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

44 PAÑCASIDDHĀNTIKĀ III.3 naturally differ. Secondly, even if all Siddhāntas had started reckoning from the same point origi- nally, the difference in the duration of their solar years would, in course of time, cause differences in longitude when computed for a particular moment of time, causing apparently a shift of the first point. Thus as the first point of the Paulīśa is about 2° east of that of the Saura or Romaka, the mean Sun is less, as in the case of the Siddhānta Śiromaṇi, which is one degree more because its first point is one degree west of that of the Saura or Romaka. It is also well-known that there is a difference of three degrees between the first point of the Caitra and Raivata Pakṣas. Now we shall explain why 20° is added to the mean Sun to form a peculiar type of Kendram to give the values. Why have the values not been given directly for intervals of mean Sun, 0° to 30°, 30° to 60° etc. The reason must be that the author has taken these values from the original Paulīśa, or the original Paulīśa itself from its source, where they would have been given for intervals of mean Sun, 0° to 30°, 30° to 60° etc. But the source or original Paulīśa's first point might have been 10° east of that of the Paulīśa here given, and it might have been shifted west in course of time to the present first point adopted, (there is evidence in the Vedas of this kind of shift being made, as evident, for instance, in the case of the beginning of the year from the Sun at Mṛgaśirā to the Sun at Kṛttikā and so on) with the result that what was originally 0° had become 10°, what had been 30° had become 40° and so on reckoned from the new point. So the values are as if they are given for 340° to 10° etc. and to make them full rāśis for convenience, 20° are asked to be added and the name kendram given to it. Thus everything is properly explained. TS have not understood the method given here. So far as the explanation of the part referring to the mean Sun goes, what they say is correct. But after that what they say is all wrong. There is the express instruction after giving the first series 11, 48 etc. that the values should be subtracted from the mean Sun. The second series 10, 48 etc. come after that in a separate sentence and a separate verse, with the instruction that the values should be added. But somehow TS have understood the two instructions to mean that the two series should first be added one to one and then the resulting new series, which they think is the equation of the centre itself, should be applied to the mean Sun. If this is done, the instruction where to add and where to subtract is lost, which they have not noted. They have failed to see that the Siddhānta gives differences of values for every 30° intervals of kendram. They have never considered why if the equation of the centre itself is given, it is given in two series which are almost identical. Again, the new series of theirs only appears to be the equation of the centre, which is because the differences of a sine-function-series is a cosine function series, which is again a sine-function-series with a lateral shift of 90° in the argument. In verifying the series they have formed by comparing it with the actual, which they have computed, they have found a difference of 6' and 7' in two terms, but waived them aside as negligible. But 6' or 7' are too large to be negligible. Further, they have failed to see that the word kendram is used here in a peculiar sense as we have already said. They have taken it to mean the regular anomaly. But the mean anomaly can be found only if the longitude of the higher apsis is given, which is nowhere to be found. They explain this by saying that the longitude of the apsis was well known and therefore not given! Different Siddhāntas give different values for the longitudes of the apsis; the Romaka gives 75°, the Saura gives 80°, and the Āryabhaṭīya and Sūrya Siddhānta give 78°. Which of these are we to take? Certain things and operations, we can understand from the context and nature of the work, but this is not a thing which can be learnt without being told, as also the instruction when to add or when to subtract the values, which, according to them, has also to be learnt otherwise. If they had only tried to work out some examples, as for instance, taking the mean Sun as 80°, using their interpretation of the rules, then they would have discovered their mistake.