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JUXE, 1888.J
JACOBI'S TABLES FOR HINDU DATES.
147
March continued to be the initial day of Vaisa- period during which the sun is moving from kha till A.D. 690, for all years which, divided by north to south. four, leave as a remainder 2. The day thus
PART II.-USE OF THE TABLES. found is, however, the civil beginning of the solar month, the day on which the astronomi. Description and Explanation of the Tables. cal beginning of the month, i.e. the Sankránti, In Tables 5 to 8, the value of four quanor entrance of the sun into a zodiacal sign, is tities, a. b. c. d., for different periods is given ; nsually celebrated. The true instant of the e.g. in Table 5 we find that in A D. 1801 (on beginning of a solar month occurred, in any the 1st January) a = 5138, b=566, c=6, year entered in the Table, at or shortly after d=479. For calculating tithis, however, only
nset of the day preceding the civil begin- a. b. c. are wanted ; and we shall therefore, ning of the solar month of that year; every for the present, speak of a. b. c. only. four years it advances by 50 minutes. For The quantity a. (plus the constant quantity example, the solar Vaisakha in A.D. 574 began 200)* gives the mean lunations expressed in astronomically on the 19th March at sunset in 10,000th parts of the unit; or the difference Lauka, or 12 hours Labkå time; and in A.D. of the mean longitudes of the sun and the 622, which year is separated from 574 by 48 moon expressed in 10,000th parts of the circle. (i.e. 12 X 4 years), 12 X 50 minutes = 10 hours And the value a=5138 denotes that, at the later, i.e. on the 19th March, 22 hours, Lanka moment in question, 0-5338 of the current mean time. The moment thus found is some minutes lanation was gone. later than the true one, but this degree of acou- b and c. give, in thousandth parts of the unit, racy will be found sufficient. The astrono- two other quantities on which depends the mical limits of the solar month are wanted for difference of the true longitudes of the sun and determining the name of the lunar months moon, which we shall denote by A. With b. and c. in cases where the true new-moon occurs turn to Tables 9 and 10; there, for the value near those limits. The initial days of the of b. and o. As arguments, is given the equation solar months are also the days of sankránti ; which, added to an gives 4.; e.g. for b. 566, we 1st Vaiśê kha, that of Mêsha ; Ist Jyaishtha, that find by Table 9, as equation, 84; for c. 6 we of Vrishabha; and so on (see at the foot of find, by Table 10, as equation, 58. Adding 84
Table 7). The Ist Magha is the first day of the and 58 to a= 5138, we get A= 5280. The uttarayana, or the period daring which the san value of A. shows whieh tithi was carrent at is moving from south to north; and the Ist the moment under consideration, as presented Śråvaņa, that of the dakshinayana, or the in the following table :Sukla-paksha.
Krishna-paksha. 1 Tithi; 4. is between 1 & 333
1 Tithi ; A. is between 5001 & 5333 334 , 666
5334 5666 667 1 1000
5667
6000 1001 , 1333
6001 > 6333 1334 1666
6334 , 6666 1667 2000
6667 7000 2001 » 2333
7001 2334 , 2866
7334 7666 2667 , 3000
8000 3001, 3333
8001 8333 3334 , 3666
8334 8666 8667 4000
8667 9000 4001, 4333
9001 9333 4334, 4666
9334 9666 4667 5000
9667 , 10000 or 0 Full-moon; 4. = 5000
New-moon; 4. = 0 or 10000 • 200-5 has been subtracted from the exact value of the mean lunation, in order that all corrections to be applied I ob. is the mean anomaly of the moon; and c. the meaa to it for finding the value of the true lunation shall be anomaly of the sun. additive quantities, and not additive in one case, and
7333
7667
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