TRUE DAILY MOTION OF MARS, ETC 151 because the rules depend upon the use of the table of Rsine-differences. It is assumed that the Rsines very uniformly, so the results obtained from the above rules are only approximate as the author himself admits. The true daily motion is required for the purpose of computing dis- placements of the planets. In the case of the Sun and the star-planets (Mars, Mercury, etc.), the daily motion is small enough and not much error is introduced by using the jivabhukti but in the case of the Moon the daily motion is so much that the use of the jivabhukti in computing displace- mets of the Moon may cause serious error. This thing was noticed by the author of the present work himself who in his smaller work, the Laghu-Bhās- kariya, has criticised the jivabhukti and has preferred the karnabhukti, i.e., the daily motion derived by the use of the instantaneous distance of the planet. Lalla, the author of the Sisya-dhi-vṛddhida, also has pointed out the above-mentioned discrepancy of the jivabhukti. In the works of Brahma- gupta, Lalla, and Sripati, the rules of finding the true daily motion of the planets are based on the distances of the planets.³ The object of devising rules depending on the instantaneous distances of the planets was essentially to obtain the instantaneous velocities of the planets, but the aim was not wholly achieved by the rules given by Brahma- gupta, Lalla, and Sripati. For the velocity obtained by their methods turned out to be the same as the mean daily motion of the planet at the intersection of the concentric and the eccentric, which was wrong. An accurate rule for the instantaneous velocity of a planet was given by Man- jula (932 A. D.) and by Aryabhata II (c. 950 A.D.). The method was fully explained by Bhaskara II (1150 A. D.). More accurate rules occur in the Tantra-sangraha of Nilakantha,5 'Instantaneous velocity is known in Hindu astronomy by the terms tātkāliki-gati, tatkala-gati, tatkṣaṇa-gati, tatsamayajā-gati, and velā-bhukti. ¹ ii. 14-15. 2 SiDV, I, ii. 43. 3 The rules are given in Br.Sp.Si, ii: 41-42; Ś¡DVṛ, I ii. 45-46; and Sise, iii. 42-43 respectively.
- See ŚiDVṛ, II, i. 13(ii) and also SiŚi, II, v. 39.
5 The rules of Mañjula, Āryabhaṭa II, Bhāskara II, and Nilakantha are given in LMā, ii. 4(ii), MSi, iii. 15 (ii). 27; SiSi, I, ii. 37, 39; and TS, ii. 51-52 respectively.
