Brihat Samhita of Varahamihira

lengths of the Ayanamsam as adopted by Mr. K. L. Chatrai and as discovered by me. The question is one of Arithmetical progression. We will suppose,

$a =$ rate of motion of Vernal Equinox when it coincided with the star Revati.

$d =$ the annual increment in the rate.

$l =$ the last term or rate of motion on the first January 1883.

$s =$ the sum of the terms or the length of the Ayanamsam.

$n =$ number of terms or number of years required.

We have the following series:

$a, a+d, a+2d, a+3d, \dots\dots\dots\dots\dots a+(n-1)d.$
$\therefore l=a+(n-1)d. \quad \quad \therefore a=l—(n-1)d.$
$s=(a+l) \frac{n}{2} = { l—(n-1)d+l } \frac{n}{2}.$
$\quad \quad = { 2l—(n-1)d } \frac{n}{2}.$
$\therefore 2s=(2l+d)n—dn^2.$
$\therefore dn^2 — (2l+d)n+2s=0.$

where $l=50''. 34.$
$\quad \quad d=0''. 00024.$
$\quad \quad s=20^\circ 24' 15''$ or $18^\circ 14' 20''.$

Substituting these values, we get $n = 14,66$ and $4,17,368$ years , or $= 1310$ and $4,17,523$ years, before first January 1883 where the bigger figures may be rejected as they refer to the position of the vernal Equinox in its second revolution. So that Varaha Mihira’s time is found to be either $1882—1466 = 416$ A. D. or $1882—1310 = 572$ A. D., according to me or Mr. K. L. Chatrai respectively. Now it is true that $572$ A. D. is in support of the supposed dates, above given, of Varaha Mihira’s birth and death. But I cannot bring myself to believe that Zeeta piscium Zeta Piscium was the Revati of the Hindus, for this simple reason, that it is not on the ecliptic. Several stars of comparatively less importance, stated by the Hindu astronomers to be on the ecliptic are found to be so when examined with the aid of modern astronomical instruments. It is therefore unreasonable to suppose that Hindu astronomers could have blundered in describing the position of the star Revati. As regards the difficulty that Varaha Mihira has quoted from Arya Bhatta—which quotation must be in his Panchasidhantika now lost—it is not improbable that the quotation is from Vridharya bhateean a secondary text by Aryabhatta.