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

XVI. 1 XVI. SAURA : MEAN PLANETS 293 Another important matter should be mentioned. In XVI. 10-11, and XVII. 10-11a, VM gives corrections, which are his own, to secure agreement with observation to make the Saura fit for correct almanac-making, which naturally will be demanded by the literate. Thus, in XVI.10-11, certain bījas are given to correct the means of Mars, Jupiter and Saturn and the śīghra of Mercury and Venus. The corrections amount, in terms of yuga-cycles, to: Mars, + 57; Mercury, + 400; Jupiter, – 33¹/₂; Venus, – 150; and Saturn, + 25. These corrections are similar and approximately equal to the famous Vāgbhāvona correction on the Āryabhaṭīya, propounded by his successors in his school, to correct his cycles to agree with their observation. I do not suggest that VM was aware of the Vāgbhāva correction in that form, but the tendency to correct the earlier results with bījas based on observations is found everywhere, whether north or south, a healthy sign of the growth of the science. One might refer also to XVII.10-11a, where VM attempts to correct Mercury and Venus to secure agreement with observation. Another thing is to be noted. In (1) the Āryabhaṭīya, in (2) the Ārdharātrika-pakṣa (which means ipso facto the Khaṇḍakhādyaka), VM's Saura and Bhaṭṭotpala-quoted Paulisa, and in (3) the Later Sūryasiddhānta, the yuga cycles are such that the mean planets are all zero at the beginning of Kali, the Moon's apogee is 90°, and the Moon's node 180°. Now the Āryabhaṭīya had equal yuga-pādas, Kṛta, Tretā, Dvāpara and Kali, i.e., they are equal in length. The other siddhāntas have unequal yuga divisions, Kṛta being 4 parts, Tretā 3 parts, Dvāpara 2 parts and Kali 1 part. If the other siddhāntas also postulate, like the Āryabhaṭīya, that the planets were created and began to move from the beginning of the Kalpa from a zero position, then the cycles should be divisible by 20. But they are not so divisible in all. This necessity is avoided by postulating a time later than the beginning of the Kalpa called 'the time of creation of planets' by the Later Sūrya-Siddhānta, as started in the verse, graharkṣadevadaityādi sṛjato'sya carācaram kṛtābdhivedā divyābdāḥ śataghnā vedhaso gatāḥ || I.24 || and by having both the number of cycles and yuga-cycles divisible by four. In the case of the Moon's apogee, the cycles should be odd, and in the case of Rāhu the cycles should be even, but not divisible by 4. These necessary conditions are indeed found in the Later Sūrya Siddhānta and its kind. Thus, if there is any observed difference in the mean planets, Moon's apogee and nodes, they must be due to the 3600 years elapsed after Kali, for the period *c.*499 A.D. But the observed differences should be only small, and due to error of observation. The cycles must have been, and have been, constructed with an eye to this also. In fact, the number of cycles have been determined by observa- tion, and by using the Diophantine equation (kuṭṭaka). The difference of just 300 days in the length of the yuga, (it does not matter much if it is 328 days, as in the Later Sūrya Siddhānta) to secure equal- ity at *c.*499 A.D., between the Ārdharātrika-pakṣa and the Āryabhaṭīya, which is called, for the sake of distinction, the Audayika-pakṣa, meaning the type beginning the day from mean sunrise at Ujjain, provided the number of cycles are the same. (See tables under XVII.11). There is a difference of just a quarter of a day accumulated from zero Kali to *c.*499 A.D. and the difference is made zero at this point of time. [ताराग्रहाणां मध्यमानयनम्] एष निशार्धेऽवन्त्यां ताराग्रहनि(र्णयोऽ)र्कसिद्धान्ते । तत्रेन्दुपूत्रशुकौ तुल्यगतौ म(ध्य)मार्केण ॥ १ ॥