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

IV.31 IV. THREE PROBLEMS 105
cara is zero there, the day-time being always 30 nāḍīs there. The Sanskrit name 'Laṅkodaya' itself
suggests this, Laṅkā representing a place on the equator.
Example 11. At a certain place the equinoctial shadow of a twelve-unit gnomon is 5 units. Find the ascen-
sional differences of the twelve āsis. (sāyana).
By III.10 the cara-vināḍīs – differences for the place, pertaining to Aries, Taurus and Gemini, are
5 × (20, 16½, 6¾) = 100, 82½, 33¾. The half-cara differences are, respectively, 50, 41, 17 vināḍīs.
in the southern hemisphere it is the other way. It is called Unmaṇḍala because it is raised in one’s
Aries : 278 − 50 = 228 Libra : 278 + 50 = 328
Taurus : 299 − 41 = 258 Scorpio : 299 + 41 = 340
Gemini : 323 − 17 = 306 Sagittarius: 323 + 17 = 340
Cancer : 323 + 17 = 340 Capricorn : 323 − 17 = 306
Leo : 299 + 41 = 340 Aquarius : 299 − 41 = 258
Virgo : 278 + 50 = 328 Pisces : 278 − 50 = 228
The procedure is thus explained: The horizon of a place on the equator (i.e. zero latitude)
appears raised towards the north pole to a person in the northern hemisphere on account of the
elevation of the pole as we go north and submerged towards the submerged south-pole. To a person
in the southern hemisphere it is the other way. It is called Unmaṇḍala because it is raised in one’s
own hemisphere. The Right ascensional differences having reference to the horizon of zero
latitude, i.e. the unmaṇḍala. But what we want are the ascensions, i.e. risings from the horizon of
the place. Therefore the risings are earlier when the declination of the rāśi is north, (for places in
the northern hemisphere), by the time the Sun takes to move from the horizon to the unmaṇḍala
along the diurnal circle, and later by the same time when the declination is south. It has been
explained that this time is equal to the half-cara vināḍīs. So, with reference to the points of the triplet
Aries, Taurus and Gemini, whose declination is north, the half-cara has to be deducted. As the
declination increases, rāśi by rāśi, the differences of half-cara have to be subtracted one by one, until
the maximum half-cara is reached. There the declination decreases as it has increased, still being
north, and the half-cara which has to be deducted decreases in the same manner. So the differences
are added in the reverse order in the second triplet, i.e. Cancer, Leo and Virgo. In the next triplet,
viz. Libra, Scorpio and Sagittarius, the south declination increases, i.e. the additive half-cara
increases, and to the half-cara differences are again added, in the regular order, because in the
third triplet the south declination increases in the same manner as the north declination in the first
triplet. Then in the fourth triplet, i.e. Capricorn, Aquarius and Pisces, the south declination
decreases, i.e. the additive cara decreases, and so the differences have to be deducted. (All this can
be seen clearly on a globe). From the explanation it can be seen that for places in the southern
hemisphere, the risings of the rāśīs are those of their seventh in the northern hemisphere.
As great circles intersect one another, the part of the ecliptic above the horizon is always half a
great circle, and therefore the distance between the rising point and the setting point of the ecliptic
is always six signs, as also that of the celestial equator. Therefore the change in the Rt. asc. of the
setting point of the ecliptic is equal to that of the rising point, with the result that the time of the
setting of a sign seventh from the rising point is that of the rising point.