पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

IX. 10 IX. SAURA-SIDDHĀNTA — SOLAR ECLIPSE 209
said that EX is equal to CS. XS is equal to CE, both being equal to 120'. Angles SXE and SCE are
also equal, since they are 180° minus the equal mean anomalies, SXA and SCA. Therefore, the two
triangles are congruent, and so angles XSE and CES are equal, as required to be shown. In the
matter of the correctness of the degrees of epicycle we have to take the authority of the work. That
it agrees with the Original Saura can be seen, the same being found also in the Ārdharātrika system
and Khaṇḍakhādyaka.
Bhujāntara correction
We shall now show why the correction called Bhujāntara is done. The Days used in the formulae are
mean solar days. (That is why the mean longitudes are taken to be proportional to them.) There-
fore the true longitudes got are for mean noon. But we want the longitudes for true noon. So we
have to apply a correction which is the motion during the interval between mean and true noons.
If the Sun's Eq.C. is positive it is east of its mean position, and reaches the meridian later than mean
noon by a certain number of prāṇas (prāṇa = 4 seconds of time, one sixth of a vināḍī) equal to the
number of minutes of arc. Being later, the Sun and Moon's motion during the interval has to be
added. If the Eq.C. is negative, then the true Sun is west of its mean position and true noon is earlier.
Therefore the motion is to be subtracted. The motion in the interval is found by the proportion:
(Since there are 21600 prāṇas in a day) 21600 : daily motion :: Minutes of Sun's equation of the
centre: motion during the interval. From this it can be seen that this correction has got to be done
not only to the Sun, but also to the Moon and the star-planets as well.
Udayāntara correction
We must add that this correction for equation of the centre is not sufficient. Another correction
has got to be made for what is called Udayāntara or reduction to the equator, i.e. reducing the
motion on the ecliptic to motion on the celestial equator which is the circle on which time has to be
measured. Both these corrections form the equation of time, being the interval between true and
mean noons. But Hindu astronomers prior Śrīpati were unaware of this correction.
[देशान्तरसंस्कारः]
पञ्चाशता त्रिभिस् त्र्यंशसंयुतैर्योजनैश्च नाड्येका ।
समपूर्वपश्चिमस्थैर्नित्यं शोध्या च देया च ॥ १० ॥
Deśāntara correction
10. One nāḍī for every 53 1/3 yojanas has to be deducted or added (to Ujjain
noon) by people in places east and west, respectively, of the Ujjain meridian,
(to get their own noon.)
Ujjain was the Greenwich of the Hindus, and the line of longitude passing through Laṅkā, Ujjain
and the North pole was taken as the prime longitude. It is well-known that noon occurs earlier and
earlier as the longitude of a place is more and more east, and vice versa. The author says that for
every 53 1/3 yojanas of distance east or west, there is one nāḍī earlier or later. The idea is that there-
fore the daily motion of the body should be multiplied by the nāḍīs got, divided by 60, and the
resulting minutes of arc should be subtracted or added to the true longitude, according as the place
is east or west, to get the longitude for local noon.
10a. A. पञ्चांशताः