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

VIII.15 VIII. ROMAKA-SIDDHĀNTA — SOLAR ECLIPSE 191
It is stated here that,
(i) The Moon’s latitude at new moon = sin (Moon ~ Rāhu) × 7 ÷ 3.
(ii) Parallax-corrected latitude = Moon’s latitude ± parallax correction given in verse 13. (The
upper sign is to be taken if both are of the same direction, and the lower sign, if of different direc-
tions, the resulting direction being that of the greater).
The latitude at new moon is the distance of the Moon north or south of the Sun, as seen by an
observer at the centre of the earth. For an observer on the surface, there is a difference in this, equal
to the parallax in latitude. Therefore they have to be combined, taking the directions into consi-
deration, to find the actual distance as observed, i.e. if of the same direction they have to be added,
and if of different directions the differences is to be taken, the direction being that of the greater.
Though the author wants this to be done at new moon, as the use of the word sama-lipta indicates
– perhaps following the instructions of the original Siddhānta – it will be better if it is done at new
moon corrected for parallax in longitude, that being generally nearer the circumstances.
It is given that the sine of (Moon ~ Rāhu) multiplied by 21 and divided by 9, (it will be easier to
multiply by 7, and divide by 3), is the latitude. From this, the maximum latitude according to this
Siddhānta = the maximum sine × 7 ÷ 3 = 120′ × 7 ÷ 3 = 280′. This agrees with verse 11 above,
as already said. But TS say here that the maximum is 270′, contradicting their statement under
verse 11, that it is 4°, i.e. 240′. Without any reason, they assume here that the maximum is 270′, and
since the maximum sine multiplied by 21 and divided by 9 does not give 270′, they say that the
multiplier and the divisor given are approximate!! The same applies also to NP, vide their derivation
(pt.II, p.63) of the result “i ≈ 4° .... (3c)” and “i ≈ 4:30° ... (10), in contrast to (3c)” (pt.II. p.64).
Further, TS’s statement, that the parallax due to the Sun has been omitted by the author on account
of its smallness, is wrong, for the intention of the author is only to give the relative parallax. The
correct statement would be, “The Sun’s parallax has not been separately computed and deducted
from the Moon’s, as the difference in effect would be negligible”.
[स्फुटबिम्बमानम्]
मध्यममानाऽभ्यस्ता स्फुटभुक्तिर्मध्यभुक्तिभक्ता च ।
भवति कलापरिमाणं तत्कालीनं रविहिमांश्वोः ॥ १५ ॥
True diameter of the orbs
15. The mean angular diameters of the Sun and the Moon, respectively,
multiplied by their true daily motions and divided by their mean daily
motions, gives the true angular diameters at the time of eclipse.
Thus:
(i) The angular diameter of the Sun = 30′ × Sun’s true daily motion ÷ 59.
(ii) The angular diameter of the Moon = 34′ × Moon’s true daily motion ÷ 791.
15. Quoted by Utpala on BS. 5.18 B1.2. भुक्तिमभुक्ति; B3. स्फुटभक्तिमध्यमभुक्तिमत्ता च
15a. A. ॰मभाना॰. A.B. न्यस्ता c. A.B.कलाप्परि. B2. परिमानं
b. A. भुक्तिमध्यमभुक्ति; d. B1.2.हिमांणो:;