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Sunday, December 1st, on which day at sunrise the 1st śukla tithi was current. The inscription therefore may be considered as correct when computed by mean lunar months.

Another, and perhaps easier, way of work for mean lunar months is, after finding the a of mean sunrise on Chaitra śukla 1st of the year in question, with its ${\displaystyle d}$ and ${\displaystyle w}$, to add from Table IV. the ${\displaystyle d}$, ${\displaystyle w}$, and ${\displaystyle a}$ of the days intervening to mean sunrise on the given day, and thus to find the ${\displaystyle a}$ of the latter. Thus, in the instance just considered, we had, for mean sunrise on Chaitra śukla 1st, ${\displaystyle a=294}$. The interval to mean sunrise of Pausha śukla 1st is 265 days.

(335) =, by Table IX., December 1st. 1 = Sunday. 31 =, by Table X., 2 h. 12 m. And this shows that the mean new-moon of Pausha occurred 2 h. 12 m. before mean sunrise on Sunday, December 1st, A.D. 989. The difference between the two methods is only 2 m.; the former method being the more accurate of the two.

93. Calculation by true lunar months and tithis was made for this date by the late Professor Kielhorn (Epig. Ind. IX., 207, No. 137), and he informs us that the true 1st śukla tithi of Pausha began, i.e., true new-moon occurred, at 5 h. 6 m. after mean sunrise on Sunday, December 1st. If so it would appear that very probably calculation had been made by mean lunar months, since, in that case, Sunday, December 1st, would have been rightly coupled with the first śukla tithi. The tithi current according to calculation by true months at sunrise on that day was the last tithi of the previous month Mārgaśīrsha, and in ordinary circumstances that tithi would have been coupled with the Sunday.

95. (See Indian Calendar, §§ 45, 46, pp. 25 to 27.) The length of a true solar month varies from, by the Sūrya Siddhānta, 29 d. 7 h. 38 m. to 31 d. 15 h. 28 m., and by the Ārya Siddhānta from 29 d. 8 h. 25 m. to 31 d. 14 h. 34 m. The length of the true synodic lunar month, new-moon to new-moon, varies from 29 d. 7 h. 20 m. to 29 d. 19 h. 30 m. Consequently it happens, roughly about once in every two or three years, that during a whole lunar month there is no saṁkrānti, and more rarely a lunar month in which there are two saṁkrāntis. Since ordinarily each of the twelve lunar months ends after each of the solar saṁkrāntis, a lunar month in which there is no saṁkrānti has to be repeated, or intercalated, and then, the second of these months ending after its proper saṁkrānti, the rotation of months continues as before. The first of the pair of months is called adhika ("added") and the second nija (or "true"). When there are two saṁkrāntis in the lunar month the name of a lunar month is suppressed, because from the point of view of the rotation of months it is superfluous; since the new-moon at the end of that month ends next after two saṁkrāntis instead of after only one. It is in this sense that there is said to be a "suppressed month," i.e., the name of one month is omitted. Such a suppressed month is called a kshaya māsa.

96. As to the naming of adhika and kshaya months there is a divergence in practice on which it is not necessary here to enter. I confine myself to the ordinary nomenclature, which calls the first (added) month adhika, "added," or prathama ("first"), and the second nija, "true," or dvitīya ("second"). And I shall not deal with the different ways of naming pūrṇimānta months. The system of work for calculating these is always the same; the only difference being in the names. But in examining dates these different practices must always be borne in mind lest a genuine date should be unjustly condemned because the name of the given month differs from that found by the ordinary system. A full discussion of the matter will be found in the Indian Calendar (pp. 25–31).