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No. 14.]
THE PLANETARY TABLES.
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reach the beginning of Dhanus the moon has to travel 240°-80o=160°, which takes her between 12 and 13 days as shown by the above table. She is, therefore, in Dhanus about 12 days after the 20th Ashādha, or about the 2nd solar Srăvana (Karkata). But by this time the Sun has entered Karkata, since her daily motion is about one degree. Accordingly the constellation is no more the one proposed; we must select that time before the new moon on 20th Ashādha when the moon had been in Dhanus, or 28 days before the 2nd Srāvana, vit. the 4th solar Ashādha. The day indicated by the given constellation of Sun and Moon is, therefore, the 4th solar Aşüdha or one of the two next. For calculation it would be best to select the 5th solar Aşādha, calculate the true Longitude of the moon, as explained in the General Tables, and select the definitive day accordingly.
2. If the year in which a given constellation occurred is not known, we can find it approximately from the signs in which Jupiter and Saturn are stated to have been. For as a revolation of Jupiter requires 12 years and one of Saturn 28 years, the same constellation of both planets will recur in about 12 x 28 = 336 years. This would be our chance if the degrees of the Jupiter's and Saturn's places in their respective signs were stated. But usually only the signs are given, and in that case we may expect a recurrence of the same constellation in about 59 or 60 years. In order to find the periods in which Jupiter and Saturn stood in any given signs, I have constructed Tables vi-viii. They are based on the Kaliyuga era and mean Bolar years. The places of both planets, their mean Longitudes, are expressed in figures, of which the integers denoto complete signs, and the decimals the fraction of the running sign. Thus 465 denotes that the planet stood in the fifth sign counting from Mēsha), vis. Simha, and had gone through 0.65 of it. -The working of the tables will be best anderstood by an example.
Example.--Given Jupiter in Simha (5th sign), Saturn in Dhanus (9th sign). Required the corresponding year of 44th century K. Y.
Answer.-The mean Longitude (according to the notation in these tables) was 4: 4:00... 5:00; h 8.00...9:00.
Rule.-- From the given Longitudes subtract the corresponding ones for the Century under consideration, in table VI, if the given Longitude is smaller than the tabular value, add 12.00 to the former, and then subtract tabular value.
viz. 4. 400 – 4-31 or 16.00 – 4-31 = 11:69 .
h. 800 - 10.67 or 20.00 - 10-67 = 9.33
These values mark the beginning of Simha for 4, and Dhanus for h ; the end of these signs are accordingly marked by (12.69 1.6.) 0.69 and 10-33 respectively. Now look out in tablo VII in the column h, 9-33 or the next higher cipher up to 10:33, and see whether the corresponding value of 4 lies between 11.69 and 0-69. This is the case only in the year 23. The Longitude of Jupiter at the beginning of 4523 is 11:27, after an inorease of 0-42 it will have the required minimum valne 11.69. Table VIII shows that 0:42 is the increase of 5 complete months. Accordingly the given constellation occurred between K. Y. 4323 VI (moan solar Āsvina) and K. Y., 4324 VI. These limits hold good for the mean places only; for the true places they may shift somewhat in either direction.
If we caloulate in the same way the preceding and following Centuries we find that the same constellation did not occur in 4000-4324, but it occurred in 4 140 near the end of that year, and in 4558 in Mārgasira ; (however both cases may prove wrong when true places are calonlated; for the time of the constellation in the first case is bat 3 months, and in the second about one month). In 46th century the same constellation occurred twice 4619 XII - 4620 V and 4679 IV - VII.
