50 LONGITUDE-CORRECTION place and the place (on the prime meridian) chosen above, which is known in the world by the utterance of the common people, is the hypotenuse. The square root of the difference between their squares (i.e., between the squares of the hypotenuse and the upright) is defined by some astronomers to be the distance (in yojanas of the local place from the prime meridian).¹ In Fig. 2, let CD be a portion of the prime meridian and AB that of the local circle of latitude. Let L be the local place and Xa place on the prime meridian. L and X being joined, we C get the right-angled triangle XYL. The above rule tells us how to deter- A- mine the distance YL of L from the prime meridian in linear units (i.e., in yojanas). The triangle XYL is suppo- sed to be plane and sides XY, YL, and XL are taken as the upright (koti), the base (bhuja), and the hypotenuse (karna) respectively. Y = X = L Fig. 2 Subtracting the degrees of the latitude of X from those of L (or Y), we get the length XY in terms of degrees. Now the circumference of the Earth is equal to 3299 minus 8/25 yojanas in linear units and to 360 degrees in circular units; therefore, multiplying the degrees of XY by 3299 minus 8/25 and dividing the product by 360, we get the upright (koți) XY in terms of yojanas. The hypotenuse XL is assumed to be known in terms of yojanas by common usage. Hence the above rule. Earth's circumference. In the above rule, as according to Bhāskara I also, the diameter of the Earth has been taken to be equal to 1050 yojanas² and π equal to 3.1416. Therefore, the circumference of the Earth = -B 1050x3.1416 yojanas 3298.68 yojanas (3299-8/25) yojanas. ¹ This rule is found also in BrSp Si, i. 36; LBh, i. 25-26; Ś¡DVṛ, I, 57-58 (i); SiSā, i. 143-144. 2 Vide infra, chapter V, stanza 4.
