Page:Sewell Indian chronography.pdf/45
65. Astronomically the Chaitrādi luni-solar year—the year, that is, which is held to begin with the beginning of the first tithi of the bright half of the amānta month Chaitra—has for its initial point the moment of the new-moon which comes next after the Mīna saṁkrānti, the last saṁkrānti of the solar year. It is always the new-moon next before the Mēsha saṁkrānti except when Chaitra is an intercalary month. The time of the apparent sidereal Mēsha saṁkrānti for each year is given in Table I. of the Indian Calendar (cols. 13 to 17, and 17a). For civil purposes the luni-solar year begins generally at sunrise of the day on which the first tithi of Chaitra is current; that is to say, at sunrise of the day next following the moment of the new-moon of Chaitra.[1] The a, b, c for this moment (taken at Laṅkā) are given in the same Table, cols. 19 to 25, with the lunation-parts and tithis expired since the moment of new-moon. Nothing more is required, therefore, for commencement of work by the sidereal apparent Mēsha saṁkrānti. as mean sunrise
66. But since there is also a mean Mēsha saṁkrānti to be sometimes calculated, which is always later than the apparent Mēsha saṁkrānti by two days and some hours, as well as a tropical Mēsha saṁkrānti, it follows that in work under the mean system, or for the tropical year, the new-moon which marks the beginning of the luni-solar year may not always be the same.
67. Take first the mean system. If a mean new-moon occurs between the moments of true and mean Mīna saṁkrānti, then the month called Chaitra under the mean system will be a month later than the month called Chaitra under the true system; because it is the rule that the lunar year begins with the new-moon next after the Mina saṁkrānti, and in this case the mean new-moon which occurred next after mean Mina was a month later than the true new-moon next after true Mina saṁkrānti. Therefore if we use the mean system, Chaitra is the month succeeding the month called Chaitra under the true system; and under the mean system the previous luni-solar year may be a month longer than under the true system, in consequence of having an intercalary lunar month. In the Indian Calendar, Table I., all the intercalations of months, both true and mean, were carefully registered; but we unfortunately omitted to frame a Table for, or enter in cols. 19 to 25, the necessary mean-system figures (d, w, a, b, c) for sunrise on the initial civil day of the years following those in which an intercalation of a lunar month has taken place under that system, but not under the true system. The figures in those columns for the third year remain unaltered, since in the second of those years there is always an intercalation of a month under the true system and none by the mean system, the civil beginning of the third year being thus the same under both.
68. This omission I rectified two years after the publication of the Indian Calendar by the Table and note given at pp. 12, 13 of my "Eclipses of the Moon in India," and I now reproduce the whole in Table XXIV. below, which contains the necessary mean-system figures for the years noted. Whenever therefore the mean system of intercalations is used the figures given for the years mentioned in those columns must be substituted for the figures in the corresponding columns of Table I. They cover the period from A.D. 300 to 1100.
69. One example will suffice. Take the years A.D. 309, 310, 311. In A.D. 310 a true new-moon took place on February 16th, and another on March 17th. True Mina saṁkrānti occurred by the Ārya Siddhānta on February 14th, and mean Mīna on February 17th. The February new-moon (both true and mean) fell between the two. Therefore by the true system the initial moon of the year was that of February 16th, and the luni-solar year began at sunrise on February 17th, as entered in Table I., col. 19. But by the mean system the initial new-moon was that of March 17th, and the luni-solar year
- ↑ See the third paragraph of § 52, p. 31, Indian Calendar, and p. 55, note 2.