SUN'S LONGITUDE FROM DECLINATION A rule for the determination of the Sun's longitude from its declination : 73 16. The radius multiplied by the Rsine of that (Sun's declination) should be divided by the Rsine of the Sun's great- est declination. The resulting Rsine reduced to arc, or (90° minus that arc) increased by three signs, or that (arc) increased by six signs, or (90° minus that arc) increased by nine signs, according as the Sun is in the first, second, third, or fourth quadrant, is the Sun's longitude.¹ The longitude thus obtained is sāyana. In the above rule a knowledge of the Sun's quadrant is assumed, but nowhere in the present work are we told how to know the Sun's quadrant. From other works on Indian astronomy we learn that it was known from the nature of the midday shadow. In the Pitāmaha-siddhanta² we are given the following criteria for knowing whether the Sun is in the first, second, third, or fourth quadrant: "(When the Sun is) in the first quadrant, the (midday) shadow of the trees is smaller than the equinoctial midday shadow and also decreasing (day to day); in the second quadrant, it is smaller (than the same) but increasing; in the third quadrant, it is greater and also increasing; and in the fourth, it is greater but decreasing". So also says Sripatis, but (for places below the Tropic of Cancer) he adds: "If the (midday) shadow fall towards the south and be on the increase, even then the quadrant is the first. Similarly, if you see that the (midday) shadow (falling towards the south) is on the decrease, you must understand that the quadrant is the second."* 1 This rule occurs also in SuSi, iii. 18-19; and LBh, iii. 32-33. This work is in prose and was edited along with a few other siddhantas in the Joytisa-siddhanta-sangraha by Pandit Vindhyeshwari Prasad Dwivedi, Banaras (1912). 3 Siśe, iv. 70. • Sise, iv. 71.
