पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

26 PAÑCASIDDHĀNTIKĀ II.1 The text here svarakṛta has been changed into kṛtasvara by interchanging the words, as the nature of the work requires it and as this kind of transposition is sometimes found in manuscripts. It is impossible that the Siddhānta itself has made this mistake, not noticing the ascending nature of the series in this part. Next, we are in doubt here about the time of the day (like sunrise, sunset, noon or midnight) for which the Sun is here given. One may think that because no time is mentioned here, not even the instruction to take the ‘Days from Epoch’, one is expected to take the Days of the Romaka or the Pauliśa and with its own time of sunset at Yavanapura, i.e. thirty-seven nāḍīs twenty vināḍīs from sunrise at Ujjain. But later, in dealing with the Romaka itself and with the Saura, the author gives different times of day for different computations (vide VIII.5, IX.1, XVI.1) and hence this doubt. It is likely that the Vāsiṣṭha Sun and Moon are given for sunrise at Ujjain, as we shall show while dealing with the Moon. Another point to be noted is this. The rule gives the ‘True’ Sun directly, without giving the ‘Mean’ Sun. This is possible because this Siddhānta, like the other Siddhāntas of the period like the Āryabhaṭīya, has taken the apogee of the Sun as fixed and, so, for a given day in the solar year there, is a given anomaly with a given equation of the centre, which means a given true Sun. (It is so with the Vākyakaraṇa also, which follows the Mahābhāskarīya based on the Āryabhaṭīya, with this differ- ence that here the days for fixed intervals of the true Sun is given, while in the Vākyakaraṇa the days for the Sun and the Sun for the days, both are given.) The rule is explained thus: In this Siddhānta the solar year consists of 365 ¼ days, (like the Julian year), i.e. of 1461 quarter-days. For convenience of computation, the Days from Epoch are also converted into quarter-days. According to this Siddhānta the true solar year began, i.e. the true Sun was at the first point of Meṣa, 1 ½ days, i.e. 6 quarter-days, before Epoch. So 6 is added to the quarter- days from Epoch to give the true Sun from the beginning of Meṣa. As after periods of 365 ¼ days, i.e. 1461 quarter-days, the Sun returns to the first point of Meṣa, we can divide the quarter-days out by 1461 and take the remainder alone to find the Sun, i.e. its position from the beginning of Meṣa. Now this Siddhānta has found empirically that the true Sun traverses Meṣarāśi in 31 ¼ days, i.e. 125 quarter-days, Ṛṣabha-rāśi in 31 ½ days, i.e. in 126 quarter-days and so on. Thus in 125 + 126 + 126 + 126 + 124 + 122 + 119 + 117 + 117 + 118 + 120 + 121 = 1461 quarter-days the Sun traverses all the twelve rāśis and reaches Meṣa again. That these numbers add upto 1461, and 1461/4 = 365 ¼, the days of the year, is proof of the correctness of our interpretation of the rule. Thus we see that the solar months Meṣa etc. contain each 31 ¼, 31 ½, 31 ½, 31 ½, 31, 30 ½, 29 ¾, 29 ¼, 29 ¼, 29 ½, 30 and 30 ¼ days, respectively. It can be seen that these fairly agree with what is given by the other Siddhāntas. Thus if 125 quarter-days are left over in the year the Sun has traversed Meṣa, if 125 + 126 are left over, it has traversed Meṣa, Ṛṣabha etc. It is obvious that its position within a rāśi is to be found by the proportion: If 30° are for the quarter-days of the rāśi, how many degrees for the quarter-days ultimately left over. Example 1.(a). Days from Epoch 4246. Find the true Sun. (b) Find the true Sun for zero day. (a) Days converted into quarter-days = 4 × 4246 = 16,984. Adding 6 we get 16,990. Dividing out by 1461, the remainder is 919. Deducting 125, 794 is left over; Meṣa is gone. Deducting 126, 668 is left over; Ṛṣabha is gone. Deducting 126 again, 542 is left over; Mithuna is gone. Deducting 126 for Karkaṭa, 416 is left over. Deducting 124 for Siṃha 292 is left over. Deducting 122 for Kanyā,