223 20. The difference between the mean longitudes of Mars and Jupiter is exactly 5 signs. Say what is the number of days elapsed since the beginning of Kaliyuga and what are the (mean) longitudes of Jupiter and Mars.¹ EXAMPLES 21-22. The Sun and Moon on a Sunday at sunrise are carefully seen by me in (the sign) Libra. The degrees of their (mean) longitudes are 12 and 2 respectively; the minutes are 1 and 40 respectively. After how many days will they assume the same longitudes again (at sunrise) on a Thursday, Friday, and Saturday respectively? (It is also given that) the (mean) longitude of the Sun is in excess by 17 seconds (over that given above); whereas from the (mean) longitude of the Moon (given above 18 seconds have to be subtracted.2 That is to say, the Sun's longitude-6 signs, 12 degrees, 1 minute, and 17 seconds; and the Moon's longitude-6 signs, 2 degrees, 39 minutes, and 42 seconds. Calculation will show that the Sun and Moon assume these longi- tudes on a Sunday 7500 days after the commencement of Kaliyuga. The problem now is to find out the aharganas when the Sun and Moon again assume the same longitudes at sunrise on a Thursday, Friday, and Saturday respectively. This is done as follows: (i) Ahargana for Thursday. Let the corresponding ahargana be 7500 +A. Obviously, in A days the Sun and Moon will describe complete revo- lutions. Also since Thursday is four days in advance of Sunday, therefore A-4 will be perfectly divisible by seven. In other words, 576A 78898A 210389' 2155625². will be whole numbers. If we assume A and A-4 7 131493125X, the first two ¹ This example has been solved in chapter I under stanza 52. See supra, p. 44. • Bhāskara I's example, occurring in his comm. on A, ii. 32-33. 8 This number is the L.C.M. of 210389 and 2155625.
