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

42 PAÑCASIDDHĀNTIKĀ III.3

Kendra	0°		30°		60°		90°		120°		150°
Mean Sun	340°		10°		40°		70°		100°		130°
Values for intervals		– 11′		– 48′		– 69′		– 70′		– 54′		– 26′
Real Anomaly	264°		294°		324°		354°		24°		54°
Values taking 140′ as maximum		– 12.9′		– 45.6′		– 67.7′		– 71.6′		– 56.3′		– 26.0′

180°		210°		240°		270°		300°		330°		360°
160°		190°		220°		250°		280°		310°		340°
	+ 10′		+ 48′		+ 70′		+ 71′		+ 54′		+ 25′
84°		114°		144°		174°		204°		234°		264°
	+ 12.9′		+ 45.6′		+ 67.7′		+ 71.6′		+ 56.3′		+ 26.0′

The procedure is explained thus: According to the Paulīśa Siddhānta there are 120 solar revolu- tions in 43,831 days. So, in any desired number of days, the Sun’s mean motion is days × 120 ÷ 43,831 revolutions, which multiplied by 12, 30 and 60 successively gives rāśis, degrees and minutes. The mean solar year begins 16½ nāḍikās after Epoch. Therefore to reckon days from the beginning of the year, 16½ nāḍikās or 33/120 days must be subtracted from the days from Epoch. As the days have already been multiplied by 120 and converted into one hundred and twentieth parts, we have to deduct 33 parts in order to deduct 33/120 days, which is the instruction. But what is called mean Sun here is not the real mean Sun. It is the real mean Sun plus the equa- tion of the centre for the beginning of the year (this makes it the true Sun) plus 7 minutes of arc. That it is so can be seen thus: At the beginning of the year the so-called mean Sun is zero, the Sun having made full revolutions, starting from the zero point 16½ nāḍikās from Epoch. The Kendram at that time is 0° + 20° = 20°. For this we have the difference or interval of equation of the centre, – 11 × 20°/30° = – 6′.67. Deducting this from rā 0-0-0, we have the true Sun rā. 11-29-53. Deducting the equation of the centre from this, the real mean Sun is got, for the true Sun is obtained by adding the equation of the centre to the real mean Sun. Thus the so-called mean Sun = the real mean Sun

• the equation of the centre + 7 minutes = the real mean Sun + 142′ (135′.8 + 6′.67), the equation of the centre at this point being 135′.8 (which we shall show presently). Thus, the so-called mean Sun is practically the true Sun at the beginning of the year (the difference being only 7′) and the beginning of the mean year is therefore practically the beginning of the true year. This, we have alluded to already in verses I.11-13. Now, as this mean Sun has the same rate of motion as the real mean Sun, everywhere the difference of 142′ between them is maintained. Now we shall verify the intervals, i.e. differences of equation of the centre. Let us assume that the longitude of the higher apsis is rā. 2-16-0, according to this Siddhānta. (As the original Siddhānta is lost, we cannot assert that it is so. But if the assumption works, i.e. explains everything to be explained, without leading to contradictions, then we have to take that it is correct.) This is very likely because according to the Romaka it is at rā. 2-15-0 (see VIII.2, where the instruction, “subtract (from the mean Sun) rā. 2-15-0 to get the kendra of the Sun” is given.) The Sūrya Siddhānta, Āryabhaṭīya etc. give rā.2-18-0 for the same; and the earlier Paulīśa may correctly give rā.2-16-0. Now, as the intervals are for mean Sun 340° to 10°, 10° to 40° etc., we can say deducting 76°, they are for anomaly 264° to 294°, 294° to 324°, 324° to 354° etc. (See table above). Assuming the maximum