एतत् पृष्ठम् अपरिष्कृतम् अस्ति

SURYA S}DDHANIA Exidence of Astronomical Method४ We now proceed to consider some of the astronomical methods of the modern Brya Siddhanta and to show thaॐ it has drawn largely from Aryabhata I and Brahmagupta. (0) Instantaneous Daily Moti०१८ ०} Planets «jected by the Hoegitality of Apsis orig. The planets meant are of course the sun and the moon according to the Siddhiruths. The rule for finding the instantaneous dily motion of either of these planets' is perhaps best instrated by considering the case of the moon. According to the modern Sway Siddhanta. (I, 39, 4B) the equation giving the longitude of the moon on any day is = } P° x R sin (}} - 2) 3) where 2 is the moon's mean longitude, ५ tle longitude of the xpogee, P°== the periphery of the moon's epicycle of ap£is where the circumference of the concentric =860° and R=3438 If 1 and n’ be the rates of the mean daily motion of the ioon and be apogee in minutes, whe instantaneous daily motion of Ahe moon is expressed as -= 8 -- (4 -)P° * Tabular difference of aimes ” at aro (0 -a ) B8° 225 = = = =

= =

=

II, 47-49. Here the term “ sine ' means the Indian sine anda is= R Kin 6 , where 8 is the are . The value of R. is also 84B8" according to Aryabhata I, but is=B270’ according to Brahmagupta and 180 &ccording to Varॐ hamihira. The Bines are calculated at intervals of 225' of arc. The above formula for instantaneous daily motion is zeadily demonsth:abed as follows: Suppose l’ to be the longitute of bhe moon after a fractiog , of a day, bhen १em + » ? = = * R . Kin {xm - c+(+ - 7t)}, 868)