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

92 PAÑCASIDDHĀNTIKĀ IV. 21
signs from sāyana-Tulā, i.e. if the declination is south, subtract the declina-
tion from the arc, the latitude is got.
That is:
i. Sine latitude = 120' × equinoctial shadow ÷ √(144 + equinoctial shadow²). The arc from this
is the latitude.
ii. Sine south zenith distance of the Sun, (SZD) = 120' × mid-day shadow ÷ √(144 + midday-shadow²).
The arc of this is the SZD.
Using SZD, Latitude = SZD±declination ('plus' should be used if the declination is north, and
minus if south.)
Example 5 (a). At a certain place the equinoctial shadow is 5 units. Find the latitude of the place.
Sin. lat. = 5 × 120' ÷ √(5² + 144) = 600' ÷ 13 = 46' 9''.
Arc of 46' 9'' = 22° 37'. The latitude is 22° 37'.
Example 5 (b). At a place when the Sun is at the end of sāyana Tulā, the mid-day shadow is found to be 9 units.
Find the latitude of the place.
From the formula, (the mid-day-Sun's) sin SZD = 9 × 120' ÷ √(9² + 144) = 1080'/15 = 72'.
SZD = arc of 72' = 36° 53'.
The declination of the Sun at the end of Libra is 11° 44'S (from 16-18). Taking the minus sign,
since the declination is south, the latitude = 36° 53' − 11° 44' = 25° 9'.
Note: Rule (i) can be used everywhere, while rule (ii) should be used only if the midday sun is
south of the zenith. If it is north, having north zenith distance, (NZD), declination = NZD =
latitude. But the work being a Karaṇa, the author intends it to be used only in North India, where
the midday zenith distance is always south, and hence this has not been mentioned by him. Further
the author envisages only north latitudes by his formulae.
Sky-sphere (Khagola)
Here onwards, explanations require a knowledge of the sky-sphere (khagola) with the stellar
sphere imposed on it. Therefore we shall describe the sky sphere. Hindu astronomers describe it
as the ‘Casket Boundary of our universe’ (Brahmāṇḍa-kaṭāha-sampuṭa), and marked by the penetration
of sunlight. Beyond that there is no sunlight. The measure of a great circle on the sky-sphere is said
to be the number of yojanas the Moon, or the Sun or any planet moves in a kalpa (yuga according to
the followers of Āryabhaṭa), — though, really, the sphere is only illusory and supposed to have an
indefinite radius. As the stellar sphere also is enormous, we can take the surfaces of the two spheres
sliding on each other, and forming spherical triangles by arcs on each intersecting those on the
other. The problems will entail the solution of these triangles. (The formulae for solution have
already been given). This will be understood by examining Fig. 6.
20-21. Quoted by Utpala on BS 2. pp. 59-60.
20a. A.सममधृष्टो; C.दिनमध्याह्नो                          d. A.C.D.छिंद्यम्
    b. A. om-रूपात्र-om.                            12b. A. चापतोक्षो. A.C.D. ॰थवा यथेष्टदिने
    c. A. शते. A.D.विंशात्                            d. A. खोक्षः