पृष्ठम्:लघुभास्करीयम्.djvu/१६२

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vs. 19] moon's visibility in the light fortnight §9 moonset), both increased by six signs, calculated by the method of successive approximations, give the duration of visibility of the Moon in the light half of the month. 1 The process of successive approximations may be explained as follows : Compute the (tropical) longitudes of the visible Moon 2 and the Sun for sunset and increase both of them by six signs Then find out the asus (A^ due to ob- lique ascension of the part of the ecliptic lying between the two positions thus obtained. Then A 1 asus denote the first approximation to the duration of the Moon's visibility at night. Then calculate the displacements of the Moon ar d the Sun for A x asus and add them respectively to the longitudes of the visible Moon and the Sun for sunset, and increase the resulting longitudes by six signs; and then find out the asus {A 2 ) due to the oblique ascension of the part of the ecliptic lying between the two positions thus obtained. Then A 2 asus denote the second approximation to the duration of the Moon's visibility at night. Repeat the above process successively until the successive approxima- tions to the duration of the Moon's visibility agree to vighath. The time thus obtained is in civil reckoning. If, however, use of the Moon's displacement alone be made at every stage, the time obtained would be in sidereal reckoning. According to theinterpretation of the commentator Sankaranarayana, the translation of the text would run as follows : "The riadis (of oblique ascension of the portion of the ecliptic) lying between the Sun as increased by six signs and the Moon (at moonrisej calculated by the method of successive approxi- mation give the time of moomise (before sunset) in the light half of the month." The process of successive approximations in this case would be as follows: Calculate the longitudes of the Sun and the visible Moon for sunset, and increase the former by six signs. Then find out the asus (flj due to oblique ascension of the part of the ecliptic lying between the two positions thus ob- tained. Then B l asus denote the first approximation to the time between moonrise and sunset. Then calculate the displacements of the Moon and the Sun for B t asus, and subtract them respectively from the longitudes of the visible Moon and the Sun for sunset, and, as before, increase the latter by six signs; and then find out the asus {B 2 ) due to the oblique ascension of the part of the ecliptic lying between the two positions thus obtained. Then B 3 2 C£MBk,vi. 27. 3 i.e., the Moon corrected for visibility corrections.