Page:Sewell Indian chronography.pdf/87
(iii.) Parallax for 27° is (Table XXXV.) 4° 20″. V being more than six signs this is additive. We therefore add half to the mean longitude of Jupiter.
| s. | ° | ′ | ″ | ||
| 10 | 17 | 56 | 48 | ||
| + | 2 | 10 | 0 | ||
| 10 | 20 | 6 | 48 | ||
| Subtract | 6 | 0 | 0 | 0 | Long. of Jupiter's aphelion by the Ārya Siddhānta. |
| W = | 4 | 20 | 6 | 48 | = Jupiter's anomaly. |
(iv.) 4 s. 20° = 140°. Equation of centre for 140° (Table XXXV.) = 3° 25′. W is less than six signs, and therefore the equation is subtractive. It has to be subtracted from the mean longitude of Jupiter.
| s. | ° | ′ | ″ | ||
| 10 | 17 | 56 | 48 | ||
| − | 3 | 25 | 0 | ||
| X = | 10 | 14 | 31 | 48 | = Jupiter's heliocentric long: |
(v.) Deduct the same equation of the centre from V.
| s. | ° | ′ | ″ | ||
| 11 | 3 | 11 | 20 | ||
| − | 3 | 25 | 0 | ||
| Y = | 10 | 29 | 46 | 20 | = second commutation. |
This is more than six signs and is therefore deducted from twelve signs.
| s. | ° | ′ | ″ | |
| 12 | 0 | 0 | 0 | |
| −10 | 29 | 46 | 20 | |
| 1 | 0 | 13 | 40 |
(vi.) Parallax for 1 s., or 30° (Table XXXV.) = 4° 49′. This has to be applied to X, and because X was in this case more than six signs it is additive.
| s. | ° | ′ | ″ | ||
| 10 | 14 | 31 | 48 | ||
| + | 4 | 49 | 0 | ||
| Z = | 10 | 29 | 46 | 20 | = Jupiter's apparent longitude. |
We have therefore determined that at mean sunrise on March 12th, A.D. 1215, or the 18th Mina of K.Y. 4315 expired, the apparent longitude of Jupiter was 10 s. 19° 20′ 48″, or 319° 20′ 48″. By Table XXII. we find that, by his apparent longitude as well as by his mean longitude Jupiter was then in the sign Kumbha.
186. I have tested by the present method a date published by the late Professor Kielhorn (Ind. Ant., XXV., 1896, p. 174, No. 16) of the Kollam era in South India. The date and time correspond to noon on April 3rd, A.D. 1607, or the 6th Mēsha, K.Y. 4708 expired, and he found that at that moment Jupiter's mean place was 11 s. 5° 55′, and his true place was 11 s. 9° 16′. By Mr. Dikshit's method, and using the Sūrya Siddhānta, I find Jupiter's mean place to have been 11 s. 5° 56′ and his true place 11 s. 9° 22′. The difference between us is only 1′ in mean and 6′ in true longitude. I am not aware how Professor Kielhorn worked in order to obtain his results, but I conclude that in all probability he calculated by the system published by him in the Indian Antiquary, Vol. XVIII. (1889), pp. 193 ff., 380 ff.
187. The general reasons for the adoption of the above process will be better understood after a short explanation. We have to find the apparent longitude of Jupiter as seen from the earth at the given moment. It is easy by our Tables to determine for any moment the mean longitude of Jupiter