Page:Sewell Indian chronography.pdf/88
and the mean longitude of the sun. Deducting the latter from the former we have our "V," i.e., the angular distance of mean Jupiter from mean sun. The true heliocentric longitude of one of our planets, or his longitude as seen from the centre of the solar system, is his mean longitude plus the equation of the centre; and the latter is calculated from his mean anomaly, which is dependent on his perihelion point. (Indian Calendar, p. 5, n. 4.) Since this point is separated by exactly 180° from the aphelion point we subtract the longitude of the latter from Jupiter's found mean longitude and thus obtain his angular distance in mean longitude from the perihelion point, which is the required mean anomaly, “W." From the mean anomaly thus found we find by the Table the proper equation of the centre, and, applying it to Jupiter's mean longitude, find his true heliocentric longitude, "X." But this is his position as seen from the sun, and to obtain the same as seen from the earth, which daily shifts its position, we have to apply the proper equation for parallax. Mr. Dikshit's principle is to find the proper parallax by applying the equation of the centre to the angular distance of mean Jupiter from mean sun (our “V”), the operation resulting in his "second commutation" (our "Y"); and thence calculating the parallax by the Table. Applying this parallax to "X," the heliocentric longitude of Jupiter as found, he finds the required apparent longitude of Jupiter at the given moment as seen from the earth.
As I have already stated, Mr. Crommelin takes exception to portions of Mr. Dikshit's system.
188. This Table, prepared to meet contingencies of the present day, carries on all the details of Table I. of the Indian Calendar, which ended with A.D. 1900, to the year 1950. To preserve complete continuity and prevent confusion it is calculated precisely in the same way as the former. That is to say, cols. 8 to 12 and 19 to 25 are computed by the Sūrya Siddhānta with the bīja, the European dates being, of course, in New Style.
189. For the times of apparent Mēsha saṁkrāntis the figures for cols. 13 to 17A were separately calculated, for the Ārya Siddhānta by the annual increment, and for the Sūrya Siddhānta after conversion of the former by use of the Table on p. 55 of the Indian Calendar; every result being checked by reference to the figures of the year removed from it by an interval of 576 years. (§ 47 above.)
190. The next process was the calculation of the beginning of the luni-solar year, cols. 19-25. We have to find the a, b, c for sunrise on the civil day following the moment of the new moon next later than the moment of apparent Mīna saṁkrānti in each year. (Cols. 13–17a.) Professor Jacobi has given us the increment in a, b, c, for a century as a = 1468.7, b = 450, c = 2.4,[1] but this is for an ordinary century. In the present case, the year A.D. 1900 not having been a leap-year the figures must be increased by the value of a day, viz.: a 339, b = 36, c = 3, and they amount to a = 1808, b 486 c = 5. Taking any year, therefore, we first note the entries in cols. 19 to 25 for a year exactly a century earlier, and calculate from this, by adding the figures for the number of days intervening between the date in col. 19 and the date on which Mēsha saṁkrānti occurred in the given year.[2] This gives us the condition of the moon on that last date, but a century earlier. Then, by deducting two days from the week-day and 1808, 486 and 5 respectively from the a, b, c so found, we find the condition of the moon on the day of apparent Mēsha saṁkrānti in the given year. This done, we add equation b and equation c to a, and by Table VIII. discover what tithi was current at that sunrise. This arrived at, we know that the