Page:Sewell Indian chronography.pdf/49

577 − 155 = A.D. 422. Since therefore we know from Table I., cols. 13 to 17, that the Mēsha saṁkrānti of A.D. 422, K.Y. 3523 expired, occurred on March 18th (Saturday), at 4 h. 25 m. Laṅkā time, we also know that the moment of Mēsha saṁkrānti of our given year (K.Y. 2947 expired) occurred on Tuesday, March 13th, 155 B.C., at 4 h. 25 m. Lankā time.

Professor Jacobi (Ind. Ant. XVII., pp. 159, 160) has given the value of ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$ for a difference of 5000 years, 1000 years, and 100 years. We take the 1000-year difference and work from a base already given us in Table I. of the Indian Calendar. The difference is ${\displaystyle a=4687.4}$, ${\displaystyle b=500}$, ${\displaystyle c=24.1}$. The thousandth year from K.Y. 2947 expired is K.Y. 3947 expired. For this year Table I. (cols. 19 to 25) gives us the starting point.

	a.	b.	c.
Mean sunrise of March 2nd, A.D. 846 (K.Y. 3947)	9961	162	225
Interval of 1000 years	4687	500	24
Mean sunrise of March 2nd, 155 B.C. (K.Y. 2947)	4648	662	249
(Table VII.VI.) Equation ${\displaystyle b}$	21
(Table VII.) Equation ${\displaystyle c}$	0
${\displaystyle t=}$	4669

By Table VIII., col. 3, we find that the 15th śukla tithi was then current. We want the moment of the preceding new-moon; since a little calculation shows that at the Mēsha saṁkrānti of K.Y. 2947, which occurred eleven days later, the moon must be waning.^[1] New-moon occurred about 15 days earlier. Find ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$ for sunrise 15 days earlier.

	a.	b.	c.
Mean sunrise of March 2nd	4648	662	249
Interval of 15 days (Table IV.)	−5079	− 544	−41
Mean sunrise of Febuary 15th	9569	118	208
Equation ${\displaystyle b}$	235
Equation ${\displaystyle c}$	2
${\displaystyle t=}$	9806

10,000 − 9806 = 194 =, by Table X., 7 h. 5 m. + 6 h. 40 m. = 13 h. 45 m., and we therefore know that, on a first approximation, new-moon occurred on February 15th, 155 B.C., K.Y. 2947 expired, at 13 h. 45 m. after mean sunrise. Hence the first civil day of the luni-solar year was February 16th, and for its ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$, at mean sunrise we add the value of ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$, for one day to the value obtained for mean sunrise of February 15th.