सिद्धान्तदर्पण (महामहोपाध्याय सामन्त चन्द्रशेखर सिंह - नग्न-नेत्र खगोल वेध एवं गणित महाकोश)

Introduction xlvii
assigned by the astronomers. We have already seen
the various rates assigned by them. As the
Surya-Siddhanta's rate of 54 seconds per year is a
close approximation to the rate known at present,
let us take this first for consdieration.
Apparently, the rate of 54 seconds is hihger by
nearly 4 seconds than the actual. I say apparently
for the rate makes the ayanamsa less, instead of
increasing it in the proporiton of about 50 to 54. It
must be therefore really lower than the true rate.
To explain the anomaly we have to consider the
Siddhanta year. The length of the sidereal year -
the year used by us instead of the tropical year in
use in Europe - is 365.25875 mean solar days
according to the Surya-Siddhanta, and is thus
greater than the true length by 0.00238 days. Now,
taking the Sun's daily motion at 59'8", we find that
during the excess the Sun moves to the East through
a distance of 8".44 nearly. But the equinoctial point
moves to the West. It is therefore clear that the
precessional rate assigned by the Surya-Siddhanta
is practically 54"-8°.44, or 45".56 per year. It is for
this reason that the ayanamsa, calculated from the
Siddhanta, apparently higher rate, becomes less
than the amount observed. Hence if we accept the
Siddhanta's length of the year, we should make the
annual precessional rate 50" 24+8" 44 or 58".68. It
is remarkable that the rate of 45".56 per year is
almost equal to the precessional rate in Right
Asscension. Whether the Siddhanta writer meant
the rate to be what we find, I cannot say, though
there are certain reason favourable to our
conjecture. The point may be illustrated by taking
other Siddhantas. Bhaskara's year consists of
365.25843 days, and is therefore longer by 0.00206