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

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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.