Page:Sewell Indian chronography.pdf/47
we gave the day of the month A.D. and the week-day on which that first tithi taken as an apparent or true, not mean, tithi ended in each year. Cols. 21, 22 show how many lunation-parts of that tithi, our "t," had expired at mean sunrise, or by how many of those lunation-parts earlier than mean sunrise. on that day the actual moment of new-moon had occurred; and how much of the first tithi of Chaitra had expired at that mean sunrise. Cols. 23, 24, 25 give the a, b, c for the same moment (§§ 19, 20 above), i.e., for mean sunrise on that civil day. We can therefore start all calculations connected with lunar months from that point. Every successive lunar month begins civilly on the day on which the 1st śukla tithi of the lunar month is current at sunrise.
73. If it is desired to find the actual moment of the Chaitra new-moon we calculate thus—(col. 21 gives the t elapsed, and the mean-time equivalent will be found in Table X. under the head "Tithi-index, t." ) Take, for instance, the year K.Y. 4648 expired, A.D. 1547. At mean sunrise, or 6 a.m., on Tuesday, March 22nd, as we find from Table I., col. 21, 183 lunation-parts had elapsed. From Table X. we have 183 = 7 h. 5 m. + 5 h. 53 m., or new-moon occurred 12 h. 58 m. earlier, or at 5.2 p.m. on Monday, March 21st. This is a close approximation. Absolute accuracy can only be obtained by the full work shown in Examples 20, 21, pp. 91, 93 below.
74. The complete method of work is detailed in § 139, pp. 77–83, of the Indian Calendar.
75. By the amānta system the lunar month ends with the moment of new-moon; by the pūrṇimānta it ends with the moment of full-moon. Calculation for the time of these moments is unaffected by difference of systems; the difference being solely in the nomenclature of the fortnights. Thus the second or dark half, beginning with the moment of full-moon, of amānta Phālguna does not, in the pūrṇimānta system belong to Phālguna but to Chaitra; but the first or bright half which follows belongs under both systems to Chaitra. The tithis of the same dark half are tithis of Phālguna in the amānta system and of Chaitra in the pūrṇimānta system; and the tithis of the following bright half are tithis of Chaitra by both systems.
76. In working therefore for a bright half, or śukla, tithi, we know that the month to which it belongs bears the same name all over India; but in working for a dark half, or kṛishṇa, tithi, we must bear in mind that in different parts of India it is considered as belonging to different months; so that if we make a mistake about this we may be a whole month wrong in the end. (See Ind. Cal., § 13, p. 4; and, for the effect of the different systems on the naming the fortnights of intercalated months, § 45, Table, p. 26, and § 51, p. 30; also Table II., Part 1.)
77. Full details for work are given in the Indian Calendar, § 139, pp. 77–83, and it would be useless to repeat them here; but it will be well that the system should be explained.
78. It is impossible to frame workable Tables showing the exact lengths of true lunar months and tithis, because the length of each of these is perpetually changing. The moon's line of apsides makes a complete revolution every nine years, and in consequence her velocity in different years at the same sidereal point alters rapidly. The time-length of her synodical revolution also changes perpetually in consequence of the daily change in the velocity of the earth at different points of its orbit. And, in addition, her daily motion varies because her own orbit is elliptical. Our system, therefore, which follows that of Professor Jacobi in Vol. XVII. of the Indian Antiquary, is, as has already been explained, to obtain the true state of the moon at any moment by adding to our a (the mean longitudinal distance