two months, as the motion of the Moon requires. According to these dates the 22d of December must be the 19th of the Moon, that is to say, the fourth day of the decrease, which in the King of Siam's Letters is set down the 3d of the decrease, the full of the Moon being supposed on the 15th which should denote the Intercalation of a daymade to the full of the Moon, unless Letters should be antedated one day, or that there is one day wanting in the resemblance which is made thereof to our Calendar.
Amongst the preceeding dates, and some others which we have examined, there are only those of October 20th and December 11th that agree well together, and with the motion of the Moon, and in which they take the very day of the Moon's Conjunction with the Sun by the first day of the month. The other dates differ some days among them; for in those of June 24th they take for the first day of the month a day which precedes the Conjunction; on the contrary in the dates of December 22d they take for the first day of the month a day which follows the Conjunction. Thus the dates which for the first day of the Month do take the very day of the Conjunction, may be thought the most regular. We have calculated these Conjunctions, not only by the modern Tables, but also by the Indian Rules, after the manner as we shall herein after declare, and we have found that they agree together in the same days of the year.
[Page 204]These Indian Rules may therefore serve to regulate the Calendar of the Siameses, though they be not at present exactly observed in the dates of the Letters, without a Calendar where the Intercalations of the months and days be regulated according to this method, it would be impossible to make use of these Indian Rules in the Calculation of the Planets, without committing the same Error which would be slipp'd into the Calendar: unless that this Error was known by the exact History of the Intercalations, and that regard was thereunto had in the Calculation.
Though by the Indian Rules is sought the number of the months elapsed from one Epocha, by the means of a Cycle of 228 solar months, supposed equal to 325 lunar months, which is equivalent to the Cycle of our golden number of nineteen years, in the number of our solar and lunar months, which it comprehends: yet it is seen by most of the Siamese dates which we have been able to observe, that the first day of their month, even in this age, is hardly distant from the day of the Moons conjunction with the Sun; and that the Calendar of the Indians is not run into the Error into which our old Calendar was fallen, where the new Moons were regulated by the Cycle of the golden number, which gives them more slow than they are: so that since they have introduced this Cycle into the Calendar (which was about the fourth Age) to the Age past, the error was amounted to above four days. But the Indians have avoided this fault; by making use of the Rules of the I. Section to find the number of the lunar months; and of the Rules of the II. Section, to find the number of the days and hours which are in this number of months; which being founded on the Hypothesis of the greatness of the lunar months, which differs not from the real one, a second cannot want above a day in 8000 years; whereas the Ancient Cycle of our golden number supposes that in 235 lunar months there are the number of days and hours which are in 19 Julian years, which do exceed 235 lunar months one hour 27′; 33″, which do make 5 days in 1563 years.
It appears also that the Calendar of the Indians is very different from that of the Chineses, who begin their year with the new Moon nearest the fifteenth of Aquarius, according to Father Martinius; or the fifth of the same Sign, according to Father Couplet (which happen'd but a month and half, before the Vernal Equinox, and who regulate their Intercalations by a Cycle of sixty years; which the Tunquineses do likewise, according to the report of Father Martinius in his Relations.
IV. The Method of comparing the Siamese dates to the Indian Rules.
TO examine whether the Siamese dates agree with the Indian Rules, we have found by these Rules the number of the months comprized in the years elapsed from the Astronomical Epocha, and the year current, and we have thereunto added the month of the year current, which we have begun to compute by the sixth month of the Civil year, for the first date which was of the eighth month before the Intercalation of a month; and for the second date which was of the eleventh month, and after the Intercalation of a month, we have begun to compute the months of the current year, with the fifth of the eleven months which were then computed, which is the same month that they have reckon'd for the sixth before the Intercalation of a month, according to the Explication which we have given to the fourth Article of the I. Section.
We have done the same thing for the following dates, having verified that it is necessary to begin to compute from the fifth month, during the residue of the Astronomical year, and during that which immediately follows the Intercalacation. And having afterwards calculated the number of the days comprized in these sums of months according to the Rules of the II. Section, we have found that the number of the days found by these Rules, agrees with the number of the days comprehended between the Astronomical Epocha of the year [Page 205] 638, and the days of the Conjunctions from whence they have taken the beginning of the months in several of these dates, and particularly in those of October 20, and of December 8, which to us have appeared the most regular.
This method, which we have used to compare the Siamese dates to the Indian Rules, has made known to us the terms in our Calendar, between which must happen the new Moon of the fifth month of the Civil year after the Leap-year, or of the sixth month of the year after a common, whereby they must begin to compute the months according to the 4th Article of the I. Section, and which may be considered as the first new Moon of a kind of lunisolar Astronomical year, which we have judged ought to begin after the Vernal Equinox, wherefore it is necessary largely to give an example of this Comparison, which will demonstrate the use of these Rules, and will serve as a demonstration of the Explication that we have made thereof.
EXAMPLE for the I. DATE.
WE have sought what, according to the Indian Rules, ought to be the number of the days comprized between the Astronomical Epocha, and the middle conjunction of the eighth month of the Indian year 2231, in this form.
By the Rules of the I. Section.
FRom the Astronomical Epocha of the Julian year of Jesus Christ 638, to the year 1687, there are 1049 years, which is the Aera according to the 1st Article; having multiply'd it by 12, according to the 3d Article, there are 12588 solar months.
It is necessary to add the months of the current year, Article 4; and because the Ambassadors computed the eighth month of the year 2231, before the Intercalation of a month, we have begun to compute from the sixth of these months, according to our Explication; thus to the eighth month, we shall have three months to add to 12588, which will make the sum of 12591.
Multiplying them by 7, Article 5thly, the Product will be 88137.
Dividing it by 228, Article 6thly, the Quotient will be 386, to add to 12591, Article 7thly; and the sum will make 12977 lunar months.
By the Rules of the II. Section.
MUltiplying this number of months by 30, Article 2d, the Product will give 389310 artificial days.
Multiplying them by 11, Article 4th, the Product will be 4282410.
Dividing this Product by 703, Article 6th, the Quotient will be 6091 437/705.
Having substracted it from 383310 artificial days, Article 8, there remains 383218 266/703. which is the number of the natural days elapsed from the Astronomical Epocha to the new Moon of the eighth month of the Indian year 2231.
The Fraction 266/703 being reduced, gives 9 hours 4′, 34″, which this Conjunction happen'd later at Siam, according to these Rules, than that of the Astronomical Epocha of the year 638.
By the means of our Calendar is found the number of the days elapsed between the twenty first month of the Julian year 1638, and June 10th of the Gregorian year 1687, by this Calculation.
From the year 638, which was the second after the Bissextile 636, to the year 1687, which was the third after the Bissextile 1684, there are 1049 years, [Page 206] amongst which there were 262 Bissextiles, which give 262 days more than as many common years. In 1049 common years of 365 days, there are 282925 days; and adding thereunto 262 days for the Bissextiles, there will be 483187 days in 1049 years, as well common as Bissextile, between March 21st. of the Julian year 638, and March 21st. of the Julian year 1687, which is March 31st. of the Gregorian year.
From March 31. to June 10th, there are 71 days, which being added to 383147, do give 383218 days between the 21st. of March of the Julian year 638, where is the Indian Epocha of the new Moons, and the 10th of June of the Gregorian year 1687, the day of the new Moon of the eighth month of the Siamese year 2231. This number of days is the same that we have found between these two new Moons, according to the Indian Rules.
To find the same number of days by the one and the other method in the Conjunction of October of the same year 1687, after the Intercalation, which appears, by comparing the date of this month with that of the month of June foregoing; it is necessary to compute 8 months, beginning with the fifth of of the eleven which were reckon'd. In the Conjunction of November are reckon'd 8; and in that of December, from whence begins the first month of the year 2232, are computed 9, adding 8 months to those of the current year, to the new Moon of the 31st. of March 1688, from whence began the fifth month of the year 2232. They began to reckon from this 5th month during the whole year, which follows the Intercalation, and which was common; and they began to compute from the 6th month only at the new Moon, which happen'd the 19th of April of this year 1689. They will also begin to compute from the 6th month, at the new Moon, which shall happen the 9th of April, to the Intercalation which shall be made in the fame year, after which they will follow the same order as after the preceding Intercalation. We have thought fit; distinctly to relate these Examples, thereby the more precisely to determine the 4th Article of the I. Section, in which it was possible to err, if it was not illustrated; and it could not be determined without several Calculations made according to the preceding method.
V. The Terms of the first Months of the Julian Years.
HAving by the same method calculated, according to the Indian Rules, the middle Conjunctions of the Moon with the Sun for several years of this and the following Age, we have always found that every one of these Conjunctions fell upon a day whereon the middle Conjunction happen'd according to our Tables, but almost three hours later than by the Indian Rules.
By this means we have determined in our Calendar the Terms between which the new Moon must happen, from whence it is necessary to begin to compute the months of the year current, according to the 4th Article of the I. Section; and we have found that in this Age this new Moon is that which happen'd between the 28th of March, and 27th of April of the Gregorian year, which are at present the 18th of March, and 17th of April of the Julian year.
We have likewise found that these Terms in the Gregorian Calendar, do advance a day in 239 years, and do go back a day in the Julian Calendar in 302 years; which it is necessary to know, to be able to make use of these Indian Rules amongst us.
To determine in these Calendars the Terms between which the new Moon must happen, from whence the Civil year of the Siameses ought to begin according to these Rules, it is necessary to establish a System of common and Bissextile years well digested in the Cycle of 19 years, which System should be such, that the fifth month of the first year after the Bissextile, and the sixth month of the other years, do begin in this Age between March 28th, and April 27th of the Gregorian year.
According to this Rule, the Civil year should begin in this Age before the 12th of December. For if it begins the 12th the year following, which would begin, December 1. would be after the common year, and according to the Rule [Page 207] they would not begin to reckon from the fifth month, which would happen the 29th of March, but with the sixth month, which would begin the 28th of April; which is contrary to what we have found by the Calculation, that in this Age it is necessary to begin to compute with the month which begins between March 28th, and April 27th. One might therefore be mistaken in the use of these Rules in the years which would begin after December 11th of the Gregorian year.
We find likewise by our Calculations, that according to these very Rules, the Siamese year should begin on the 12th of December in the Gregorian year 1700, which will not be Bissextile. This will therefore be the most advanced Term, that must be a whole month distant from the preceding Term. Thus the new Moon, which will happen the Age following between the 12th of November, and the 12th of December, will be that from whence according to these Rules the Civil year of the Siamese ought to begin.
Nevertheless we have lately seen a date of the first of January 1684, wherein it is supposed that the beginning of the Siamese year was at the new Moon, which happen'd the 18th of December 1683. This date being compared with those of the Ambassadors of Siam, wherein it is supposed that the beginning of the year 2231, was at the new Moon, which happen'd the 16th of November 1686, would shew that the Terms of the first month of the Siamese year, according to the usage of these times, are at least 32 days distant from each other, altho' according to the Rules, they ought not to be more than a lunary month, or thirty days distant.
This confirms what we have already remark'd, that in this Age they conform not exactly to these Rules in the dates, altho' they differ not much therefrom. But as these Rules are obscure, and that it is necessary to supply some Circumstances which are not distinctly expressed, it may easily happen that the People be mistaken.
Thus after having determined what should be done according to these Rules, it is necessary to learn from the Relations of Travellers what is actually practised. Mean while we know by the dates which we have seen, that the present Practice is not much different from these Rules.
VI. Divers Sorts of Solar Years according to the Indian Rules.
EVery one of these Terms whereof we have discoursed, may be consider'd as the beginning of a kind of Solar Year, the greatness of which is a mean between the Julian and Gregorian Year, seeing that we have remarked, that in the succession of Ages these Terms do advance in the Gregorian Year, and go backward in the Julian: the Term which falls at present on 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.
'Tis 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 [Page 208] 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.
'Tis 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 [Page 209] 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.
'Twould 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 the place of the Heavens, where the Indians place the beginning of the Signs of the Zodiack according to the IV. Section, and the following Sections, there is not any considerable Star; there are only thereabouts some of the smallest and most obscure Stars of the Constellation of Pisces, but it is the place where was the Aequinoxial Point at the time of their Astronomical Epocha, from whence the fixed Stars advanced afterwards towards the East; so that the Sun, by its annual motion, returns not to the same fixed Star till about 20 minutes after its return to the same Point of the local Zodiack. It was difficult to perceive this little difference in few years to the Ancients, who did not immediately compare the Sun to the fixed Stars, as it is at present compared, and who compared only the Sun to the Moon during the day, and the Moon to the fixed Stars during the night, tho' from the day to the night the Moon changes place amongst the fixt Stars, as well by its own motion, which is quick and irregular, as by its Parallax, which was not well known to the Ancients. Wherefore they very lately only perceived the difference that there is between the Tropical year, during which the Sun returns to the Points of the Aequinoxes and the Solstices, and the Astral year during which it returns to the same fixed Stars; and then they had a Solar year of 365 days and a quarter, which is found at present to be the mean between the Tropical and the Astral, and that it surpasses the Tropical by 11 minutes, and is shorter than the Astral by 9 minutes.
VII. The Determination of the Magnitude of the two sorts of Indian Years.
IT is easie to find the greatness of the year which is supposed in the IV. Section, by dividing 292207 days by 800 years, each of which is found to consist of 365 days, 6 hours, 12′, 36″.
It is a little more difficult to find that which results from the I. and II. Sections, in which it is necessary to supply some Rules which are there wanting, to be able to make this use thereof. For in the I. Section it is supposed that the years are composed of entire lunar months, and that the number of the months which remain, is known besides: And in the II. Section it is supposed that the entire months have been found by the I. Section, and that the number of the days which remain, is known besides: yet a number of solar years, which is not but very rarely composed of entire lunar months, must have not only the number of the months, but also the number of the days determin'd. Indeed, we find that these Rules do tacitly suppose a solar year composed of months, days, hours and minutes, which regulate the lunisolar years.
The way of finding it by these Rules, is to resolve a year into solar and lunar months, by the 3d, 5th, 6th and 7th Rules of the I. Section, and not to neglect the [Page 210] fraction which remains after the division made by the 6th Article of the same Section; but to reduce it into days, hours, minutes and seconds, or into the decimal parts of a month, going to a thousand millions, to prepare it for the operations which must be performed according to the 1st, 2d, 3d, 4th, 6th and 8th rules of the II. Section, as well for this fraction, as for the whole months; and in fine, to reduce after the same manner the fraction called Anamaan in the II. Section.
After a plainer manner may likewise be found the greatness of this year, by making use of the Hypotheses, which we have infolded in these two Sections, to find a period of years, which should be composed of a number of intire lunar months, and likewise of a number of intire days.
By supposing, according to our explication of the Hypotheses of the II. Section, that a lunar month is equal to 30 artificial days, and that 703 artificial days are equal to 692 natural days, it will be found that in 703 lunar months there are 20760 [...] natural days; and adding thereunto the Hypothesis of the I. Section, according to which the number of 228 solar months which do make 19 years) are equal to 235 lunar months, it will be found that in 13357 solar years there are 165205 entire lunar months, which do make 4878600 natural days, from whence it results that a lunar month, according to these Hypotheses, consists of 29 days, 12 hours, 44′, 2″, 23‴, 23″″, and the solar year of 365 days, 5 hours, 55′, 13″, 46‴, 5″″.
This Indian year conceal'd in the tacit Hypotheses of these two Sections, agrees within two seconds with the tropical year of Hipparchus and Ptolomy, which consists of 365 days, 5 hours, 55′, 12″; and to near 13 seconds with that of Rabbi Adda an Author of the third Age, which consists of 365 days, 5 hours, 55′, 26″. If it could be verified that these years and these months, had been determined by the Indians on the Observations of the Sun, independently from the Western Astronomy, this agreemet of several Astronomers, of different Nations, so remote one from the other, would serve to prove that the Tropical year has anciently been of this bigness, though at present it is found lesser by 6 minutes, which in 10 years do make an hour, and in 240 years a whole day. But it is probable that this greatness of the year has been determined only by the Observations of the Eclipses and other Moons, and by the Hypothesis that Nineteen solar years are equal to Two hundred thirty five lunar months; which Hypothesis so nearly approaches the truth, that it was difficult to observe the difference thereof, but in the succession of Ages; which prevented Hipparacus and Ptolomy from departing therefrom in the determination of the greatness of the solar year.
VIII. The Antiquity of these two sorts of Indian years.
WE have not a more precise knowledge of the Indian years, than that which we have drawn from these Rules. Scaliger who has carefully collected all the Memoirs that he could gather from the ancient Authors, from the Patriarch of Antioch, from the Missionaries, and different Travellers, and who has inserted them, not only in his work de Emendatione temporum, but also in his Commentaries upon Manilius, and in his Isagoge Chronologica, judging that these Memoirs might please all those that have any curiosity for Learning, establishes nothing thereon which satisfies Patavius; and it is certain, that Scaliger's Indian year refers neither to the one nor the other of those which we have now found.
But in the Cardinal de Cusa's Treatise of the Calendar, there are some vestigia of these two sorts of Indian years. That which we have drawn from the IV. Section, is there found almost in formal terms; that which we have drawn from the Comparison of the I. and II. Section is found there also, but after a manner so obscure, that the Author himself who relates it has not comprehended it.
This Cardinal says, that according to Abraham Aven Ezra, an Astronomer of the Twelfth Age, the Indians do add (to the year of 365 days) the fourth [Page 211] part of a day, and the fifth part of an hour, when they speak of the year in which the Sun returns to the same Star. This year consists then of 365 days, 6 hours, and 12′; and it agrees to near 36 seconds with the year that we found by the Hypothesis of the IV. Section. This Author adds, that they who speak of the year according to which the Indians do regulate their Feasts, do alledge that from the fourth part there results a day more in 320 years. Ex quarta plus 320 annis diem exurgere: which he explains after a manner which cannot subsist. This year, saith he, is greater than our common year, by one fourth, 23 seconds, and 30 thirds, which in 353 years do make a day. The means of drawing a reasonable sense from this explication is not evident. For a day divided in three hundred fifty three years gives to each year 4 minutes, 4″, 45‴; and not 23″, 30‴. The true sense of these words, Ex quarta plus 320 annis diem exurgere, is in my opinion, that 320 years of 365 days and a quarter, do by one whole day surpass 320 of these Indian years. One day divided in 320 years, gives to each 4 minutes, 30 seconds; which being deducted from 365 and a quarter, do leave 365 days, 5 hours, 55 minutes, and 30 seconds; which will be the greatness of the year, which regulates the Indian Feasts. This year exceeds not but by 16 seconds, the greatness of the year, which we have found by the comparison of the Hypotheses of the I. and II. Section of the Indian Rules: wherefore there is no reason to doubt but it is this which is here treated of.
IX. The Epocha of the Synodical solar years of the Indians
THis sort of solar years, drawn from the rules of the two first Sections, may be called Synodical, because that it results from the Equality which is supposed to be between 19 of these solar years, and 235 lunar months, which terminate at the Conjunction of the Moon with the Sun. For the Epocha of these years may be taken the day and hour of the middle Conjunction of the Moon with the Sun. which happen'd the very day of the Astronomical Epocha, to near a day of the middle Equinox of the Spring; tho some may infer from the 5th, 6th, and 8th Articles of the II. Section, that for the Epocha of these years they take the minute which immediately follows this middle Conjunction, at the Meridian to which the rules of this Section were accommodated. Thus in particular calculations, there will be no more need of the Operation prescribed in the 5th Article of the II. Section, which is founded on the difference which was between the instant of this middle Conjunction and the midnight following, at a particular Meridian more occidental than Siam; nor of the Operations prescribed in the 8th Article of the VII. Section, and at the 9th Article of the X. Section, which we have judged to denote the minutes of the motion of the Sun and Moon, between the Meridian of Siam, and the Meridian to which the rules of the II. Section had been accommodated; and it will suffice to have had regard to these three Articles once for all.
The Epocha of these Synodical years will therefore be the 21st of March in the 638th year of Jesus Christ, at 3 a clock, 2 minutes in the morning at the Meridian of Siam.
The greatness of these years, according to the VII. Chapter of these Reflexions, consisting of 365 days, 5 hours, 55′, 13″, 46‴, 5″″, we shall find the beginning of the following years in the Julian years, by the continual addition of 5 hours, 55′, 13″, 46‴, 5″″, deducting a day from the summ of the days which results from this addition in the Bissextile years; thus we shall find the beginnings of these solar Synodical years, the dates of which we have examin'd as we have here calculated them, at the Meridian of Siam with the hours computed after midnight.
In the Julian Years. | ||||
Days | H. | M. | ||
1683 | March 17 | 21 | 57 | |
Biss. | 1684 | March 17 | 3 | 52 |
1685 | March 17 | 9 | 47 | |
1686 | March 17 | 15 | 42 | |
1687 | March 17 | 21 | 38 | |
Biss. | 1688 | March 17 | 3 | 33 |
Astronomical years compleat. | In the Gregorian years. | ||
Days. | H. | M. | |
1045 | March 27 | 21 | 57 |
1046 | March 27 | 3 | 52 |
1047 | March 27 | 9 | 47 |
1048 | March 27 | 15 | 42 |
1049 | March 27 | 21 | 38 |
1050 | March 27 | 3 | 33 |
These beginnings of years happen a day and a half before the middle Equinoxes of the Spring, according to Ptolomy; and five days and a half before the same Equinoxes, according to the moderns: wherefore they may be taken for a kind of middle Equinoxes of the Indians. The first new Moon after the beginnings of these solar Synodical years, must be the fifth of the Civil year when the Intercalation precedes these beginnings, as it happen'd in the year 1685 and 1688; and it must be the sixth of the Civil year in the other years.
These are the first new Moons since the Equinoxes of this sort, calculated for the preceding years.
Astronomical years compleat. | Gregorian years current. | |
1045 | 1683 | |
1046 | Biss. | 1684 |
1047 | 1685 | |
1048 | 1686 | |
1049 | 1687 | |
1050 | Biss. | 1688 |
Solar Astronomical years current. | The first Conjunctions of the Astronomical years current. | |||
Afternoon. | ||||
Days. | H. | M. | ||
1046 | April 25 | 22 | 41 | |
1047 | April 14 | 7 | 30 | |
1048 | April 3 | 16 | 18 | |
1049 | April 22 | 14 | 50 | |
1050 | April 11 | 22 | 38 | |
1051 | March 31 | 7 | 27 |
Of the Indian Period of the 19 years.
TO know the first Conjunctions of the solar synodical Indian years in our Calendar, it is sufficient to calculate the beginnings of the year from 19 to 19 years after the Èpocha.
[Page 213]For every nineteenth solar synodical year from the Epocha ends with the middle Conjunction of the Moon with the Sun, from whence begins the twentieth year. The greatness of this period is found by resolving 19 years into lunar months by the 3d, 5th, 6th and 7th Articles of the I Section, and by resolving the lunar months into days by the 2d, 4th, 6th and 8th Articles of the II Section; and in fine, by reducing the fraction of the days called Anamaan, into hours, minutes, seconds and thirds: and by this means it will be found that the Indian period of 19 years, consists of 6939 days, 16 hours, 29 minutes, 21 seconds, 35 thirds.
Tho this Indian Period of 19 years agrees in the number of the lunar months, which it comprehends, with the periods of Numa, Meton, and Calippus, and with our Cycle of the Golden number, as we have remarked in the Explication of the I. Section; yet it is different in the number of the hours.
That of Meto which contains 6940 days is longer by 7 hours, 30 minutes, 38 seconds, 25 thirds, than the Indian. That of Calippus and of our golden number which contain 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 7/22 [...] of a lunar month is equal to a solar month.
The Indian Epact of the first month, is therefore 7/22 [...] 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 252/22 [...] 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. | 24/22 [...] |
Thus the Epact of six years, is | [...]8/22 [...] |
The Epact of 18 years, is | 1 [...]4/22 [...] |
And adding thereunto the Epact of a year, which is | [...]4/22 [...] |
The Epact of 19 years would be | 22 [...]/228 |
which do make a lunar month▪
[Page 214]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 end that the term might be as a medium between the several beginnings of the years, some of which commence sooner, [Page 215] 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 [Page 216] 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 number of lunar months, according to the modern Astronomers, by 1 day and 14 hours, which is almost the Epact of 11 years: and by the method of the XIII. Chapter, it will be found that the Anticipation of the Aequinoxes in regard of this number of synodical years of the Indians is 54 days and 5 hours. If they retrench 11 years from this period, there will be one of 13346 years, composed [Page 217] of 165069 lunar months, or of 4874564 days, which will be more conformaable to the modern Hypothesis.
XV. The great lunisolar Equinoxial period, conformable to the preceding corrections.
BUt instead of correcting the great period foregoing, it is more proper to find out a much shorter, which brings back the new Moons and the Equinoxes to the same hour under the same Meridian, thereby to establish some Astronomical Epocha's more near, and to abridge the Calculations which are so much the longer, as the Epocha's are more distant from our time.
It is extreamly difficult, or rather it is impossible to find some short and precise periods, which conjunctly reduce the new Moons and the Equinoxes to the same Meridian. Vieta proposes one for the Gregorian Calendar of 165580000 years, which comprehends 2047939047 lunar months.
It is not possible to verifie the exactness of these periods by the comparison of the Observations that we have, the ancientest of which are only of 25 Ages; and these long periods serve not our design, which is to bring the Epocha's nearer.
It is better to make use of the shortest, tho less exact periods, and to denote how they want of being exact according to the Hypotheses which we follow.
By the rules of the first Section, and by our additions, it is found that 1040 synodical Indian years do make 12863 lunar months, and 157851/1000000; and by the rules of the II. Section it is found that this number of 12863 months without the fraction makes 379851 days, 21 hours, 24 minutes, 19 seconds.
According to the correction made by the method of the XII. Chapter of these Reflexions, to this number of days it is necessary to add 2 hours and 49 minutes, to render it conformable to the Hypotheses of the Modern Astronomers: thus in this number of 12863 months, there are 379852 whole days, and 13 minutes, 19 seconds of an hour.
The same number of months, with the fraction according to the Rules of the II. Section, and according to our additions, makes 379856 days, 13 hours, 16 minutes, 43 seconds; which do make 1040 synodical Indian years.
The difference by which these years exceed the Tropical years, by our method of the XIII Chapter of these Reflexions, is found of 4 days, 13 hours, 28 minutes, 25 seconds; and this difference being deducted from 379856 days, 13h, 16′, 43″, there remains 379851 days, 23 hours, 48 minutes, 28 seconds, for 1040 Tropical years, and to make 379852 whole days, there wants only 11 minutes and 32 seconds, during which the proper motion of the Sun is not sensible.
XVI. A Modern Epocha of the New Moons, extracted from the Indian Epocha.
HAving added 1040 years to the Indian Epocha of the 638th year of Jesus Christ, there will be the year 1678 for a new Epocha, in which the Conjunction of the Moon with the Sun will happen the day of the middle Equinox, 13 minutes of an hour later in respect of the same Meridian, and 25 minutes later in respect of the middle Equinox; so that the Conjunction happening in the year 638 at Siam, at 3 a clock, 2 minutes in the Morning: in the year 1678 it will there happen at 3 a clock, 15 minutes in the Morning.
During this interval the Anticipation of the Equinoxes in the Julian Calendar is 8 days, which being deducted from 21, there remains 13; and thus the middle Equinox, which in the year 638 was on the 21 of March, is found in the year 1678 on the 13 of March of the Julian year, which is the 23 of the Gregorian year. The middle Conjunction will therefore happen in the year 1678, [Page 218] on the 23 of March at 3 a clock, 15 minutes in the morning at the Meridian of Siam; that is to say, the 22 of March at 8 a clock, 41 minutes of the Evening at the Meridian of Paris.
XVII. Modern Epocha's of the Apogaeum, and Node of the Moon.
BEcause that in this Epocha the new Moons, the Apogaeum, and Node of the Moon were too remote from the Equinox, we have found an Equinoxial Epocha of the Apogaeum, which precedes by 12 years that of the new Moon; and an Epocha of the Nodes, which follows it 12 years.
At the middle Equinox of the Spring, in the year 1666, the Apogaeum of the Moon was at the Twentieth degree of Aries; and at the end of the present Julian year 1689, the North Node of the Moon will be at the beginning of Aries; but at the middle Equinox of the Spring 1690, it will be in the 26 degree and half of Pisces, at 3 degrees and half of the Sun.
The Apogaeum of the Moon performs a revolution according to the succession of the Signs in 2232 days, according to the Indian Rules; or in 2231 days and a third, according to the modern Astronomers. The Nodes of the Moon, of which there is no mention in the Indian Rules, do perform a revolution contrary to the succession of the Signs in 6798 days ⅕.
By these Principles there will be found as many Epocha's of the Apogaeum and Nodes, as shall be desired.
XVIII. An Epocha of the new Moons near the Apogaeum, and the Nodes of the Moon, and the middle Equinox of the Spring.
IT is not found that the Equinoxial new Moon should happen nearer our time, and altogether nearer its Apogaeum and one of its Nodes, than the 17 of March in the year of J. Christ, 1029. This day at noon, at the Meridian of Paris, the middle place of the Sun was in the middle of the first degree of Aries, at 3 degrees and half from the middle place of the Moon, which joyned with the Sun the Evening of the same day.
The Apogaeum of the Moon preceded the Sun a degree and half; and the descending Node of the Moon preceded it a degree, the Apogaeum of the Sun being in the 26th degree of Gemini.
'Twould be needless to seek out another return of the Moon to its Apogaeum, to its Node, to the Sun, and to the Vernal Equinox. The concourse of all these circumstances together being too rare, it is necessary to rest satisfied with having some Epocha's separated at diverse other times, of which here are three the most exact.
The middle conjunction of the Moon with the Sun in the middle Equinox of the Spring, happened in the year of J. Christ 1192 on the 15 of March about Noon at the Meridian of Rome.
The Apogaeum of the Moon was at the beginning of Aries, in the middle Equinox of the Spring, Anno 1460, on the 13 of March.
The descending Node of the Moon was at the beginning of Aries, in the middle Equinox of the Spring, Anno 1513, on the 14 of March.
'Twill not be needless to have some particular Epocha's of the new Moons proper for the Julian Calendar, to which most of the Chronologers do refer all the times past.
Julius Caesar chose an Epocha of Julian years, in which the new Moon happened the first day of the year. 'Twas the 45th year before the birth of Jesus Christ, which is in the rank of the Bissextiles, according as this rank was afterwards established by Augustus, and as it is still observed.
[Page 219]The first day of January of the same forty fifth year before Jesus Christ, the middle conjunction of the Moon with the Sun happened at Six a clock in the Evening, at the Meridian of Rome.
And the first of January in the 32d year of Jesus Christ, the middle conjunction happened precisely at Noon at the Meridian of Rome.
The most commodious of the Epocha's, near the middle conjunctions in the Julian years, is, that which happened the first of January, Anno 1500, an hour and half before Noon at the Meridian of Paris.
XIX. An Ancient Astronomical Epocha of the Indians.
IN the III. Chapter of these Reflexions we have remarked, that the Siameses in their dates make use of an Epocha, which precedes the year of Jesus Christ by 544 years, and that after the twelfth or thirteenth month of the years from this Epocha, which do now end in November or December, the first month which follows, and which must be attributed to the following year, is yet attributed to the same year: which has given us ground to conjecture, that they attribute also to the same year, the other months to the beginning of the Astronomical year, which begins at the Vernal Equinox. This conjecture has been confirmed by the report of Mr. de la Loubere, who likewise judges that this Ancient Epocha must also be an Astronomical Epocha.
The extraordinary manner of computing the first and second month of the same year after the twelfth or thirteenth, may cause a belief that the first month of these years, which begins at present in November or December, began anciently near the Vernal Equinox, and that in process of time, the Indians, either thro negligence, or to make use of a Cycle too short, as would be that of 60 years which the Chineses do use, have sometimes failed to add a thirteenth month to the year which ought to be Embolismick, whence it has happen'd that the first month has run back into the winter; which having been perceived, the winter months, now called first, second and third, have been attributed to the preceding year, which according to the ancient institution ought not to end but at Spring.
Thus the Indian year, which was called 2231, at the end of the year 1687 of Jesus Christ, ought not to end, according to the Ancient Institution, till the Spring of the year 1688. Having substracted 1688 from 2231, there remains 543, which is the number of the compleat years from the ancient Epocha of the Indians, to the year of Jesus Christ. This Epocha appertains therefore to the current year 544 before Jesus Christ, according to the most common way of computing.
In this year the middle conjunction of the Moon happened between the true Equinox, and the middle Equinox of the Spring, at 15 degrees distance from the North Node of the Moon, the 27th of March, according to the Julian form, a Saturday, which is an Astronomical Epocha almost like to that of the year 638, which has been chosen, as more modern and more precise than the former.
Between these two Indian Epocha's there is a period of 1181 years, which being joyned to a period of 19 years, there are two periods of 600 years, which reduce the new Moons near the Equinoxes.
XX. The Relation of the Synodical years of the Indians, to those of the Cycle of the Chineses of 60 Years.
ACcording to the Chronology of China which Father Couplet published, and according to Father Martinius in his History of China, the Chineses do make use of lunisolar years, and they destribute them into sexagenary Cycles, the 74th of which began in the year of J. Christ 1683; so that the first Cycle should have begun 2697 years before the birth of Jesus Christ.
[Page 220]By the Indian Rules of the first Section, in 60 synodical years, there are 720 solar months, and 742 lunar months, and 24/228 It is necessary to reject this fraction, because that the lunisolar years are composed of entire lunar months. Yet this fraction in 19 sexagenary Cycles, which do make 1140 years, amounts to 456/22 [...] which do make two months: therefore if the sexagenary Cycles of the Chineses are all uniform, 1140 Chinese years are shorter by two months, than 1140 synodical years of the Indians. Wherefore if the Indians have regulated the Intercalations of their civil years by uniform sexagenary Cycles, the beginning of the civil year 2232, ought to precede by a little less than four months, the term of their synodical years, which is at present on the 27 of March of the Gregorian year; as it happened indeed; which confirms what we have conjectured in the foregoing Chapter of the anticipation of the civil years.
To equal the years of the sexagenary Cycle to the synodical years regulated according to the Cycle of 19 years, it would be necessary that among 19 sexagenary Cycles there were 17 of 742 lunar months, and 2 of 743; or rather it would be necessary that after 9 Cycles of 742 months, which do make 740 years, the tenth Cycle following, which would be accomplish'd in the year 600, was of 743 months.
But there is ground to doubt whether they use it thus, seeing that the Chinese year has several times had occasion of being reformed, to refer its beginning to the same term; in which nevertheless the modern Relations accord only to 10 degrees: Father Martinius denoting it at the 15th degree of Aquarius, and Father Couplet at the 5th of the same Sign; as if the Term had retreated 10 degrees since the time of Father Martinius.
It is unquestionable that a great part of the Eclipses, and of the other Conjunctions which the Chineses do give as observed, cannot have happened at the times that they pretend, according to the Calendar regulated after the manner as it is at present, as we have found by the Calculation of a great number of these Eclipses, and even by the sole examination of the Intervals which are remarked between the one and the other: for several of these Intervals are too long, or too short, to be possibly determined by the Eclipses, which do happen only when the Sun is near one of the Nodes of the Moon; where it could not possibly return at the times denoted, if the Chinese years had been regulated in the past ages, as they are at present. Father Couplet himself doubts of some of these Eclipses, by reason of the Compliment which the Chinese Astronomers made to one of their Kings, whom 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 [Page 221] 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 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.
[Page 223]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:
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. 'Tis 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 [Page 224] 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 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. 'Tis 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. 'Twas 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 2h, 20′; a tenth is 0h, 42′; a third of 7 minutes is 2′: the summ added to 7 days 8 hours, makes 7 days, 11h, 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 8h, 56′: adding thereunto half a lunar month, which is 14 days, 18h, 22′, the middle opposition will be found on the 29th of March, at 3h, 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, 2h, 12′, for the first, double for the second, triple for the third (borrowing a month of 29 days, 12h, 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 [Page 226] 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.
'Tis 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.
'Twere 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.
[Page 227]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, 12h, 44′, 3″, 5‴, 28″″, 48‴″, 20‴‴; and the Alphonsine Tables do suppose it 29 days, 12h, 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, 12h, 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 LOƲIS 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 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.
[Page 228]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. 'Tis 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 [Page 229] 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 of the Transverse immediately inferior.
3. When the way is interrupted, they re-assume two cases underneath that which they filled; and if there remains no case underneath, or that there remains but one, the first case of the upright is thought to return in order after the last, as if it was indeed underneath the lowest.
11 | 24 | 7. | 20 | 3 |
4 | 12 | 25 | 8 | 16 |
17 | 5 | 13 | 21 | 9 |
10 | 18 | 1 | 14 | 22 |
23 | 6 | 19 | 2 | 15 |
[Page 230]As Bachet has not given the demonstration of his method, I have search'd it out, not doubting but it would give me also that of the Indian method: But to make my demonstration understood, it is necessary that I give the method of Bachet.
1. The square being divided by cases, to be filled with numbers in the Magical order, he augments it before all things by the square sides in this manner. To the upper part of the first transverse, he adds another transverse, but contracted by two cases, viz. one at each end. Over this first transverse contracted he adds a second contracted by two new cases. To the second he adds a third more contracted than he former, to the third a fourth, and so on, if it is necessary, until that the last transverse have but one case. Underneath the last transverse he adds likewise as many transverses more contracted one than the other: And in sine, to the first upright no the left, to the last upright on the right, he adds also as many uprights thus contracted.
EXAMPLES.
a | b | a | ||
b | b | |||
a | b | a |
b | ||||||||
a | b | b | b | a | ||||
b | b | |||||||
b | b | b | b | |||||
b | b | |||||||
a | b | b | b | a | ||||
b |
aa are the squares of 9 and 25 cases, bb are the cases of Augmentation.
The square being thus augmented, Bachet there places the numbers according to the natural order, as well of the numbers as the cases, in the following manner.
1 | ||||
4 | 2 | |||
7 | 5 | 3 | ||
8 | 6 | |||
9 |
1 | ||||||||
6 | 2 | |||||||
11 | 7 | 3 | ||||||
16 | 12 | 8 | 4 | |||||
21 | 17 | 13 | 9 | 5 | ||||
22 | 18 | 14 | 10 | |||||
23 | 19 | 15 | ||||||
24 | 20 | |||||||
25 |
In this disposition it is evident that the cases of the true square are alternately full, and alternately empty, and that its two Diameters are entirely full. Now the full cases receive not any change in the sequel of the operation, and the Diameters remain always such as they are by position in the square augmented: but [Page 231] for the cases of the true square, which are likewise void, they must be filled with the numbers which are in the cases of Augmentation, by transporting the high ones lower, and the low ones higher, each into its upright; those of the right to the left, and those of the left to the right, each into its transverse, and all to as many cases, as there are in the side of the real square. Thus in the square of 9 cases, which has only three in its side, the unite, which is in the case of Augmentation at the top, is removed to the third case below in the same upright; 9, which is in the case of Augmentation below, is removed to the third case above in the same upright; 3, which is in the case of Augmentation on the right, is remov'd toward the left, to the third case in the same transverse; and in fine, 7, which is in the case of Augmentation on the left, is removed towards the right, to the third case in the same transverse.
After the same manner, in the square of 25 cases, which has 5 in its side, the numbers, which are in the cases of Augmentation above, do descend 5 cases below each in its upright. Those of the cases of Augmentation below do ascend five cases above each in its upright. Those of the cases of Augmentation on the right do pass 5 cases to the left, each in its transverse: and those of the cases of Augmentation on the left do pass 5 cases to the right, each also in its transverse. It ought to be the same in all the other squares proportionably, and thereby they will become all Magical.
Definitions.
1. IN the augmented square of Bachet, the ranks of Augmentation shall be called Complements of the ranks of the true square, into which the numbers of the ranks of Augmentation must be removed: and the ranks which must receive the Complements, shall be called defective ranks. Now as by Bachet's method every number of the cases of Augmentation must be removed to as many cases as there are in the side of the true square, it follows that every defective rank is as far distant from its Complements, as there are cases in the side of the true square.
2. Because that the true square, that is to say, that which it is necessary to fill with numbers according to the Magical Order, is always comprehended in the square augmented, I will consider it in the square augmented, and I will call its ranks and its diameters, the ranks and diameters of the true square: but its ranks, whether transverse or upright, shall comprehend the cases, which they have at both ends; because that the numbers which are in the cases of Augmentation, proceed neither from their transverse nor from their upright, when removed into the cases of the true square, according to Bachet's method.
3. The diameters of the square augmented are the middle upright. and middle transverse of the true square, and they are the sole ranks which are not defective, and which receive no complement. They neither acquire, nor lose any number in Bachet's operation: they suffer only the removal of their numbers from some of their cases into others.
4. As the augmented square has ranks of another construction than are the ranks of the true square, I will call them Bands and Bars. The Bands descend from the left to the right, as that wherein are the numbers 1, 2, 3, 4, 5, in the preceding example, the Bars descend from the right to the left, as that, wherein are the numbers 1, 6, 11, 16, 21, in the same example.
Preparation to the Demonstration.
THE Problems of the Magical squares consists in two things.
The first is that every transverse and very upright make the same sum, and the second that every diameter make likewise that same sum. I shall not speak at present of this last condition, no more than if I sought it not. And because that to arrive at the first, it is not necessary that all the numbers, which ought to fill a Magical square, be in Arithmetical proportion continued, but [Page 232] that it suffices that the numbers of a Band be Arithmetically proportional to those of every other Band, I will denote the first numbers of every Band by the letters of the Latin Alphabet, and the differences between the numbers of the same Band by the letters of the Greek Alphabet: and to the end that the numbers of a Band be Arithmetically proportional to the numbers of every other Band, I will set down
a | ||||||||
b | ωτa | |||||||
c | ωτb | ψχa | ||||||
d | ωτc | ψχb | χτa | |||||
e | ωτd | ψχc | χτb | φχa | ||||
ωτe | ψχd | χτc | φχb | |||||
ψχe | χτd | φχc | ||||||
χτe | φχd | |||||||
φχe |
the differences of the numbers of each band by the same Greek Letters.
1. Nothing hinders why the Sign—, may not be placed instead of the Sign †, either before all the differences, or before some, provided that the same Sign be before the same difference in each band: for so the Arithmetical proportion will not be altered.
2. The greater a square shall be, the more Latin and Greek Letters it will have; but every band will never have but one Latin Letter, and all the Greek Letters; and the Latin Letter shall be different in each band. Every bar on the contrary shall have all the Latin Letters, and all except the first shall have a Greek Letter, which shall be different in every bar.
Demonstration.
FRom hence it follows. 1. That the diameters of the augmented square have each all the Latin and all the Greek Letters, because that they have each a case of every band, and a case of every bar, and that the cases of every band do give them all the Latin Letters, and the cases of each bar all the Greek. The sum then of these two diameters is the same, viz. that of all the Letters, as well Greek as Latin, taken at once. Now these two diameters do make an upright and a transverse in the Magical square, because that in the operation of Bachet, their sum changes not by the loss or acquisition of any number, as I have already remarked.
2. As the ranks of the true square, whether transverse or upright, are as distant from their complements, as there are cases in the side of the true square, it follows that the bands, and the bars, which begin with a complement, or above this complement, touch not, that is to say, have no case at the defective rank of this complement; and that the bands and the bars which begin with a defective rank or above, have no case in its complement: the Letters then of the defective rank, are all different from those of the complements; because that different bands have different Latin Letters, and that different bars have different Greek Letters. But because that all the bands, and all the bars, have each a case in all the defective ranks, or in their complements: then every defective rank whatever, will have all the Letters, when it shall have received its complement; it will have all the Latin, because that all the bands, passing through every defective rank, or through its complement, do there leave all the Latin [Page 233] Letters; and it will have all the Greek, because that all the bars, passing also through every defective rank, or through its complement, do there leave all the Greek Letters. And thus all the defective ranks will make the same sum in the Magical square, and the same sum as the diameters of the square augmented, which are the two sole ranks not defective of the true square.
That this Method cannot agree to even Squares.
THE Demonstration which I have given, agrees to the equal squares, as well as to the unequal, in this that in the augmented equal square, every defective rank and its complement do make the sum, which a range of the Magical square ought to make: But there is this inconvenience to the equal squares, that the numbers of the cases of Augmentation, do find the cases of the true square filled with other numbers, which they ought to fill; because that every case is full, which goes in an equal rank after a full case, and that in the equal squares, the cases of the defective ranks do come in an equal rank, after those of the complements, the defective ranks being as remote from the complements, as the side of the square has cases, and the side of every equal square having its cases in equal number.
Of the Diameters of the unequal Magical Squares.
BY Bachet's operation it is clear, that he understands that the diameters are such as they ought to be, by the sole position of the numbers in the augmented square: and this will be always true, provided only that it is supposed, that the number of the case of the middle of each band, be a mean Arithmetic proportion between the other numbers of the same band, taken two by two: a condition, which is naturally included in the ordinary Problem of the Magical squares, wherein it is demanded that all the numbers be in Arithmetical proportion continued. Alternando the mean number of each bar, will be also a mean Arithmetic proportional between all the numbers of the same bar taken two by two: and hereby every mean, taken as many times as there are cases in the band, or in the bar, which is all one, will be equal to the total sum of the band, or of the bar. Therefore all the means of the bands, taken as many times as there are cases in every band, or which is all one, in the side of the square, will be equal to the total sum of the square: then taken once only, they will be equal to the sum of one of the ranks of the Magical square; and it will be the same of the means of the bars: and because that the means of the bands do make one diameter, and the means of the bars the other, it is proved that the diameters will be exact by the sole position of the numbers in the augmented square, provided that every mean of a band, be a mean Arithmetic proportional between all the numbers of its band, taken two by two.
In a word, as in the squares there are no augmented pairs, nor true square, nor diameters of the true square, because that the bands of the equal squares have not a mean number, 'tis likewise a reason, which evinces that this method, cannot be accommodated to the equal squares.
Methods of varying the Magical Squares by Bachet's Square augmented.
1. BY varying the order of the numbers in the bands, or in the bars, provided that the order which shall be taken, be the same in all the bands, or the same in all the bars, to the end that in this order the numbers of a band or of a bar, be Arithmetically proportioned to those of every other band or bar: but it is necessary that not any of the diameters loses any of its numbers.
[Page 234]2. Or rather (which will amount to the same) by varying the order of the bars amongst them in the augmented square: for this troubles not the Arithmetical proportion, which is the ground of the preceding demonstration: but it is necessary to remember to leave always in their place the band and the bar, which do make the two diameters.
3. By not putting the first number of each band, in the first case of each band: As for example
d | ||||||||
e | a | |||||||
b | c | a | ||||||
a | d | b | c | |||||
c | e | a | d | b | ||||
b | c | e | a | |||||
d | b | c | ||||||
a | d | |||||||
e |
d, a, e, c, b, are the five letters of the first band, the order of which is arbitrary, and the letter d, which is in the first case of this first band, is not found in the first case of any other band: but in the fourth case of the second band, in the second of the third, in the fifth of the fourth, and in the third of the fifth. Besides the succession or order of the Letters must be the same in every band. But because that in the bands where the Letter d is in a case lower than the first, there remains not case enough underneath, to put all the other Letters successively, the first cases of the bands do return in order after the last, and are in this case thought the last cases of their bands. A circumstance which it is necessary carefully to observe.
If then in an augmented square the numbers are disposed in each band, as in the bands of this square I have disposed the Letters a, b, c, d, e, and which one continues to operate like Bachet, that is to say, to remove as he does, the numbers of the cases of Augmentation into the void cases of the real square, the true square will be Magical, at least as to the ranks, whether transverse or upright, for I speak not as yet of the Diameters.
I shall call those capital cases, wherein are found the Letters like to the Letter which is put in the first case of the first band, which I will call the first capital case.
Preparation to the Demonstration.
1. IT is necessary to observe in disposing these Letters, that after having chosen the capital case of the second band, near a Letter of the first band, which I will call the Letter of Indication, so that this second capital case be also the second case of the bar which begins with this Letter of Indication, one may chuse the capital case of the third band, near the Letter of the second band, like to the first Letter of Indication, so that this third capital case be the third of the bar, wherein shall be the second Letter of Indication. After the same manner shall be determin'd the capital case of every band, near the Letter of Indication of the precedent band. From whence it follows, that there are as many capital cases as bands, and no more.
It follows also, that not only the Letter d is always under the Letter c in the same bar, but that all the other Letters are always under the same Letters in the same bars, and that the Letters have likewise the same order in all the bars, as they have the same in all the bands, though the orders of the Letters in the bars, is not the same as the order of the Letters in the bands.
[Page 235]1. The choice of the capital case of the second band, which determines that of the rest, is not entirely arbitrary. To regulate it 'tis necessary to have regard to the number of the ranks of the true square, which is the number 5 in the preceding example, and which is always the square root of the number, which expresses the multitude of the cases of the true square, and so I will call it the root of the square.
Take then a number at your own choice, provided nevertheless that it be less than the root of the square, and first to this very root, and that by adding two points, it be still first at the same root of the square: 'Twill be by this number, that we shall determine the choice of the second capital case: and we call it the number determining.
The second capital case must not be the second case of the second band, because that this second case is found in the upright diameter of the augmented square, and that there must not be two Letters alike in any of the diameters of the augmented square: and so as the first capital case is already in the upright diameter, the second cannot be there. It is necessary on the contrary, that the case which you shall chuse in the second band, for the second capital, be as far distant from the second case of the upright diameter, as your determining number shall have Unites, and at the same time your second capital shall be removed from the first capital case as many transverses, as your determining number † 2 shall have Unites. Thus in the preceding example, the second capital case, viz. the case of the second band, where is the Letter d, is the second case after that, which is in the upright diameter, and it is in the fourth transverse underneath the first capital case, which alone is looked upon as a transverse, and the number 2, which determines this second capital case, is first to 5, which is the root of the square, and 2 † 2 that is to say 4, is likewise first to 5, the third case of the second band is therefore the first, which removes from the upright diameter, and it is with this that it is necessary to begin to compute the distance of the rest: so that the first case of this second band is in this sense the remotest of the second case, though to reckon after a contrary sense it touches it.
You may then in the preceding example, where the root of the square is 5, take either 1 or 2, or 4, which do give you three different cases, of which you may make your second capital case, 1 is first to 5, and 1 will give you the case wherein is b, three transverses distant from the first capital case. 2 is first to 5, and 2 † 2 that is to say 4, is also first to 5, and 2 will give you the case wherein is d, 4 transverses distant from the first capital case. 3 is also first to 5, but because that 3 † 2, that is to say 5, is not first to 5, 3 can give you in this example only a false capital case. 4 is first to 5, and 4 † 2 that is to say 6, is also first to 5, but from 6 it is necessary to deduct 5 which is the root, and there will remain 1. And 4 will give you the case wherein is e, the fourth in distance from the case of the diameter rising, and has a transverse near the first capital. The number 4 will give you then Bachet's disposition, who has placed all the capital cases in the first bar: and as often as for a determining number you shall take a less number by an Unite, than the root of the square, you will fall into Bachet's disposition.
3. From hence it follows, that the diameter ascending will not have any other capital case than the first, which it has already, and that so it will not have twice the Letter, which shall be in the capital cases. To prove it let us suppose that our bands be sufficiently extended towards the right, to make as many new uprights as we desire; and let us mark the first upright, which shall be as distant from the diameter ascending, as the root of the square has Unites: that is to say, which shall be the fifth on the right of the diameter ascending, if the root of the square is 5. And at a like distance from this first upright marked, let us mark a second, and then a third, and a fourth, always at an equal distance one from the other, until that there are as many uprights marked, as the determining number has Unites. In this case as the determining number and the root of the square are first amongst them, the last upright marked will be the sole one, whose distance to take it from the diameter ascending, would be divisible by the determining number.
[Page 236]Suppose also, that now the bands are long enough, the capital cases are marked all together, and without ever returning to the first cases of the bands, as it was necessary to do, before that the bands were extended, because that then they had not cases enough after the capital, to receive all the Letters successively. I say that in these suppositions, none of these marked uprights will have a capital cases except the last: because that it is the sole marked upright, whose distance from the diameter ascending unto it, is divisible by the determining number: for as the uprights, wherein are the capital cases, are as remote (viz. the first from the upright, the second from the first, the third from the second, and so successively) as the determining number has Unites, it follows that no upright has a capital case when the distance from the upright diameter unto it, is not divisible by the determining number. 'Tis proved then that no marked upright, except the last, will have a capital case: and the capital case which it shall have will be the first beyond the number of the cases necessary to your augmented square, because that in counting the first capital case, there will be as many others before this, as the root of the square has Unites.
Now when you mark the capital cases in a square augmented, according to the methed which I have given, so that when you arrive at the last case of a band, you return to its first case, as if it was after the last, you do no other thing, than successively to place all the capital cases, in respect of the diameter ascending, as in the case of the extension of the bands, you will place one after the other in regard of all the uprights successively marked. And none of your capital cases, except a first supernumerary, can fall into your ascending diameter, as no other, except a first supernumerary, could fall into your last upright marked.
4. But if you consider the first capital case, as a transverse, and that you make the same suppositions as before, so that there are as many transverses marked, as the determining number † 2 shall have Unites, and as distant (viz. the first from the first capital case, the second from the first, the third from the second, and so successively) as the root of the square shall have Unites: From this that the root of the square and the determining number † 2 are first amongst them, and from this that the determining number † 2 expresses the distance of the transverses, wherein will be the capital cases, you will prove that there shall be only the last transverse marked, which has a capital case, which will be the first supernumerary: and consequently, that the defective rank, the first capital case of which is the complement, will have no capital case, because that it is the first transverse marked: and you will prove also that the first supernumerary capital case must return to the transverse of the first capital case, and as it must return likewise to the upright diameter, it follows that the first supernumerary case, that is to say, that which you would mark after the last of the necessary, is the first capital case, because there is only this which is common to its transverse, and to the upright diameter.
5. From the order of the letters, alike in all the bands and alike also in all the bars, you will prove that all the letters alike, are at the same distance one from the other, and in the same order amongst them, as the letters of the capital cases amongst them, and that so all the cases which contain letters alike may be considered as capital, so that two letters alike, are never found in the same upright, nor in the same transverse, nor in a defective rank, nor in its complement. Which needs no other demonstration.
Demonstration.
THis supposed, the demonstration of the Problem is easie, for whereas no letter is twice in any of the diameters of the augmented square, nor in any defective rank and its complement, it follows that every of the two diameters, and every defective rank and its complement have all the letters, and that consequently they make the same summ.
Of the Diameters.
THe Band which makes one of the diameters being Magical by position, as it ought to be, continues Magical, because that it receives not any new Letter, nor loses any of its own. The bar which makes the other diameter is found Magical by the disposition, and the proof is this.
As far as the bar of the second capital case is removed from the first bar, so much the bar of the third capital case, is removed from the bar of the second, and so successively, the first bars to which you return, being reckon'd in this case as coming after the last. Now the bar of the second capital case is as far distant from the first as there are Unites in the determining number † 1. Therefore if the determining number † 1 is first to the root of the square, the preceding demonstration sufficeth to prove, that not any bar will have two Letters alike, wherefore the bar which shall serve as the diameter, will not have two Letters alike, and so it will have all the Letters once.
But if the determining number †1 is an aliquot part of the root of the square, then each bar will have as many Letters alike, as there shall be Unites in the determining number † 1, and there will be as many different Letters, as there shall be Unites in the other aliquot part of the root of the square, which shall be the quotient of the division made from the root by the determining number † 1. These several Letters will be therefore in an odd number, because that this quotient can be only an odd number, being an aliquot of an odd number Of these Letters in an odd number, the one will be the middle of the first band, the others, taken two by two, will be like to the Letters of the first band, which taken also two by two, will be equally remote from the middle, the one towards the head of the band, the other towards the tail: So that if the order of the Letters of the first band, is as the middle by its situation, or middle proportional between all the others, which, taken two by two, shall be equally remote from it, then the bar which shall serve as diameter will be Magical, because that if it has not the middle Letters of all the bands, it will have the power thereof; for the other Letters, which shall not be mean, if being taken two by two, the one is weaker than the middle of its band, the other will be stronger as much as the middle of its own; and thus the two together will countervail the middle of their bands. As for example, in the square of 81 cases, the root of which is 9, if the determining number is 2, as 2 † 1, that is to say, 3 is the aliquot part of 9, the corresponding aliquot of which, that is to say that, which returns from the division of 9 by 3, is also 3, there will be in each bar three several Letters which will every one be there repeated three times. The first of the different will be the middle of the first band, the two others between the different, will be alike to two of the first band equally distant from the middle. After the same manner in the square of 225 cases, the root of which is 15, if the determining number is likewise 2, as 2 † 1, that is to say, 3 is the aliquot part of 15 (of which 5 is the aliquot corresponding) it will happen that in every bar there will be 5 several Letters repeated every one three times. The one will be the middle of the first band, the 4 others will be alike to 4 of the first band, which taken two by two will be equidistant from the middle.
The Conclusion is then, that when the determining number † 1, is first to the root of the square, the bar which serves as diameter can only be Magical: but that if the determining number † 1, is aliquot of the root of the square, the bar which serves as diameter cannot be Magical; that the middle Letter of the first band, cannot be the middle Arithmetic of all the other Letters of its first band two by two, and that it is not the Letters of its band, which, taken two by two, are at equal distances from it, and the like of which ought to enter into the bar, which shall serve as diameter. After this the order of the Letters of the first band is arbitrary.
In a word, the nearest of these equidistant Letters, shall be each as distant from the middle, as the determining number † 1 shall have Unites, the following [Page 238] shall be as remote from these first, every one from its own, and so successively.
I have said that it is necessary to take the second capital case in the second band, tho it may be taken in such other band as one pleases, provided that the band of the third capital case be as distant from the band of the second case, as this shall be from the first, and that the band of the fourth capital case be at this very distance from the band of the third, and so successively, the first bands returning in order after the last. But besides this, it is necessary that this distance be expressed by a number first to the root of the square, and the thing will return to the same, that is to say, to put a capital case in each band. But if you put the second capital case in a band, whose distance from the first band, was not expressed by a number first to the root of the square, then several capital cases would fall in the first band, which being supposed full of all the different Letters, could not receive the like Letters, which fill the capital cases.
Another way of varying the Magical Squares.
YOU shall double the preceding variations, if you perform in the bars what you did in the bands, and in the bands what you performed in the bars; taking for one of the diameters, a bar which should be Magical by position, and rendring Magical by disposition the band which shall be the other diameter.
From these Principles it follows, that the square of 9 cases is always the same, without being able to receive essential varieties, because that it can have only two for the determining number: and because that the removing of the bands, or of the bars amongst them, makes only a simple subversion, by reason that there are only two bands and two bars subject to transposition, and that the band and the bar which serve as diameters cannot be displaced.
It follows also, that always one of the diameters at least must be Magical by position: and that the greatest and least of the number proposed to fill a Magical square, can never be at the center, because that the center is always filled by one of the numbers of the diameter by position, in which, be it band or bar, the greatest nor smallest number cannot be.
On the contrary, the middle number of the whole square, that is to say, that which by the position is at the center of the augmented square, will remain at the center of the Magical square, as often as the diameter by position shall have the capital case at one of its ends, but in every other case it will go out thence, and yet it will never depart from the diameter by position.
All which things must be understood according to the suppositions above explained. Besides I know that the uneven Magical squares may be varied into a surprizing number of ways, unto which all that I have said would not agree.
In fine, one of the diverse methods, which result from the Principles which I have explained, is Indian, as may be proved, by removing into an augmented square the numbers of an Indian Magical square, in such a manner, that the cases of Augmentation be full of the Numbers, which they must render to the true square. It will be seen how the numbers shall be ranged in the augmented square, in one of the methods which I have explained.
An Illustration of the Indian Method.
AS I had communicated to Mr. de Malezieu, Intendant to the Duke of Mayne, the Indian unequal squares, without saying any thing to him of my Demonstration, which I had not as yet fully cleared, he found out one which has no relation to Bachet's augmented square, and which I will briefly explain, because that the things which I have spoken, will help to make me understood.
[Page 239]Let there be a square which we will call natural, in which the numbers should be placed in their natural order in this manner.
1 | 2 | 3 | 4 | 5 |
6 | 7 | 8 | 9 | 10 |
11 | 12 | 13 | 14 | 15 |
16 | 17 | 18 | 19 | 20 |
21 | 22 | 23 | 24 | 25 |
The business is to dispose these numbers magically into another square of as many cases and empty.
1. In considering this square, I see that the two diameters, and the middle upright and transverse means do make the same summ: which Mr. de Malezieu thought to have given ground to the Problem, out of a desire of rendering the other transverses and other uprights equal also, without destroying the equality of Diagonals.
2. I see that the first transverse contains all the numbers, from the unite to the root of the square: that the second transverse contains these same numbers and in the same order, but augmented every one with a root: that the third contains also these very numbers in the same order, augmented every one with two roots: that it is the same in every transverse, save that the fourth has every one of these numbers augmented with three roots, that the fifth hath them augmented with four roots, and so in proportion of the other transverses, if there were more.
3. It therefore occurs naturally to my mind to consider another square, where in every transverse I will place the same numbers, which are in the first, that is to say from the unite to the root of the square, without augmenting them with any root in any transverse; and I find presently that the transverses will be equal in their summs, having each the same numbers; and that the uprights of this new square, will have the same surplusage one over the other, as the uprights of the natural square, because that the difference of the uprights in the natural square, proceeds not from the roots affixt to the numbers, but from these numbers which are repeated in every transverse, as it is seen in this example, where the strokes annext to the numbers, do denote the roots wherewith each number is augmented in the natural square.
1 | 2 | 3 | 4 | 5 |
1′ | 2′ | 3′ | 4′ | 5′ |
1″ | 2″ | 3″ | 4″ | 5″ |
1‴ | 2‴ | 3‴ | 4‴ | 5‴ |
1″″ | 2″″ | 3″″ | 4″″ | 5″″ |
4. It is evident that in this square all the transverses are equal, in that they have every one the same numbers, and that the uprights are only unequal because that they have not every one all those different numbers which are in every [Page 240] transverse, but on the contrary one alone of these numbers repeated as many times as there are squares in every upright. Therefore I shall render the uprights equal to one another, if I make that not one of these numbers be twice in every upright, but that all be there once. And because that these very numbers do bear every one the same number of roots in the same transverse, I shall also render the transverses equal, if I make that every transverse have not all these several numbers of it self, but that it borrows one of every transverse. Thus the diameters are already equal, because that they have every one the several numbers that it is necessary to have, and that they take one from every transverse, that is to say, one without the root, the other augmented with a root, the other with 2, the other with 3, and so successively.
The true secret then is to dispose all the numbers of every transverse in a diametrical way, that is to say slanting, so that having placed one number, the following will be in another transverse and another upright at the same time. Which cannot be better performed than after the Indian manner.
1 | ||||
5 | ||||
4 | ||||
3 | ||||
2 |
These are the numbers of the first transverse placed slanting—, so that there is not two in the same upright nor in the same transverse. I must therefore dispose the numbers of the second transverse after the same manner, and because that I must avoid placing the first number of this transverse, under the first of the other, I cannot do better than to place it under the last in this manner.
1 | 3′ | |||
5 | 2′ | |||
4 | 1′ | |||
5′ | 3 | |||
2 | 4′ |
With the same Oeconomy I dispose the other transverses, placing always the first number of the one under the last of the other; and for one of the diameters I put the middle transverse, because that naturally it is Magical.
2‴ | 4″″ | 1 | 3′ | 5′ |
3″″ | 5 | 2′ | 4″ | 1‴ |
4 | 1′ | 3″ | 5‴ | 2″″ |
5′ | 2″ | 4‴ | 1″″ | 3 |
1″ | 3‴ | 5″″ | 2 | 4′ |
It is clear that in this disposition not any transverse, nor any upright have two numbers, neither from the same transverse, nor from the same upright of the natural square, and that the diameter which we have not made by position, has also only one number from every transverse, and every upright of the natural square. This is what M. de Malezieu thought, without having had the leisure to fathom it further; and it is evidently the Principle, on which the Indian Method and that of Bachet are grounded, and all the others, of which I have shown, that it is possible to vary the Magical squares. And if care be taken that in a Magical square the ranks parallel to the diameters are defective, and that they have their complements, it will be seen that Bachet's augmented square, and the Magical square have opposite proprieties. In the augmented square, the bands which are the true ranks, are not Magical, and its defective ranks augmented with their complements are. On the contrary, in the Magical square the ranks are Magical, and the defective ranks and their complements do contain, every one, what a band of the augmented square contains.
To finish what M. de Malezieu has thought, it is necessary only to accommodate what we have said concerning the choice of the capital cases: and because that this is easie to do, I will speak no more of it.
M. de Malezieu thought likewise, that this principle might serve to the even squares, and this is true: but here likewise there is found difficulty in the execution, because that in the even squares, the defective ranks and their complements have every one a case in the same diameter, or have none at all, so that by dispersing the numbers from a transverse into a defective rank, and its complement, two numbers of this transverse are put into the same diameter, or else none at all, and the one and the other of these two things is equally bad. Besides there is no transverse in the even squares, which can furnish a diameter by position: and so it would be necessary to remove a little into the even squares, after the Indian manner of dispencing the numbers, and to put one into each rank and one into each diameter. But the Method presents not it self immediately. However here is the first example thereof.
8 | 11 | 14 | 1 |
2 | 13 | 12 | 7 |
9 | 6 | 3 | 16 |
15 | 4 | 5 | 10 |
Of the Indian Method of the Even Squares.
I Thought to have divined it from the examples of the squares of 16, 36, and 64 cases, which Agrippa has given us.
1. As the ranks are in even number in the even squares, they may be considered two by two. Comparing then the first to the last, the second to the last save one, the third to the last but two, and so successively, by equally removing us from the first and the last ranks, we will call them opposite, be they transverse, or upright.
Now because that the numbers of one rank, are arithmetically proportional with those of another rank of the same way, it is clear to those who understand arithmetical proportion, that two opposite ranks do make the same total sum as two other opposite ranks, and that if this sum be divided into two equals, each half will be the sum that a Magical rank ought to make.
2. The opposite numbers are also the first and last of the whole square, the second and last save one, the third and last but two, and so successively, by removing as equally from the first and last numbers: so that the sum of two opposite numbers is always equal to the sum of other opposites.
From hence it is evident, that the numbers opposite to those of one rank, are the numbers which are in the opposite rank, and that to render the sums of two opposite ranks equal, it is necessary only to take the moity of the numbers of one of the ranks, and to exchange them for their opposites, which are in the other. As for Example
1 | 14 | 15 | 4 |
13 | 2 | 3 | 16 |
1, 2, 3, 4, do make the first natural rank of the square of 16 cases, and 13, 14, 15, 16, do make the last rank thereof. To render them equal, it is necessary only to take 2 and 3, which are the moity of the numbers of the first, and to exchange them for 14 and 15, their opposites; and so 1, 14, 15, 4, will make the same sum as 13, 2, 3, 16.
The transverses between them, and the uprights between them, may render themselves equal by this Method: but because that the choice of the opposite numbers may be made after several ways, the Indians have chosen one, that is easie to retain, which leaves the diameters such as they are in the natural square, because that they are such as they ought to be, and ranges the uprights, when it is intended only to range the transverses. The whole Method consists then in knowing how to range two opposite transverses▪ and the rules are these.
1. They take the half of the numbers of the upper transverse, and remove them to the lower: and they take their opposite numbers in the lower transverse, and remove them to the upper.
2. The numbers which remain in each rank, do remain there in their natural place, and in their natural order: the transprosed do place themselves every one in the case of its opposite, and consequently in a subverted order.
3. The first and the last numbers of every rank do continue in their natural rank, the second and third are transprosed, the fourth and the fifth remain, the sixth and the seventh are transprosed, and so alternatively two are transprosed, and two remain.
1 | 63 | 62 | 4 | 5 | 59 | 58 | 8 |
57 | 7 | 6 | 60 | 61 | 3 | 2 | 64 |
1, 2, 3, 4, 5, 6, 7, 8, do make the first natural rank of the square of 64 cases; 57, 58, 59, 60, 61, 62, 63, 64, do make the last thereof. 1 and 8 the first and last numbers of the first rank remain there, and in their natural place, 57 and 64 the first and last numbers of the last rank do remain there and in their place. Afterwards 2 and 3 are transprosed, 4 and 5 remain, 6 and 7 are transprosed: and after the same manner the numbers of the opposite rank 58 and 59 are removed, 60 and 61 do remain, 62. and 63 are removed. 1, 4, 5, 8, which remain in the first rank, are in their natural cases, and consequently in their natural order. 2, 3, 6, 7, which are removed, are in the cases of their opposites, and are in a subverted order. After the same manner 57, 60, 61, 64, which remain in their rank, are in their natural cases, and in their natural order. 58, 59, 62, 63, which are removed, are in the cases of their opposites, and in a subverted order.
All the opposite ranks must be ranged according to these few rules: but it is not always certain that it may be necessary to put the first number of the rank in the first case on the left; for after this manner the first and last uprights would keep all their natural numbers, and would not be equal. Therefore it is necessary to render them equal by the same rule as the transverses, by removing half of the numbers of the first upright into the cases of their opposites, leaving the first and the last in their upright, removing the second and the third, leaving the fourth and the fifth, removing the sixth and the seventh, and so successively according to the rules that we have given for the transverses. The head of every transverse will be then on the right, or on the left, according as its first number shall be continued or removed, to the first or to the last upright, to the right or to the left.
1 | 63 | 62 | 4 | 5 | 59 | 58 | 8 |
56 | 10 | 11 | 53 | 52 | 14 | 15 | 49 |
48 | 18 | 19 | 45 | 44 | 22 | 23 | 41 |
25 | 39 | 38 | 28 | 29 | 35 | 34 | 32 |
33 | 31 | 30 | 36 | 37 | 2 | 26 | 40 |
24 | 42 | 43 | 21 | 20 | 46 | 47 | 17 |
16 | 50 | 51 | 13 | 12 | 54 | 55 | 9 |
57 | 7 | 6 | 60 | 61 | 3 | 2 | 64 |
[Page 244]But these rules suffice only to the squares equally even; and there is some particular observation for them unequally even.
Every square unequally even, if you thence deduct a compass (that is to say the first and the last transverses, the first and the last uprights) leaves a square equally even, which must be ranged according to the aforesaid rules with a little alteration, which we will declare. It is necessary therefore to see how the first and last transverses do range themselves, because that the first and last uprights do range themselves after the same manner.
1. The transverses, being of a square unequally even, have each a number of cases unequally even: but if care be not taken about the two middle cases of each transverse, then there will remain in every one a number of cases equally even, which we will call the cases equally even. The first rule is therefore to remove half of the numbers of the cases equally even, and to remove those, which should be chosen for this purpose, into a transverse of a square equally even. Thus the first and the last numbers do remain in their cases, the second and the third are removed, the fourth and the fifth continue, the sixth and the seventh are removed, and so successively: but I speak only of the numbers of the cases equally even, and I only comprehend those in the account which I make, nomore than if the middle cases had no numbers.
2. The removed numbers pass not to the cases of their opposites, but into the cases which are against theirs, that is to say in their upright: and so they are not found in a subverted order in the transverse into which they pass.
1 | 4 | 7 | 10 | ||||||
2 | 3 | 8 | 9 |
I have not set down the numbers 5 and 6 in this example, because that they are those of the two middle cases of the first transverse, and that the number of the two middle cases of the first transverse, in every square unequally even have a particular rule, which I will give. As to the eight other numbers, 1, 2, 3, 4, 7, 8, 9, 10, which are those of the cases equally even, they are, ranged according to the rules which I have given. 1. The first and last are in their natural cases, then the second and third are removed, the fourth and the fifth remain in their natural cases, the sixth and the seventh are removed. 2. The removed, viz. 2, 3, 8, 9, are in the cases over against theirs, and in their natural order, and not in an inverted order.
3. As to the two middle numbers, the first continues, and the second is removed: but the first remains not in its natural case. It passes to the case of the second, and the second is not removed to the case which is over against its own, but into that of its opposite: because that it is not necessary that the first leaves its natural case to its opposite, which shall be transported into this first transverse, and that the second leaves also to its opposite, the case which is over against its own.
1 | 4 | 5 | 7 | 10 | |||||
2 | 3 | 6 | 8 | 9 |
The numbers 5 and 6 are the middle. 5 remains in its transverse, but it passes to the case of 6, and 6 is removed to the case of its opposite, and not to that which is over against its own.
[Page 245]4. The numbers of the last transverse are ranged after this manner. The first and the last remain in their cases, the others fill the cases which are vacant, in the two transverses, and it is necessary to place them there successively, but in an inverted order. After this manner the two transverses become equal, because that they have given one to the other half of the numbers of the cases equally even, and that their middle numbers do make the like sum in every transverse, the opposites being together, and not in different transverses. It is possible if desired to range the second transverse as we have ranked the first, but then 'twould be necessary to rank the first as we have marked the second.
1 | 99 | 98 | 4 | 96 | 5 | 7 | 93 | 92 | 10 |
91 | 2 | 3 | 97 | 6 | 95 | 94 | 8 | 9 | 100 |
The numbers 91 and 100, which are the first and the last of the last transverse, do remain in their natural places, the others which are 92, 93, 94, 95, 96, 97, 98, 99, do fill the cases, which remained vacant in the two transverses, and they are there placed successively, but in an inverted order.
5. The first and the last uprights of the squares unequally even do rank themselves one in relation to the other, as the first and the last transverses: and by this means the whole square unequally even is found Magical, and by a Method easie to retain, and to execute by Memory.
The demonstration thereof is palpable. For to consider the numbers, as we have ranked them in the first and last transverses; it is evident that the opposite numbers, taken two by two, are there placed either diametrically in the first and last cases of every transverse, or directly opposite in the same upright, and because that the opposite numbers taken, thus two by two, do always make equal sums, it follows that these two transverses being at the top and at the bottom of the squares equally even, and interior already Magical, will add equal sums to the diameters, and to the uprights of this interior square equally even; and that so the uprights and diameters of the square unequally, will be equal in their sums. It will be the same of the transverses of the square unequally even, because that its first and its last uprights will likewise add equal sums to the transverses of the interior square equally even. And our demonstration would be compleat, were not the two numbers mean as well of the first, and last transverses, as of the first and last uprights: for these numbers not being placed every right against its opposite, do add unequal sums to the middle transverses and uprights of the interior square equally even. Therefore to repair this inequality, which is only of two points, it is necessary to make a little alteration in the interior square equally even, which will be the last rule of this Method.
6. By ranging the interior square equally even, according to the rules of the Magical squares equally even; it is necessary to invert the order, which according to these rules of the squares equally even, the two middle numbers of the last transverse of the square of 16 cases, which is at the center of all, and the two middle numbers of the last upright of the same square of sixteen cases, ought to have, you will thus weaken the first middle upright, and the first middle transverse of the square equally even: forasmuch as in the first transverse of the square of 16 cases, the first middle number is always stronger than the second, and that in the last upright of the same square of 16 cases, the middle superior number is stronger than the inferior.
1 | 35 | 34 | 3 | 32 | 6 |
30 | 8 | 28 | 27 | 11 | 7 |
24 | 23 | 15 | 16 | 14 | 19 |
3 | 17 | 21 | 22 | 20 | 18 |
12 | 26 | 9 | 10 | 29 | 25 |
31 | 2 | 4 | 33 | 5 | 36 |
This square is that of Agrippa, save that I have placed on the right, what he has put on the left, because that he has taken the squares which he gives, after the Hebrew Talismans, where the natural order of the numbers is from the right to the left, according to the Hebrew's manner of writing.
1 | 99 | 98 | 4 | 96 | 5 | 7 | 93 | 92 | 10 |
90 | 12 | 88 | 87 | 15 | 16 | 84 | 83 | 19 | 11 |
80 | 79 | 23 | 24 | 76 | 75 | 27 | 28 | 72 | 21 |
31 | 69 | 33 | 34 | 66 | 65 | 37 | 38 | 62 | 70 |
60 | 42 | 58 | 57 | 45 | 46 | 44 | 53 | 49 | 51 |
41 | 52 | 48 | 47 | 55 | 56 | 54 | 43 | 59 | 50 |
61 | 39 | 63 | 64 | 35 | 36 | 67 | 68 | 32 | 40 |
30 | 29 | 73 | 74 | 26 | 25 | 77 | 78 | 22 | 71 |
20 | 82 | 18 | 17 | 85 | 86 | 14 | 13 | 89 | 81 |
91 | 2 | 3 | 97 | 6 | 95 | 94 | 8 | 9 | 100 |
In the square of 36 cases the numbers 9 and 10, which are the middle of the last transverse of the square of 16 cases, which is at the center, are in an order contrary to that which they ought to have, according to the rules of the squares equally even. Thus 14 and 20, which are the middle of the last upright of the same square of 16 cases, are in a contrary number, to that which they ought to have by the same rules: for it would be necessary that 10 was before 9, and 14 under 20.
[Page 247]In the square of 100 cases at the seventh transverse, the middle numbers 35 and 36 are placed against the very rules of the squares equally even: 36 ought to precede 35 according to the rules: and 44 and 54 which are the middle of the seventh upright are also inverted, because that 44 ought to be under 54.
In every square equally even ranged Magically, according to the rules which I have given, it is infallible that in the transverse, which is immediately under the middle transverses, the two middle numbers should be in an inverted order, that is to say, the strongest precedes the weakest: for either these middle numbers are removed, and consequently in an inverted order, or they are not removed, and they are likewise in an inverted order, because that then their transverse begins at the right: forasmuch as if the middle numbers of each rank are not removed as it is supposed, the middle of the first upright are not, and so the middle transverses begin on the left, therefore the transverse underneath begins on the right. By a like ratiocination it will be proved, that according to the rules of the squares equally even, the middle numbers of the upright, which is immediately after the middle uprights, are ranged in such a manner, that the strongest is always above the weakest.
This is Agrippa's Method of the even squares, which in my opinion are the Indian, the merit of which consists not in giving the sole possible manner of ranging the even squares, but the most easie to execute by memory: For it is to this principally that it seems, that the Indians should addict themselves. In a word, the Indian even squares are also Magical in the Geometrical Progression.
The Indians have two Principles for the Problem of the Magical squares, the one of which they have applied to the uneven squares, and the other to the even. The Mathematicians of this Country, which have laboured herein, have known only one of these two Principles, which is that of the even squares; but they have adapted it likewise to the uneven squares, and moreover they have added a singular condition to this Problem, which is that the Magical square be so ranged, that in deducting its first compass, that is to say its first and its last transverses, its first and its last uprights, the interior square which shall remain is found Magical, after this very kind, that is to say, being able to lose all its compasses one after the other, and to leave always for the rest a Magical square, provided that this residue have at least 9, or 16 cases; because that the square of 4 cases cannot be Magical.
Monsieur Arnoud has given the solution of this last Problem at the end of his Elements of Geometry, and before that he had printed it the first time, I had also resolved this Problem in its whole extent, having been proposed to me by the late Monsieur de Fermat, Counsellor in the Parliament of Tholouse, whose Memory is yet in Veneration amongst the learned: but then I divined not Agrippa's Principle of the unequal squares, nor the reason of Bachet's Method.
In fine, I am obliged to render this Testimony to Monsieur Sauveur, Professor of the Mathematics at Paris, that he found out a Demonstration of the Indian uneven squares, which Monsieur de Melezieu communicated unto him: and that he has also invented a Method to range the even squares. I leave unto him the care of publishing this, and several other things of his own Invention, because that this Chapter is already too long.
The Care of the Manners amongst the Chineses, and of the Antiquities of their History.
CHina is happily situated, having no foreign war to fear. It has no other Neighbours then Tartary on the North, and Tonguin on the West. Every where else it is bounded either by the Ocean, or with a desart of several days Journey, or with Woods, and Mountains almost impassable. Tonquin is a very little state, if compar'd to China: and it is seated under those hot climates, from whence it never comes out as Conqueror. The Tartar is continually [Page 248] accustomed only to make incursions on his Enemies, and not wars in form. A wall on the frontiers of China, which stops the passages, has sufficed during a long succession of Ages, to stop all the Enterprizes of the Tartars.
It is no wonder then if the Chineses are little addicted to War, and if the Tartars, tho more weak, and otherwise less proper to make Conquests, have yet subdued them twice in the space of three or four thousand years.
But as much as the Chineses have ignored war, as much are they experienc'd in the knowledge of Government. Their good natural wit has made them to improve it with so much care in the repose which their Country has almost continually enjoyed, that next to the Laws which God gave unto Moses, there are none perhaps which do make a compleater body of Policy, nor whose parts concur better to the same end, than the Chinese Laws. Thus this people is the most numerous that has ever been in the World, except perhaps the people of God: which, in my opinion, is the best sign of an happy Government.
I have sufficiently declared in my relation, how the Chineses have suited their Religion to their Policy, by making of the spirit of Heaven, and of the other spirits an invisible Republick like to theirs, of which they suppose that the members have a secret correspondence with the members of theirs, and that they punish the hidden faults of their Kings, of their Magistrates, and of every one of their Citizens in particular.
I have observed likewise how they have provided for the Perpetuity of their Laws, by the dread of their dead Parents, whom they suppose to be provoked in the other life, with the faults which their Children commit in this, and especially with the great want of respect which it would be in the Chineses towards their Ancestors, to change the Laws which they have left them. 'Tis not therefore a vain Ceremony that they mourn for three years with an extream Austerity, and separated from all public Employment, which the Chinese Laws do order Children to observe at the death of their Father and Mother, and from which they dispence not even their Kings. They cannot too much imprint in their minds this respect, which has always been their greatest support.
But what I most admire in the Laws of China, is the care which they have taken to form the Morals, seeing that it is only good manners, which can maintain the Laws, as it is only good Laws that can make good manners. Plato, methinks, understood the whole importance of this Maxim, and if my Memory fails me not, he requires in some places of his Laws, that they intermeddle with the privacy of the Oeconomy of his Citizens: and because he feared that this might appear too new to the People, so free as the Greeks were in his time, he sought some excuse for the little which he delivered thereof.
The Chineses, on the contrary, have not scrupled to give Laws to almost all the Actions of men. One of their most ancient Books regulates not only the Rites, which concern Religion and the Sacrifices, but all the Duties of Children to their Father, and of the Father towards his Children; of the Husband to the Wife, and of the Wife to the Husband; of Brethren and Friends to each other; of the King to his Subjects, and of the Subjects to their King; of the Magistrates to the People, and of the People to the Magistrates. In this Book, which has the Authority of a Law, the old men are considered as the Fathers of all the People, and of the King himself, the Orphans are there considered as his Children, and all the Citizens as Brethren amongst them. Father Martinius reports,Hist. sin. p. 352. that there is almost no humane action, how small soever it be, to which this Book prescribes not Laws, even to cause trouble for an exceeding small particular. I doubt not that all the Europeans would judge like him, if this Book came to our knowledge, but this is nevertheless a very ancient Testimony, of the extream care which the Chineses have continually taken of good manners.
And because they knew the prevalency which the example of Kings has over People, their greatest study has always been to inspire Vertue into their Kings. The People, they say, is like the Ears of Corn wherewith a field is covered, the Morals of the Prince are like the Wind, which inclines them, where it listeth.
Their Policy has therefore no particuluar manners for their Kings, and other manners for the People. Their Kings are obliged to respect old men: they [Page 249] nourish them in every City; and the Chinese History honourably mentions such of their Kings, which have rendered them most respect, and some others, who have caused their illegitimate Brethren, which precede them in Age, to sit down at their Table, and above them. Their Kings are obliged to the three years mourning upon the death of their Father and their Mother, and to abstain during this time from the cares of the Government, altho perhaps this Law has lost it Vigour in the last times. When China was as yet divided into little States, which were as so many Fiefs of this great Empire, Ven-cum King of Cin chased out of his little Kingdom by his Step-mother, would not undertake a war to re-enter, till he had mourn'd for his Father three years.
They believe amongst other things, that their dead Parents can shorten or prolong the life of their Children; they desire of them a long and happy life, and upon this ridiculous ground, they have in the same terms with us, this precept, which we have from God himself, and of which his eternal verity is protecter unto us: Honour thy Father and thy Mother that thou mayest enjoy a long life.
Xin the first King of the Race Cina, having banished his Mother for her incontinence, and because that his Adulterer made use of the favour of this Princess to revolt, and to assemble a great Army, was constrained by all his Ministers to recall her from exile, altho he had made himself King by force, and that thereby he seemed to be stronger than the Laws.
Hoei the second King of the Race Hana, having also an unchast Mother, dared not to punish her: but not being willing to reign and suffer her debaucheries, he abandon'd the Government to her out of an extream Piety, and plunged himself into debauchery: so that Hiaovu the sixth King of the same Race, put the Queen his wife to death, for fear of leaving behind him a debauched Widdow, and a Mother incommodious to his Successor.
I should not end if I would relate all the examples of the extream respect which the Chineses have for their Father, and for their Mother: I will add only that they change not their Officers, as they innovate nothing in their Laws.
They are instructed also not to have less respect for their Governors, than particular persons have for their masters. Their Governor they call Colao, whom they generally make their chief Minister, as the Grand Segnior calls his Grand Vizier Lala, that is to say Governor. This respect is so entire amongst them, that they chastise, as I have said, in some place of my Relation, the Governor of the Prince the presumptive Heir of the Crown, for the faults which that Prince commits, and that there are found some Princes, who being become Kings have revenged their Governors.
Besides the Colao, who is the King's principal Council, he has other Officers, whose sole Function is to reprehend him publicly for his Faults. Yvus the first King of the race Hiaa, who according to their History began to reign 2207 years before Jesus Christ, gave full liberty to all good persons to give him counsel: and yet because that he found himself once reproved with too much sharpness, in the presence of his principal Councellors, he was so vexed thereat, that he had resolved to put him to death who had given him this affront: but his Wife appeased him. Being adorned more than ordinary, she presented her self before him: and as he was smitten with this dress, which in the perplexity wherein he was, seemed to him improper, she told him, that she came to congratulate him, for having in his Court such couragious and faithful Servants, as dare to tell him the truth. This liberty of admonishing the Prince, passed afterwards into a Law: There were, as I have said, some Offices purposely created for the exercising it; yet without taking it away from any other Officer of State: and the Chineses have always been so jealous of this Prerogative, that several have died to maintain it, and that there have been some examples, even in this Age, that when the King was obstinate not to hear any important reproof, the Officers of the Court, to the number sometimes of two Thousand, have entered into his Palace, there to lay down the Badges of their Offices. So that it is impossible that a King of China can continue King, if he is vicious to a certain degree. Thus, some tell him incessantly, that it is his example, which must render the Magistrates, and the People virtuous; and that if he departs [Page 250] from the Vertue of his Ancestors, the Magistrates and People growing debauched in their Morals, would forget their fidelity which they owe him, and which is their first duty, and their first Vertue. Examples hereof are frequent in their History: in which they have not better provided for the security of their Master, than all the other Despotic States. According to them it is 4000 years that their Kingdom has continued in these Maxims, which render it the admiration of all its Neighbors. St. Francis Xavier reports in his Letters that the Japponeses incessantly objected to him, that the Christian Religion could not be true, seeing that it was not known by the Chineses. Yet I know that the Chineses have some Vices, but they perhaps sin less against their Moral Law, than we do against ours. How much have our Morals degenerated from those of our Ancestors? and the Chineses, more antient than us, do still esteem it a disgrace to violate their Morals in public, and to fail in the respects which they owe to one another, either by any disobedience to their Parents, or by any quarrel with their equals. They are Infidels, say some, in Commerce; but it may be they are only so with Strangers; as the Hebrews lent money to usury to Strangers only: and besides, the Chineses which have Commerce with Strangers, are those of the Frontiers, whose manners this very foreign Commerce has depraved.
The greatest Vice of the Chineses is doubtless an extream Hypocrisy: but besides that it reigns every where, because it is a Vice which is free from the censure of the Laws, it is perhaps a less evil, than a publick corruption.
But if the Chinese History may be credited, 'tis Vertue alone that has formed this great Empire: the love of their Laws, which were at first established in a corner of this Country, gradually drew all the Neighbouring Provinces under the same yoke, it not appearing that the Chineses have conquered these Provinces by any war. It is true that all these little States, which were at the beginning as so many hereditary Fiefs given usually to the Princes of the Royal Blood, have been reunited to the Crown by Civil Wars, when the Royal race has changed, and that Usurpers have expelled the lawful Kings from the Throne; but it appears that the first subjection of all these little States to the Crown of China has been voluntary. They say that 44 Kingdoms, enamoured with the Vertue of Venvam, submitted to his Laws. He reigned over the two thirds of China, when it was yet divided. However it be, the Chineses have been continually Enemies to war, as the principal cause of the corruption of manners, and they have preferred Morality before all the Glory of Conquests, and all the advantages of Commerce with Strangers.
King Siven, the ninth of the Race Hana, 60 years before the birth of Jesus Christ, dreading the consequences of any motion of the Tartars, which sometime before had been confined within their Mountains by Hiaovu, and who were returned to seize on the flat Country, resolved to prevent them, and make war upon them, before they had put themselves in a condition to carry it into China. In another Country this Prudence might have been approved, but it was not at China, where the care of good manners is the main affair of the State. The History therefore relates, that his Chief Minister disswaded him from this Enterprize by this discourse. What, Sir, do you think to invade foreign Countrys, when there are such great things to reform in your own. A Prodigy to this hour unheard of amongst us! in this year a Son has slain his Father, seven younger Brothers have killed their 25 elder Brethren. These are the signs of an intolerable boldness, and which presage a very dangerous corruption in our manners. 'Tis what we ought to be alarumed at; it is to what a speedy remedy must be applied; for so long as these Crimes shall not be suffered at China, China will have nothing to fear from the Tartars: but if they were once permitted, I fear that they would not only extend themselves into all the Territories of the Empire, but even into the Imperial Palace.
Under Juen, the Tenth King of the same race, the Provinces of Qnantong, and Quangsi, and the Isle of Hainan revolting, he levied as many forces as it was possible to reduce them to their Obedience: but Kiasu, whom he appointed for their General diverted him from this war, by these words. Anciently [Page 251] the Kingdom of China, was bounded on the East by the Ocean, on the West by the Sandy Desart, and on the South by the River Kiang: but by little and little it enlarged its limits less by Arms, than by Vertue. Our Kings do kindly receive under their Empire, those who voluntarily submit themselves out of Love to our Justice and Clemency, and several neighbouring Provinces submitted thereunto: not any was compelled by force. 'Tis my advice that you abstain from this war, and that imitating the good Kings which have lived before you, you may make them to revive in your Maxims. The way to reduce a rebelious People to Obedience, is by the allurement of Vertue, and not by the horror of Arms.
Yet China has had some conquering Kings, but two or three at most, if I am not mistaken: though they say, that Hiaovu, who was one of these, repented of the wars which he had made, and took no care to preserve his Conquests.
Gu-Cupn one of the Disciples of Confucius, asked him one day what things were necessary to a good Government, Plenty of Provisions, replied he, a sufficient quantity of Souldiers and Ammunition for War, of Virtue in the King and his Subjects. I understand what you tell me, replied the Disciple, but if it were necessary to lack one of these three things, which will you quit the first? The Souldiers, answered the Philosopher. But if there was a necessity also of lacking Provisions or Vertue, which of these two losses would you chuse? I would chuse, saith he, to want Provisions. He could not better testifie the Contempt of War, and the Love of good Morals. Plato would have but a small number of Citizens in his Republic, because that he dreaded the corruption in too great a Multitude, and that he cared not so much as his Republic should last, as that it should be happy, and consequently virtuous, so long as it did last.
In fine, the Chineses have never neglected the instruction of the People. Besides that it is easie to know the Laws which are public, and which never alter, they publish every fifteen days, by Proclamation a small number of Precepts, which are the ground of their Moral Law, as the Commandments of God are ours.
They have not neglected Punishments, seeing that the Magistrates do answer for the faults of their Family, the Parents for the faults of their Children, the Superiors for the crimes of their Inferiors, and that they all have a right to punish the faults of those, for whom they answer: but I have already handled these things, and some others in my Relation,
This is what I had to say, concerning the care which the Chineses have had to to preserve their Morals, the duration of which is doubtless the greatest wonder, that we have seen among men. It may be suspected, that their History is flattering in some things. They can lye, without fearing to be contradicted by their Neighbors: and it is probable that they have not always spoken the Truth, seeing that their History is the work of their policy. The Office of an Historian is amongst them a public Office. The History of a King is written after his death, by the order of his Successor, who sometimes has been his Enemy; and not any History is published, till the Race of the Kings whereof it treats, is extinct, or at least driven from the Throne. It is not lawful for any Historian, to call in question the History already written, nor for any particular person to write History: every one only may make Abridgments of the Histories already published. There is therefore but one single general History, and no particular Memoirs. Yet there is no appearance that they have corrupted the most important of the Events; and the Roman Historians cannot perhaps have been more faithful in what they have writ to the Honor of their Country, and to the Shame of their Enemies.
But a particular reason casts a great doubt on the Chinese History, from the beginning of their Monarchy to about 200 years before Jesus Christ, because that Xin the first King of the Race Cina, who reigned about 200 years before Jesus Christ, burnt as far as it was possible, all the Books of China, which treated not of Medicine or Divination. Their History shows that he exercised great cruelties, against those which concealed Books, and that so few escaped his fury, and almost none entirely: A very singular event amongst those who continually destroy the Memorial of things past. This therefore sufficeth in my opinion to doubt, if one will, whether this great Empire could be formed without any war.
[Page 252]Notwithstanding this loss of their Books, the Chineses cease not to give a compleat History not only from the beginning of their Monarchy, but from the Origine of Mankind, which they make to re-ascend several thousands of years beyond the Truth. Nevertheless they themselves acknowledge that their History has the semblance of a Fable in whatever precedes the beginning of their Monarchy; but it has been hitherto difficult to perswade them that they had not had a long succession of Kings before Jesus Christ, which remounts beyond the time where our common Chronology places the flood: insomuch that several amongst the Missionaries have thought it necessary to have recourse to the Chronology of the Septuagint, according to which the Deluge is more ancient by several Ages, than according to the common Chronology. What render'd the Chinese History more probable, is, that under every King it records the Eclipses, and other celestial Phaenomena of his Reign: but Monsieur Cassini having examined the time of a Conjunction of the Planets, which they place under their fifth King, he has found it above 500 years later than their History makes it: and he proves this very misreckoning of 500 years by another Astronomical remark, referred to the Reign of their seventh King. Thus the Chinese Monarchy appears less ancient by 500 years than the Chineses have thought, and it may be presumed that in this succession of Kings, which they give us, they have put those who have reigned at the same time in diverse Provinces of China, when it was divided into several little Feudatary States under the same Lord.
Monsieur Cassini having given me his Reflexions upon this subject, I have thought fit to add them here, and once again to adorn my work with a Chapter after his fancy. And because he has communicated unto me a thought which he had about the sitution of the Taprobane of the Ancients, I have besought him to give it me: whatever respects the Indies being not improper in this Book, and whatever comes from Monsieur Cassini being always well received by all.
Reflexions on the Chinese Chronology, by Monsieur Cassini.
I. The System of the Chineses.
THe years of the Chineses are lunisolar, some of which are Common of 12 lunar Months, others Embolismick of 13.
The first day of the month is ordinarily the first day after the Conjunction of the Moon with the Sun, so that the Eclipses of the Sun do ordinarily happen the last day of the month, as may be seen in the Chinese Chronology of Father Couplet.
If the beginnings of the months do remove from this Epooha of the Conjunctions, it is easie to restore them after the observation of an Eclipse of the Sun.
The order of the Common and Embolismick years, is regulated by the Cycle of 60 years, in which 22 are Embolismick, and the others Common.
According to Father Martinius in his Chinese History, the years at the Moons Conjunction with the Sun, the nearest the fifteenth degree of Aquarius: that is to say, the point of the Zodiack which is at equal distances from the points of the Winter Solstice, and of the Vernal Equinox: which according to this Author has been observed from the twenty fifth Age before the Birth of Jesus Christ to the present Age: tho this beginning has varied according to the will of diverse Emperors, and that they have been obliged sometimes to correct the year, from the Errors which were crept therein.
[Page 253]There may be more error in the Epocha of the years, than in the Epocha of the months, because that the points of the Zodiack, which determine the first month of the year, are not immediately visible, as the Eclipses of the Sun, which determine the beginnings of the months.
It is certain, as Father Martinius remarks, that after a period of 60 lunisolar years, the Conjunctions of the Moon with the Sun return not to the same point of the Zodiack, but that they anticipate three degrees, which the Sun runs through only in three days, which in ten periods of 60 years amount to 30 days. Thus to hinder the beginning of the year from removing above a Sign from the fifteenth degree of Aquarius, it would be necessary that the Chineses should add to every period of 600 years a month extraordinary, above the 22 months which are added to every period of 60 years. Yet Father Martinius relates that they have no need of any intercalation: which I suppose it is necessary to understand of these three days apart, but not of the extraordinary intercalations of the months, when this difference of three days is mounted to an whole month.
II. Doubts upon the Chinese Chronology.
BUt it is not known whether this be regularly practised, or whether the Chineses do add some months extraordinary to their years without rule, when they perceive that the beginning of the year is too remote from the middle of Aquarius; and whether the Intercalations of the months, as well ordinary as extraordinary, are made on purpose.
We have reason to doubt of what Father Couplet, who has been a long time in China, says in his Treatise of the Chinese Chronology, that the Chineses begin their years at the Conjunction of the Moon with the Sun the nearest the fifth degree of Aquarius, which must be so at present: So that from Father Martinius to the present Epocha of the Chinese years, they would have run back 30 degrees.
If the Observation related by Father Martinius in his seventh Book of his History was true, the beginning of the Chinese year would be several Signs distant from the fifteenth degree of Aquarius, since the time that this degree has been assign'd for a middle limit of the Chinese years: for he says that according to the Chinese Historians, whose credit he suspects, the 204th year before the Epocha of Jesus Christ, in the beginning of the year, five Planets appeared in the Constellation of Cing, which at present extends from the beginning of Cancer to the beginning of Leo, and then consequently extended from the 4th or 5th of Gemini to the same degrees of Cancer. It may be seen without any other calculation, that this observation agrees not to the System of the Chinese years: for seeing that Mercury removes not from the Sun above 28 degrees, nor Venus above 48; it is certain that Venus could not be in the Constellation Cing, before that the Sun had passed half of the Sign Aries, which is two whole Signs distant from the middle of Aquarius; and that Mercury could not appear in this Constellation unless the Sun had passed the beginning of Taurus, and because it was necessary that at least one of these two Planets should appear in this Constellation to accomplish the number of five, or both, if the Moon meet not therein: (for the Sun in this Hypotheses could not be there) it is certain that the Sun could not be less remote from the middle of Aquarius than two whole Signs in the beginning of the year, at which this Conjunction is marked. The Chinese History remarks also, that at several times there is found some digressions in the Chinese years, which have obliged several Emperors to restore them to the first Epocha. These digressions may have happened for having intercalated the months too frequently, or for having neglected the intercalations of the months when it was necessary to make them, and as we have not the History of these intercalations, it is not possible to remove the perplexities which there is, for this cause, in the Chinese Chronology.
[Page 254]It is known what has been that of the Chineses in this very age: for notwithstanding the Antiquity of their magnificent Observatories, furnished with all sorts of Instruments, and the ample Colledges and Governments of Astronomy, this Nation so very jealous of its own Glory, and an Enemy to Strangers, has been obliged to joyn with its Astronomers for the correction of their Calender, the Jesuits, which went thither to introduce a Religion contrary to theirs, and to heap Honors on the Fathers Licci, Schall, Verbiest, and Grimaldi, who in the time of his absence in Italy, was elected by the Emperor of China for President of Astronomy. From whence it may be judged that the Chineses had not so certain a method of regulating their years, that they have owned, that they are not capable of regulating them all alone without great Errors.
III. An ancient Observation of the meeting of the Planets in the Constellation Xe.
FAther Martinius attributes to the fifth Emperor of China, whom he reports to have reigned from the year 2513 to the 2435th year before Jesus Christ, the rule of beginning the year with the new Moon nearest the 15 of Aquarius.
He says that, according to the Author of the Chinese History, this Emperor saw five Planets joyned together on the same day of the Conjunction of the Sun and Moon in the Constellation Xe, which at present begins about the eighteenth degree of the Sign Pisces, and extends to the fourth degree of Aries, and that he took this day for the beginning of the year.
He relates not in what year of his Reign the Conjunction of the Planets was: but as this Conjunction is very rare, we may search whether it could happen between the 2513 and 2435th year before Jesus Christ in this Constellation of Xe.
This research is important, forasmuch as this Epocha would be several Ages ancienter than the Deluge, according to the calculation of those who place it about 2200 years between the Deluge and the Birth of Jesus Christ.
IV. Of the Chinese Constellations.
FOR the understanding of this Celestial Character, we have examined the Chinese Constellations, of which Martinius in his History and in his Chinese Atlas gives the Catalogue calculated for the year 1628, after the European method, and we have compared them with our Constellations calculated for the same year.
We have found by this comparison, that every Chinese Constellation begins ordinarily with some considerable fixed Star, which in the year 1628 is found in Tycho's Catalogue almost always in the same minute, as the beginning of the corresponding Constellation in the two Catalogues of Father Martinius, except 3 or 4, in which it appears, that there is a mistake of numbers in the two Catalogues, where the distance taken from the point of the Equinox, accords not with the degrees and minutes of the Sign of the Zodiac, to which these Constellations are referred, as it agrees in the other Constellations.
Wherefore we do here insert them after two ways, according to the numbers of Father Martinius, and according to our correction.
Nomen. | Longitudo. | Gradus. | Signa. | |||||
Kio | ♃ | 198 | 39 | 18 | 39 | ♎ | ||
Kang | ♀ | 209 | 14 | 29 | 14 | ♎ | ||
Ti | ♄ | 219 | 54 | 9 | 54 | ♏ | ||
Fang | ☉ | 237 | 48 | 27 | 48 | ♏ | ||
Sing | ☽ | 242 | 34 | 2 | 34 | ♐ | ||
Vi. | ♂ | 250 | 7 | 20 | 7 | ♐ | ||
corrige | 260 | 7 | ||||||
Ki | ☿ | 265 | 43 | 25 | 43 | ♐ | ||
Teu | ♃ | 275 | 3 | 5 | 3 | ♑ | ||
Nieu | ♀ | 298 | 54 | 28 | 54 | ♑ | ||
Neu | ♄ | 306 | 35 | 6 | 35 | ♒ | ||
Hiu | ☉ | 318 | 14 | 18 | 14 | ♒ | ||
Guei | ☽ | 328 | 13 | 28 | 13 | ♒ | ||
Xe | ♂ | 346 | 20 | 18 | 20 | ♓ | ||
corrige | 348 | 20 | ||||||
Pi | ☿ | 4 | 1 | 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 | ♎ |
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.
[Page 257]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 not so considerable anciently, when these Stars were near the Colure of the Solstices.
VI. A Determination of the time of the meeting of the five Planets in the Constellation Xe.
HAving reduced these Stars to the Equinoxial in the twenty fourth and twenty fifth Age before the Birth of Jesus Christ, we have not found, that between the Circles of the declinations which pass through these Stars, five Planets could be found joyned together, neither in these Ages, nor in two others before and after, whilst that the Sun was in the sign of Aquarius, as the Chinese History imports.
But we have found that Saturn, Jupiter, Venus, Mercury, and the Moon met in that Chinese constellation determined by this method, the Sun being in the 20th of Aquarius, in the 2012 year before the Epocha of Jesus Christ, the 26th of February according to the Julian, the 9th according to the Gregorian form, which runs at present, and that the day following 10/27 of February at 6 a Clock in the morning at China, happen'd the conjunction of the Moon with the Sun, which may be that which was taken as the Epocha of the Chinese years.
Then according to the Catalogue of Tycho, and the motion which he gives to the fixed Stars, the first of the wing of Pegasus from which began the constellation Xe, was at 26 degrees 50 minutes of Capricorn, and the Circle of its declination cut the Ecliptick at 24 degrees of the same sign.
The last of the wing of Pagasus was at 12 degrees and a half of Aquarius, and its Circle of Declination cut the Ecliptick, and carry'd it back to the eleventh degree of the same sign.
The Morning of February 8/2 [...] in the Crepusculum at China.
The beginning of the Constellation Xe was | ♑ | 24 |
Saturn. | ♑ | 24 |
Jupiter. | ♑ | 26 |
Mercury. | ♑ | 27 |
Venus. | ♒ | 4 |
The Moon. | ♒ | 8 |
The end of the Constellation Xe. | ♒ | 11 |
And in 24 hours or thereabouts happened the Conjunction of the Moon with the Sun.
The Chinese Chronology places the Conjunction of the Planets between the 2513 and 2435 years before the Birth of Jesus Christ. There will be therefore a difference of 5 Ages between the time denoted by this Chronology and the true time. Thus the Chinese Epocha will be five Ages later then the Chinese Historians suppose it.
VII. An Ancient Observation of a Winter Solstice made at China.
THis difference of five Age whereby it appears according to this calculation, that the Chineses do make their Epocha too antient, is confirmed by another place of Father Martinius his History, where this Author reports that under Jao the seventh Emperor of the Chineses, the Winter Solstice was observed about the first degree of the constellation Hiu, which at present begins about the 18th of Aquarius, so that since this time the Solstice is removed above 48 degrees from its first place; he refers this Observation to the 20th year of Jao, which he reports to have been the 2341 before the Birth of Jesus Christ.
It appears by the Table that this constellation Hiu began with the Star which is in the left shoulder of Aquarius, which in the year 1628 was at 18 degrees, 16 Minutes of Aquarius; but the 20th year of Jao it was in 29 degrees of Sagitarius and some minutes, seeing that the Winter Solstice, which is always at the beginning of Capricorn, was at the first of the constellation Hiu. The distance between these two places of the Zodiac is 49 degrees 16 minutes, which the fixed Stars according to Tycho's Table do make in 3478 years, by reason of 51 seconds per annum: from whence having deducted 1625 years at most, which are elapsed from the Epocha of Jesus Christ, the 20th of Jao would be the 1852 year before the Birth of Jesus Christ, which Father Martinius according to the Chinese History placeth in the 2347th year before Jesus Christ, making it more antient by about 497 years. Thus there are about 5 Ages difference between this Epocha taken from the Chinese History, and the same drawn from the motion of the fixed Stars made in this interval of time, as we have found by the Examination of the Observation of the 5 Planets in the Constellation Xe.
According to Father Martinius in the beginning of his History of China, it seems that the Chineses do reckon but five Planets, Saturn, Jupiter, Mars, Venus, and Mercury, and that they suppose at the time of their fifth Emperor, the concourse of those five Planets in the Constellation Xe, on the same day that there was a Conjunction of the Moon with the Sun. But if this Chinese observation must be thus understood, 'twould be a meer groundless mistake: such a concourse having not happened at the time denoted by the Chineses, nor long before it, so that it cannot be known perhaps how to take it.
The Historians supported with Astronomical Observations, do merit therefore to be examined beforc that credit be given thereunto. Thus an account of Eclipses, which is at the beginning of Diogenes Laertius, and which he relates after Sotion, is condemned as false by Monsieur Cassini. Sotion reckoned 48863 years between Vulcan and Alexander the Great, and in this interval he placed 373 solar Eclipses, and 832 lunar.
A too ready belief must not likewise be given to an History, because it gives us a well ranged succession of Kings. The Persians do give us one of this Nature, which we know to be full of falsities: and we have the Genealogies of our Kings from Adam, which are yet more spurious. 'Tis not only from a well adjusted succession, that the Histories to which we give credit, do take their certainty, but from that they are confirmed one by the other: All the Nations that can have a knowledge of the same things, relating them after the same manner, at least as to the most important circumstances, so that where there is a diversity of [Page 259] advice we fall into doubt. The History of the Chineses has neither been contradicted, nor confirmed by their Neighbours: no Authority can be drawn from their silence; and thus all that we have to do, is to believe it true in the gross, especially from about 200 years before Jesus Christ; but not in what oppugns our Histories, which are better attested than theirs.
Concerning the Isle Taprobane, by Monsieur Cassini.
THE situation of the Isle Taprobane, according to Ptolomy in the seventh Book of his Geography, was over against the Promontary Cari.
This Promontary is placed by Ptolomy between the Rivers Indus and Ganges, nearer Indus than the Ganges.
This Isle Taprobane was divided by the Equinoxial Line into two unequal parts, the greatest of which was in the Northern Hemisphere, extending to 12 or 13 degrees of Northern Latitude. The least part was in the Southern Hemisphere, extending to two degrees and a half of Southern Latitude.
Round about this Island there were 1378 little Isles, among which there were 19 more considerable, the name of which was known in the West.
The Promontory Cory could be no other than that, which is at present called Comori, or Comorin, which is also between the Indus and Ganges, nearer the Indus than the Ganges.
Over against this Cape there is not at present so great an Isle as Taprobane, which could be divided by the Equinoxial, and environed with 1378 Isles: but there is a multitude of little Isles, called Maldivae, which the Inhabitants report to be to the number of 12 Thousand. According to the Relation of Pirard, who lived there five years, these Isles have a King, who assumes to himself the Title of King of 13 Provinces, and 12 Thousand Isles.
Every one of these thirteen Provinces is an heap of little Isles, each of which is environed with a great bank of Stone, which incloses it all round like a great wall: they are called Attolons. They have each Thirty miles in circumference, a little more or less, and are of a figure almost round, or oval. They are end to end one from the other, from the North to the South; and they are separated by Channels of the Sea, some broad, others very narrow, These Stone-banks which environ every Attollon, are so high, and the Sea breaks there with such an impetuosity, that they which are in the middle of an Attollon, do see these banks all round, with the Waves of the Sea which seem as high as the Houses. The Inclosure of an Attollon has but 4 Avenues, two on the North-side, two others on the South-side, one of which is at the East, the other at the West, and the largest of which is 200 paces, the narrowest somewhat less than 30. At the two sides of each of these Avenues there are some Isles, but the Currents and great Tides do daily diminish the number thereof. Pirard adds, that to see the inside of one of these Attollons, one would say that all these little Isles and the Channels of the Sea, which it incloses, are only a continued plain, and that it was antiently only a single Island, cut and divided afterwards into several. Every where almost is seen the bottom of the Channels, which divide them, so shallow they are, except in some places: and when the Sea is low, the water reaches not up to the girdle, but to the middle of the leg almost every where.
There is a violent and perpetual Current, which from the month of April to the month of October comes impetuously from the West, and causes the continual rains which do there make the Winter; and at the other six months the Winds are fixed from the East, and do bring a great heat, without any rain, which causes their Summer. At the bottom of these Channels, there are great Stones, which the Inhabitants do use to build with, and they are also stored with a kind of Bushes, which resemble Coral; which renders the passage of the Boats through these Channels extreamly difficult.
[Page 260] Linscoten testifies that according to the Mallabars, these little Isles have formerly been joyned to the firm Land, and that by the succession of time they have been loosed thence by the Violence of the Sea, by reason of the lowness of the Land.
'Tis therefore probable that the Maldivae are a remainder of the great Island Taprobane; and of the 1378 Islands which did encompass it, which have been carryed away, or diminished by the Currents, there remaining nothing else but these Rocks, which must formerly be the bases of the Mountains: and what remains in the inclosure of these Rocks, where the Sea dashes so, that it is capable only of dividing, but not of carrying away the Lands which are included within their Circuit.
It is certain that these Isles have the same situation in regard of the Equinoxial and Promontory, and of the Rivers Indus and Ganges, that Ptolomy assigns to several places of the Isle Taprobane.
The Lords Prayer and the Ave Mary in Siamese, with the Interlineary Translation, to be inserted in Page 180.
Father our Po raou who art in Heaven. you savang. The Name of God Scheu Pra be glorified hai pra kot in all places touk heng by People all kon tang tai offer to God praise. touai Pra pon The Kingdom of God Meuang Pra I pray to find co hai dai with us ke raou to finish hai leou conformable ning to the heart of God tchai pra in the Kingdom of Meuang the Earth Pen-din even as semo of Heaven. savang The Nourishment of us Ahan raou of all days touk van I pray co to find hai dai with us ke raou in day van this ni I pray co to pardon prot the offences bap of us raou even semo as we raou pardon prot persons pou who do tam offences bap to us ke raou. do not let Ya hai us raou fall tok into nai the cause kovan of Sin bap deliver hai poun out of kiac evil anerai all. tang-poang. Amen.
Ave Maria full of Grace Ten anisong, God be Pra you in the heng place of you. nang. You just-good Nang soum-bou more than yingkoua all nang tang tai. With Toui Sons louk Womb cutong, in the place heng of you nang God pra the person Ongkiao of Jesus Yesu just charitable soum-boui more than ying koua all. tang tai. Sancta Maria Mother Me of God Pra assist thoui by prayer ving to God von Pra for pro us raou people kon of Sin bap now teit-bat-ni and te in the time moua of our dying, raou tcha tai, Amen.