58 DIRECTION, PLACE AND TIME mouth and tail of the fish-figure indicates the north and south directions with respect to the gnomon.¹ the point where Let ENWS (See Fig. 3) be the circle drawn on the ground, and O its centre where the gnomon is set. Let W₁ be the shadow enters into the circle (in the forenoon), and E, the point where the shadow passes out of the circle (in the afternoon). Join E, and W₁. The line E₁W₁ is directed east With E, as centre and with E,W₁ as radius² draw an arc of a circle, and with W, as centre and with the same radius draw another arc cutting the former at the points N₁ and S₁. Join N₁ and S₁. The line N₁S₁ is directed north to south. to Fig. 3 Let the line N₁S₁ meet the circle in the points N and S and the line through O drawn parallel to E,W₁ in E and W. Then E, W, N, and S are respectively the east, west, north, and south directions relative to the gnomon, i.e., for an observer situated at O. E E X²₂0 W S The figure N₁E,S,W₁N₁ is called "fish or fish-figure", and the points N₁ and S, are called the mouth and tail of the fish-figure. As the Sun moves along the ecliptic, its declination changes. By the time the shadow moves from OW₁ to OE₁, the Sun traverses some distance of the ecliptic and so, theoretically speaking, its declination gets changed. It follows that EW is not the true position of the east-west-line. Brahmagupta (628 A.D.) was probably the first. Hindu astronomer who prescribed the determination of the east-west line with proper allowance for the change in the Sun's declination. The details of the method intended 1 This rule is found also in SuSi, iii. 1-4; BrSpSi, iii. 1; LBh, iii. 1; SiDV, I, iii. 1; MSi, iv. 1-2, Sise, iv. 1-3; and Sisi, I, iii. 8-9. 2 In general, as Parameśvara says in his comm. on LBh, iii-1-3 this radius may be any length greater than (1/2) E₂W₁. 3 Varahamihira calls this figure "yava (barley or barley-figuresr. also. See PSi, iv. 19.
