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

368 Sun's at the point of first contact and the moment of con- junction respectively. We may also use calculus to obtain δT, the variation in time for a variation of δβ in β and a variation of δm₁ in m₁ ignoring the small variation in s₁, as follows. T² = ((P + r)² - β²) / (m₁ - s₁) ∴ 2T δT = [(m₁ - s₁) × -2β δβ - ((P + r)² - β²) δm₁] / (m₁ - s₁)² ∴ δT = - β δβ / [T (m₁ - s₁)] - δm₁ ((P + r)² - β²) / [T (m₁ - s₁)²] The first term on the Right hand side gives the variation for δβ and the second for δm₁. Fig. 76 shows the case of totality. [Diagram: Fig. 76] Fig. 76 M₁ M₂ = N₁ C₁ + C₁ C₂ ∴ The Moon has to over- take C from the moment of the beginning of totality to the moment of opposition by the distance C₁ N₁ with a relative velocity of m₁ - s₁. Hence the time of Sammilana- Marda-Khanda is equal to [√(C₁M₁² - β²) × 60] / (m₁ - s₁) = [√((R - r)² - β²) × 60] / (m₁ - s₁) as given, taking β to be constant. Similarly the Un- milana-Marda-Khanda from the position (M₂ C₂) to the position (M₃ C₃) will also be the same, taking β to be constant.