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Col. 2. The entries are all given for the same period, i.e., the mahāyuga, for the sake of comparison; but it should be noted that the Vēdāṅga Jyōtisha and the Paitāmaha Siddhānta made use of a yuga of only 5 years, the Rōmaka one of 2850 years, the Pauliśa and the Original Sūrya one of 180,000 years, while the Brāhma, Parāśara, and Second Ārya Siddhāntas used the Kalpa of 1000 mahāyugas; so also the Siddhānta Śirōmaṇi and, apparently, the Rājamṛigānka.

Col. 7. "(D)" means calculation by the late Sh. B. Dikshit.

"(Sch.)" means calculation by Dr. Schram.

Col. 8. The entry for the Original Sūrya Siddhānta was given to me by Dr. Fleet, from the Pañchasiddhāntikā, vv. 7, 8. have taken those for the Brāhma, Parāśara, Second Ārya, and Present Sūrya Siddhāntas, and for the Siddhānta Śirōmaṇi, from the Table in Burgess and Whitney's "Sūrya Siddhānta," p. 27, and Jacobi's article in Epig. Ind., Vol. I., pp. 440, 442, §§ 75, 83; for the Pauliśa Siddhānta from J. Burgess, J.R.A.S., 1893, p. 759.

Col. 9. The entry for, respectively, the Parāśara, and Second Ārya Siddhāntas, and the Siddhānta Śirōmaṇi, is taken from the Table in Burgess and Whitney's "Sūrya Siddhānta," p. 281; and for the Brāhma Siddhānta from Jacobi's article quoted above (with correction of a misprint).

2. The Paitāmaha Siddhānta. In the Indian Calendar (Table, p. 6) Mr. Sh. B. Dikshit and gave the length of the solar year according to this authority as 365 d. 8 h. 34 m. Mr. Dikshit, who prepared the Table, did not show how he arrived at this figure. Dr. Fleet, however, has kindly looked into the matter for me, with the following result. The elements of the Paitāmaha Siddhānta are given by Varāhamihira in his Pañchasiddhāntikā, chapter 12, verses 1 to 3. The editors, Dr. Thibaut and Mahamahopadhyaya Sudhakara Dvivedi, were dealing with a manuscript which was very corrupt throughout; and in their edition (Benares, 1889) they found it necessary in verse 1 to emend trishadyāptuṁ into dvishashṭyā tu. With this quite reasonable, and in fact unavoidable, emendation, the elements as given there are identical with the elements of the Vēdāṅga Jyōtisha, including the yuga of five years, with 366 days as the length of the solar year, with the insertion of an intercalated lunar month in thirty solar months, and with the expunction of a tithi, or lunar day, in every sixty-two tithis. The three verses in question were quoted by Bhaṭṭōtpala in his commentary below Varāhamihira's Brihat Saṁhitā, 8, 22; and in that commentary as edited by Sudhakara Dvivedi (Benares, 1895) they stand essentially as in the Pañchasiddhāntikā (there are only a few various readings which do not affect the meaning). But it would appear from Dikshit's Bhāratīya Jyōtiḥśāstra, p. 153, that he had a manuscript of Bhaṭṭōtpala's commentary with a different reading which lays down an intercalated lunar month in thirty-two (instead of thirty) solar months; that he found this reading also in Mahādēva's commentary on Śrīpati's Ratnamālā; that he preferred to accept the Paitāmaha as laying down the expunction of a tithi in every sixty-three (instead of sixty-two) tithis; and that on these two bases he arrived at the conclusion that the Paitāmaha, while specifying a yuga of five years, really dealt with a period of eight years measuring ⁠2922+6/7⁠ days; which gives 365 d. ⁠21+3/7⁠ gh., or 365 d. 8 h. 34 m. ⁠17+1/7⁠ s., as the length of the solar year. This conclusion is not admissible; and Dr. Fleet is of opinion that the Paitāmaha Siddhānta is in fact only the Vēdāṅga Jyōtisha under another name.

5. The Pauliśa Siddhāntas known to Utpala. The length of the solar year according to these was the same as that in the Original Sūrya Siddhānta. (Ind. Cal., p. 6, note 2.)

6. The Original Sūrya Siddhānta. For the value of the śōdhya see the end of § 39B in the text.

10. The Second Ārya Siddhānta. See Text, §§ 167B and 167C; and "Additional Notes," II., above, p. xii.

11. The Rājamṛigānka. I give the length of the solar year from the figures supplied by Mr. Sh. B. Dikshit in the Indian Calendar, p. 6. Dr. Fleet tells me that, so far as he can ascertain, no translation of this work is known, nor even a published text.

13. The Siddhānta Śirōmaṇi. The figures in cols. 2, 3, and 4 have been verified for me from the original text by Dr. Fleet.

General Note. The values given in cols. 5, 6, 10 have been calculated from the known values given in cols. 2, 3, 4.