170 ECLIPSES The direction (of the akşa-valana) for the middle of the ecliptic is the same as that for the first contact. In the forenoon, the directions (of the akşa-valana) in the eastern and western halves of the disc (of the eclipsed body) are north and south respectively. To the west of the sky (i.e., in the afternoon), the akşa-valana is always of the contrary direction.¹ The great circle of the celestial sphere which has the centre of the eclipsed body as one of its poles is called the horizon of the eclipsed body. Suppose that the prime vertical, the equator, and the ecliptic intersect the horizon of the eclipsed body at the points E₁, T₁, and Y, respectively towards the east of the eclipsed body. Then the point E₁ is called the east point of the horizon of the eclipsed body; the arc E₁T₁ (which denotes the deflection of the equator from the prime vertical on the horizon of the eclipsed body) is called the akşa-valana; and the arc T₁Y₁ (which denotes the deflection of the ecliptic from the equator along the same circle) is called the ayana-valana. The formula for the akşa-valana stated in the text is Rversin H x Rsin R Rsin (akṣa-valana) = = where H denotes the hour angle (nata-kāla) and the local latitude. This formula is based on inference. Early Hindu astronomers noted that when the eclipsed body was at the intersection of the meridian and the equator, the Rversed-sine of the hour angle was zero and the Rsine of the akṣa-valana was also zero; and that with the increase of the Rversed-sine of the hour angle the Rsine of the akṣa-valana also increased; and further that when the eclipsed body was at the intersection of the horizon and the equator, the Rversed-sine of the hour angle was equal to its maximum value R and the Rsine of the akşa-valana was also maximum and equal to the Rsine of the latitude. They, therefore, supposed that the Rsine of the akşa-valana varied as the Rversed-sine of the hour angle, and to obtain the Rsine of the akṣa-valana for the desired time they made use of the The same rule is found also in ŚiDVṛ, I, iv. 23 and Sise, v. 18. By the eclipsed body here is meant the position of the eclipsed body on the ecliptic.
