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

374 Comm. Clear. Verse 20. To get what is called the Valana. The hour-angle of the eclipsed body expressed in nādīs, multiplied by 90 and divided by half the duration of night (if it be lunar eclipse) or half the duration of day (if it be solar) as the case may be will give the degrees of an angle, whose H sine being multiplied by the H sine of the latitude and divided by (H cos δ, (where δ is the decli- nation of the eclipsed body), gives the H sine of what is called Ākṣavalana which is north when the hour angle is east, and south otherwise. Comm. This subject of Valana requires a detailed treatment as is given in the Golādhyāya by Bhāskara. Here only a practical formula is given to proceed with the computation. For an understanding of this formula we have to necessarily draw upon the treatment in Golādhyāya. The word ‘Valana’ means ‘deflection’. The problem posed is at what point of the disc of the eclipsed body does the eclipse begin and at what points it ends. Since an observer sees the disc of the eclipsed body on the back- ground of the spherical surface of the sky, the specification of the point of first contact must necessarily be made with respect to east, west, north and south. These directions could be specified with respect great circles drawn second- ary to the prime-vertical. But the Earth's shadow moves along the ecliptic and the Moon is also very nearly moving on the ecliptic at the moment of an eclipse. Thus ‘Valana’ should give the angle between the ecliptic and the prime-vertical; rather it should be described by two diameters of the Moon's disc, one a secondary to the prime-vertical and one a secondary to the ecliptic. In other words we have to get the angle subtended at the centre of the Moon's disc between those diameters.