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

XVIII.11 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 319
iii. If the padas are in the next following sector, i.e. 376 to 391, (1486 – padas × padas' ÷ 24 + 5ʳ
9° 30′ + 6ʳ 4° 10′, where the padas used are those gone in that sector.
Though the instructions are laconic, comparison with the Moon's computation makes things
clear. The increasing-motion sector is obviously the 180° from apogee to perigee, where the rate
of motion is supposed by this siddhānta to increase uniformly from a minimum to a maximum. The
apogee is at 180 padas (= 166°) and the perigee at 376 padas(= 345°). The last 16 padas, continued
by the first 180 padas form the diminishing half circle where the rate of motion diminishes
uniformly from the perigee to the apogee. Differentiating the formula, (constant ∓ pada) pada'/24,
the increase or decrease in the rate of motion is found to be 2′/24 = 1′/12 per pada. There may be
a small hiatus at the junction, apogee and perigee, owing to the unequal division of 391 into 196
and 195, to avoid half pada. But the average of the rates at apogee and perigee, (1165′ and 1486′)/
24 = 55′ 1/4, agrees with the mean motion forming one pada. (Incidentally, this justifies our amend-
ment of viṣayarasonā into viṣayaraseṣāḥ. There are other justifications also, as we shall show later).
Further, the first sector being a continuity of the third, the rate during the first pada in the first sec-
tor must follow next to the rate during the 16th pada of the third sector. Since 1486′/24 is taken as
the motion of the first pada, the motion of the 16th is (1486-30)/24 = 1456′/24. This must be the
commencement of the third sector, and this is what is given. We can also see that the fastest rate,
(at perigee), is 1486′/24 = 62′, and the slowest, 1165′/24 = 48′ 1/2, (at apogee), giving the mean
value 55′ 1/4, of the pada, already found. But the rate for the 196th pada, ending which there is the
apogee, is, (1486 − 195 × 2)′/24 = 1096′/24. But the minimum motion falling at apogee is given
as 1165′/24. This hiatus*must also be due to the fact that the 2′/24 increase in the rate per pada is
only approximate, and the actual is a little less than 2′/24. But the formulae are so given that the
total of the first sector is (1456 − 180) 180′/24 = 5ʳ 9° 30′, as given. The total of the second sector
is, (1165 + 195) 195′/24 = 6ʳ 4° 10′. The total of the third sector is, (1486 − 16) 16′/24 = 16° 20′.
These add up to 12 rāśis, exactly, as they should. Incidentally, this justifies my emendation of
guṇāṁśāḥ into yugamśāḥ, pāñcaguṇite into padaguṇite, and giving the meaning of tryaṣṭaka as 3 × 8
= 24. The justification for correcting vidhṛtayaḥ into khadhṛtayaḥ to get 180, and rasonā into raseṣā
to get 1165, are also reinforced by this perfect agreement found here.
TS and NP also give khadhṛtayaḥ:, seeing the reason for that. TS emend rasonāḥ into rasenā (= 1265),
which will give the total 6ʳ 17° 43′, far from the correct 6ʳ 4° 10′. The text itself gives 6ʳ 3° 10′, one
degree off. TS give 6 rāśis exactly, not knowing the peculiarity of this Siddhānta. Using cakrārdhe
thus, they are left with guṇāśaḥ daśa ca kulāḥ. This they interpret as 13° (wrongly, for it can mean
only 30 or 103). Emending daśa ca kalāḥ into paraśakale, they say that this 13° is the total motion of
the third sector. They do not realise that the 16 padas of the third sector is near perigee, and the
total motion must be greater than the mean motion, 14° 44′. Not knowing the nature of the method
here, they think that the total of the third sector also should be given. It has no use, and Varāhamihira
has not given it.
About pāñcaguṇite tryaṣṭakabhājite, I have emended pāñca into pada, to delete the one mātrā in
excess, and to give the agreement already seen. tryaṣṭaka is 24, as already said. TS retain the pañca,
but emend tryaṣṭaka into aṣṭaka, making it 5/8, leading nowhere.
As for NP, they generally follow TS's emendations. But, for the divisor 8 they suggest the alter-
native 83 (tryaṣṭaka). Unlike TS, they realise that the three sectors must add upto 12 rāśis and make
their own emendation of the last part of verse 11, as dviguṇāṁśā daśa sadalā, interpreting it as 20°
30′. NP have given the gist of verse correctly, but making a lot of unnecessary emendations. They
have wondered in Part II, why such small units, as padas, have been taken. This is because, they