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to the calculation made by the authors of Burgess's "Sūrya Siddhānta" the mean places of Jupiter at the given moment by that authority with and without the bīja were found to be 2 s. 26° 0′ 7″ and 2 s. 22° 41′ 41″ respectively. My result is precisely the same in one case, and only 2″ different in the other. Further proof of the accuracy of my Tables will be found in Example 61 below.
184. I give below (para. 184a) an exact reproduction in my own words of the process laid down by Mr. S. B. Dikshit for finding the true or apparent longitude of Jupiter on any day. It will be found in § 160 (c), pp. 155–157 of the Indian Calendar, "Additions and Corrections." Mr. Dikshit was a most painstaking, careful and accurate worker, well versed in the Hindū astronomy and in European mathematics, and it is to be assumed that his process represents faithfully the method which would have been adopted, probably which was adopted, by Hindū calculators in both ancient and recent times; at any rate until the period when they began to depend on European almanacs and astronomical methods. If such be the case, results obtained by the use of his process will more accurately tally with the figures and fixtures of a date as calculated and determined by a Hindū Pañchāṅg than will any result obtained by a process used by a trained European astronomer. And it is for that reason that I have considered it advisable to reproduce in its integrity Mr. Dikshit's method of calculation.
But I am bound to warn my readers that Mr. Dikshit's method is open to criticism in two respects. Mr. A. C. D. Crommelin, of the Greenwich Observatory, has most kindly subjected the process to a close examination, and he raises the following objections to it. The first operation, after ascertaining the mean longitude of Jupiter as well as that of the sun at the given moment, is to deduct the latter from the former, thus obtaining the angular distance of mean Jupiter from mean sun; calling the result "V," or "the first commutation." The next process is to apply half the parallax of Jupiter to Jupiter's mean longitude, and then to subtract from the sum the longitude of Jupiter's aphelion, in order to obtain the anomaly which I call "W." Now Mr. Crommelin points out that it is wrong at this stage to apply any parallax at all; for, so far as the calculation has proceeded, we are not concerned with the earth's orbit or the earth's position in any way, but only with the relative position of Jupiter and the sun with reference to the fixed sidereal first point of Mēsha. To apply the parallax as advised is certainly wrong from a consideration of the true system of the universe, and apparently would be equally wrong even from a Hindū point of view.
If the application of half the parallax were omitted from Mr. Dikshit's process at this stage, the greatest difference in the result would be about half a degree.
The next process, after having found Jupiter's anomaly, is to find from it the proper equation of the centre; and, deducting this from Jupiter's mean longitude and from the "first commutation," V, to obtain Jupiter's heliocentric longitude, X, and the "second commutation," Y. Mr. Crommelin states that there has been omitted from this operation the application of the sun's equation of the centre to the sun's longitude, which is necessary in order to find his true longitude (the important point here) from his mean longitude as already found. The greatest solar equation of the centre is about 2° 10′ 33″.
184a. With this preface by way of warning, I proceed to explain in detail Mr. Dikshit's system for finding Jupiter's true or apparent longitude.[1]
(i.) First find the mean longitudes of Jupiter and the sun as directed above.
- ↑ The apparent longitude of a planet in Hindu astronomy is its actual angular distance from the fixed first point of Mēsha, measured along the ecliptic. Its mean longitude is this calculated angular distance as it would be if the planet moved with an unvarying or mean velocity.