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 there∣unto 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 Intercala∣cation. 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 num∣ber 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 begin∣ning of the months in several of these dates, and particularly in those of Octo∣ber 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 Astrono∣mical 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 In∣tercalation 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 Astro∣nomical 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 Conjun∣ction happen'd later at Siam, according to these Rules, than that of the Astro∣nomical Epocha of the year 638.
By the means of our Calendar is found the number of the days elapsed be∣tween 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 hap∣pen'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 il∣lustrated; and it could not be determined without several Calculations made ac∣cording to the preceding method.
