Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/309
the time of the apparent Mesha saṅkrânti (as given in Table I., cols. 13 to 17, or 17a). The sum is the moment of the mean Mesha saṅkrânti. Find the interval in days, ghaṭikâs, and palas between this and the given time (for which Jupiter's place is to be calculated). Calculate the mean motion of Jupiter during the interval by Table Y below, and add it to the mean longitude at the moment of mean Mesha saṅkrânti. The sum is the mean place of Jupiter at the given moment. The motion of the sun during the interval (Table Y) is the sun's mean place at the given moment.
II. To find, secondly, the apparent longitude.
(i.) Subtract the sun's mean longitude from that of Jupiter. Call the remainder the "first commutation". If it be more than six signs, subtract it from twelve signs, and use the remainder. With this argument find the parallax by Table Z below. Parallax is minus when the commutation is not more than six signs, plus when it is more than six. Apply half the parallax to the mean longitude of Jupiter, and subtract from the sum the longitude of Jupiter's aphelion, as given at the bottom of Table Z below. The remainder is the anomaly. (If this is more than six signs, subtract it from twelve signs, as before, and use the remainder.) With this argument find the equation of the centre[1] by Table Z. This is minus or plus according as the anomaly is 0 to 6, or 6 to 12 signs. Apply it to the mean longitude of Jupiter, and the result is the heliocentric longitude.
(ii.) Apply the equation of the centre (plus or minus) to the first commutation; the sum is the "second commutation". If it is more than six signs, use, as before, the difference between it and twelve signs. With this second commutation as argument find the parallax as before. Apply it (whole) to Jupiter's heliocentric longitude, and the result is Jupiter's apparent longitude.
Example. We have a date in an inscription.—"In the year opposite Kollam year 389, Jupiter being in Kumbha, and the sun 18 days old in Mîna, Thursday, 10th lunar day of Pushya."[2] Calculating by our method "C" in the Text, we find that the date corresponds to Śaka 1138 current, Chaitra śukla daśamî (10th), Pushya nakshatra, the 18th day of the solar month Mîna of Kollam 390 of our Tables, or March 12th, A.D. 1215.[3]
To find the place of Jupiter on the given day.
| gh. | pa. | |||
| Apparent Mesha saṅk. in Śaka 1137 (Table I., Cols. 13—15) | 25 Mar. (436)(84) | Tues. (3) | 3 | 32 |
| Add śodhya (Table Y) | 2 (436)2 | (3)2 | 8 | 51 |
| 27 Mar. (436)(86) | Tues. (5) | 12 | 23 | |
| The given date is Śaka 1138 | 12 Mar. (436) | |||
| (350) | ||||
350, then, is the interval from mean Mesha saṅkrânti to 12 gh. 23 pa. on the given day.
The interval between Śaka 1 current and Śaka 1137 current is 1136 years.
- ↑ Neglecting the minutes and seconds of anomaly, the equation may be taken for degrees. Thus, if the anomaly is 149° 7′ 49″, the equation may be taken for 149°. If it were 149° 31′ 12″, take the equation for 150°. And so in the case of commutation. For greater accuracy the equation and parallax may be found by proportion.
- ↑ Indian Antiquary, XXIV., p. 307, date No. XI.
- ↑ The year 389 in the original seems to be the expired year. There are instances in which the word "opposite" is so used and I am inclined to think that the word used for "opposite" is used to denote "expired" (gata). The phrase "18 days old" is used to shew the 18th day of the solar month. [S. B. D.)