सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)

367
[चित्र: Fig. 75]
Fig. 75
the opposition precedes the Moon’s position at the node
β₃ < β₂ < β₁. Also, when β changes, M₁ M₂ does not
exceed C₁ C₂ exactly by C₁ N₁. So, on both the counts,
the formulae, given in verse 12 are approximate. What
is done in practice is that β is computed for the moment
of opposition and estimating the Sparsa-Sthiti-Khanda by
the formula given above, and subtracting it from the time
of opposition the moment of first contact is got. Then β is
computed for that time and again the formula is applied
to get the Sparsa-Sthiti-Khanda. Repeating the process,
we rectify the Sparsa-Sthiti-Khanda. Even then, we do
not have the actual value of the Sparsa-Sthiti-Khanda,
because M₁ M₂ does not exceed C₁ C₂ exactly by C₁ N₁.
A more correct procedure would be to compute the
time between the moment of first contact and the moment
of opposition and by that time, to compute the length of
M₁ M₂ and take [m' (β₁ ~ β₂) / (M₁ M₂)] in the place of m' and use the
formula of verse 12. This nicety, however, need not be
attended to with respect to the duration of totality, for,
it does not make much difference.
Another way of obtaining a better value for T, the
Sparsa-Sthiti-Khanda is to take average values for β₁ and
β₂, m₁ and m₂, s₁ and s₂ where m₁ and m₂ are the values of
the Moon’s daily motion and s₁ and s₂ are those of the