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which his calculation may be assumed to be sufficiently accurate. The Table given below in § 162 shows the time-difference to be applied in any year to the moment of mean Mēsha saṁkrānti according to the Ārya Siddhānta in order to obtain that moment according to the Original Sūrya Siddhānta.

I shall first give the rule for work according to the full process, which explains itself, and afterwards give a rule for shorter work which may be adopted in practice.

(a) The full working-rule. Take down the day, hour, and minute for true Mēsha saṁkrānti in the given year by the Ārya Siddhānta. Add the amount of the Ārya Siddhānta śōdhya. This gives the moment of mean Mēsha saṁkrānti by that authority.^[1] Apply the time-difference for the year as given in the Table in § 162. This gives the moment of mean Mēsha saṁkrānti by the Original Sūrya Siddhānta. Deduct the amount of the Original Sūrya Siddhānta śōdhya. This gives the required moment of true Mēsha saṁkrānti by the latter. We are thus enabled to obtain the moments of both true and mean Mēsha saṁkrānti by the Original Sūrya Siddhānta, as required.

For an example take the year A.D. 300. We want the moments of true and mean Mēsha saṁkrānti by the Original Sūrya Siddhānta in that year. (M.S. = Mēsha saṁkrānti; Ā.S. = Ārya Siddhānta. O.S.S. = Original Sūrya Siddhānta):—

True Mēsha saṁkrānti according to the Original Sūrya Siddhānta, therefore, took place in A.D. 300 on March 16th at 12 h. 27 m. after mean sunrise. Mean Mēsha saṁkrānti by that authority took place in that year on March 18th at 18 h. 12 m. after mean sunrise.

(b) The shorter rule. It will be observed that the difference in results between the two authorities depends on two elements, (i) the difference in the value of the śōdhya between the two Siddhāntas, and (ii) the time-difference given in the Table in § 162. Since we take the value of (i, the śōdhya, as a constant in each case, the difference between them is also a constant. It amounts to 2 d. 5 h. 45 m. 12 s, − 2 d. 3 h. 32 m. 30 s., or 2 h. 12 m. 42 s., by which interval the true Mēsha saṁkrānti by the Original Sūrya Siddhānta was in every year earlier than the moment of true Mēsha saṁkrānti by the Ārya Siddhānta. The time-difference (ii) shown in the Table in § 162 varies every year. We can, therefore, take at once the moment of true Mēsha saṁkrānti for any year according to the Ārya Siddhānta; deduct (i) the constant, or śōdhya-difference, roughly 2 h. 13 m.; apply (ii) the time-difference for the year (Table in § 162, p. 57); and thus obtain the moment of true Mēsha saṁkrānti by the Original Sūrya Siddhānta.

We take, again, the year A.D. 300:—

This result is precisely the same as that obtained by the longer process.

1. ↑ Or obtain the same by use of Table XXXVIII.C.