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2. In the a, b, c system, adopted by Prof. Jacobi in the Indian Antiquary, Vol. XVII., and by us in the Indian Calendar and in the present volume, we find a final value, after calculation, in terms True and
mean time. of t or lunation-parts, each of which is 1/10000th of a mean lunation. This is converted into time by Table X., which gives the value of t (or n or y or, in mean calculations, of a) in mean time. Each unit of t, or in mean calculations of a, is on an average 4.25 minutes, so that t = 4 means 17 minutes. But actually the time value of 1/10000th of an apparent, or true, lunation constantly varies. It is therefore only possible to tabulate for mean time. The value of t arrived at by the first process of calculation (see working on p. 81, Ind. Cal.) is approximate. When the processes are continued the final result is accurate. In the case of mean added months the value of a (which then) is at once absolutely accurate. (Ind. Cal., § 82, p. 50.) But when these values are converted into time by Table X. the result is in mean time. For conversion to true time, for the latitude of the place and for the time of year, see Prof. Jacobi's article in Epigraphia Indica, Vol. II., and Tables F and G of my Eclipses of the moon in India.
3. Since the processes recommended in this work compel us to add together figures representing whole units, in the case of which fractions below half are ignored, it sometimes happens that one Small differences
in calculations. element a little too large cancels the irregularity of another a little too small; it also sometimes happens that the total is one unit too small or too large, rarely two. Every very close or doubtful case should therefore be freshly examined by Prof. Jacobi's "Special Tables" in the Epigraphia Indica, Vol. I.
4. The Tables in this work are principally concerned with the First Ārya Siddhānta and Present Sūrya Siddhānta. The Siddhāntas. As to the dates from which these authorities came to be relied on by the framers of Hindū almanacs, and to the parts of India in which their use became prevalent, see §§ 4, 6–13A, and generally in the Text above. The Tables are not, unless specially so mentioned, to be relied on for calculation by other authorities or for other times and places.
5. Calculations by the true or apparent motions of the sun and moon must always begin, for True and mean
calculations. solar dating, from true Mēsha saṁkrānti; and by the mean motions from mean Mēsha saṁkrānti. Similarly, for lunar dating, calculation by true lunar months and tithis must begin from the first true new-moon of the year, and by mean lunar months and tithis from the first mean new-moon of the year.
6. When calculating by mean intercalations of lunar months Table XXIV. must be used. Table XXIV. It takes the place of Table I. for the a, b, c and date of the first civil day of the luni-solar year in the case of a year which does not contain a mean intercalation, but which immediately follows a year which does contain one and in which there was no "true" intercalation.
7. No suppression of a lunar month seems to be possible except in the case of a year separated Suppressions of lunar months. by one of the following intervals of years from a year which contained a suppressed month: 19, 38, 46, 65, 76, 122, 141.
8. Table I., cols. 8 to 12, Indian Calendar, contain the calculations for intercalations and suppressions of lunar months by the true or apparent system; Conversion of results for
intercalations and suppressions
of lunar months. cols. 8A to 12A contain the same by the mean system, of months; calculated, that is, in the first case by the true motions of the sun and moon, and in the second by their mean motions. (For the meaning of "lunation- parts" see Arts. 80, 81, pp. 49, 50.) All these are calculated according to the Sūrya Siddhānta. If results by the First Ārya Siddhānta are required, they must be converted by the rules and examples given. The a, b, c entries given in cols. 23–25 are the same by both these authorities.