Page:Sewell Indian chronography.pdf/52

and number to the second civil day. In other words, it is repeated. But the tithi itself, as a tithi, runs its natural course, and is not repeated. Similarly if a tithi, in consequence of its length being less than the interval between two sunrises and its commencement occurring very shortly after the first sunrise, is not current at either sunrise, but falls altogether between two successive sunrises; then, since the first of the two civil days concerned bears the name and number of the next preceding tithi and the second of the two bears the name and number of the next following tithi, the tithi in question confers its name and number on no civil day. In other words it is expunged from the point of view of civil days. But the tithi itself runs its natural course and is not expunged.

88. The repetition and expunction of tithis then does not affect the tithis themselves, but refers to the tithi-number and name conferred on the civil day with which it is connected.

89. Consequently karaṇas, which are half-tithis, follow one another always in regular order, and since the tithi itself is never repeated or expunged there is no repetition or expunction of karaņas.

90. A true synodical new-moon takes place when, with reference to her and the sun's true position, i.e.. taking into account the lunar and solar equations (equation ${\displaystyle b}$ and equation ${\displaystyle c}$), the centres of the moon and sun are in the same plane with the earth. If the three are in the same straight line a total eclipse of the sun takes place. A mean synodical new moon occurs when, without any reference to the moon's or the sun's true position, i.e., leaving out of account the lunar and solar equations, the distance of the moon from the sun in mean longitude is nil. A mean synodical lunar month measures 29 d. 12 h. 44 m. A true synodical lunar month varies in length from 29 d. 7 h. 20 m. to 29 d. 19 h. 30 m. There is therefore very often a considerable difference between the moments of true new-moon and mean new-moon. A mean tithi is one-thirtieth of a mean lunation, or 23 h. 37 m. 28.093 s. In calculating with our Tables by mean lunar months and tithis we find the position of the mean moon from our ${\displaystyle a}$ alone, which, when increased by the constant 201 as explained above (§ 20), gives us the distance of the moon from the sun in mean longitude; and this is all that we have to consider in such computations. Table I., cols. 19, 20, 23, and Table XXI. enable this to be done.

91. I assume that calculation by mean lunar months and tithis had for its starting point the moment of that mean new-moon which marked the astronomical beginning of the luni-solar year, just as in calculation by true lunar months and tithis the moment of true new-moon is the starting point. An example from an actual inscription-date will best illustrate the method of work. We are given as date Sunday, the 1st śukla tithi of Pausha in K.Y. 4090 expired, A.D. 989–90.

92. Turning to Table I., cols. 19, 20, 23, we find that at mean sunrise on the first civil day of Chaitra in that year, viz., on March 11th, A.D. 989, the 70th day and a Monday, ${\displaystyle a=93}$, or 93 lunation-parts had elapsed since new-moon. Add the constant 201. Then the actual ${\displaystyle a=294}$. This, in mean time, is (Table X.) 14 h. 10 m. + 6 h. 40 m., total 20 h. 50 m. Approximately therefore mean new-moon took place 20 h. 50 m. before mean sunrise on March 11th, or on (1) Sunday, March 10th, the 69th day, at 3 h. 10 m. Laṅkā time. Interval to mean new-moon of Pausha, which is the beginning-point of the given tithi (Table XXI.) = 265 d. 18 h. 36 m., with 6 week-days.

334 = (Table IX.) November 30th. (0) = Saturday. The mean new-moon of Pausha occurred at 21 h. 46 m. after mean sunrise of Saturday, November 30th, A.D. 989, or 2 h. 14 m. before sunrise of