English
One of them con- cerns the radical places at the epoch from which the motions are counted, the other concerns the mean motions themselves, that is to say, the mean rate, or angular velocity of the planet. Of these the first remains fixed, and its effect at all times is the same : the second again is variable, and its effect increases proportionally to the time. If, therefore, they are opposite, the one in excess and the other in defect, they must partly destroy one another ; and the one, increasing continually, will at length become equal to the other, when there will of consequence be no error at all ; after which the error will fall on the opposite side, and will increase continually. Here the moment of no error, or that when the tables are perfectly correct, is evidently distant from the time Digitized by Google X PEEFACE. of the construction of the tables, 8uid may be very long either before or after that period. Suppose, for example, that in constructing tables of the sun's motion, we are to set off from the beginning of the present century, and that we make the sun's place f&r the beginning of the year 1801 more advanced by half a degree than it was in reality. Suppose also that the mean moticm set down in our tables is erroneous, in a way opposite to the former, and is less than the truth by 1" in a yeiar. The pkce of the Sim then, as assigned froiA tables for every year subsequent to 1800, will, from the first of the above causes, be half a degree too far advanced, and, from the seconds it will be too little advanced, by as many seconds as there are years ; when the number of years becocte as great As that of the seconds im 30', th4t is, when it is equal to 1800> the two errors will desttoy one another, and the tables will give ^e place of the sun perfectly exact. Were we, therefore, to ascertain the age of the tables by Mrv Bentley'B rule> we should commit an error g^ 1800 yesurs ; from which we may judge o£ the credit due to that nde, as a guide in chronological researches." Here iSie reviewer's plausible sophistry may be clearly see^ through. He assumes an error in the sun's ^lace at the epoch of the tables of 30", and an error in the mean motion of I" per year. All this. Digitized by Google PR£FAC£. XI we see, is upon one side, and a mere assumption. Have I not the same right to assume a similar error in one of the pliwets, that is, an error of 30', in its radical position, and an error of V per annum in its motion, so that in 1800 years the error of 30' would be cancelled ? Now if this error so assumed be of an opposite nature to the one he assumed, the one cancels the other, and the epoch ^ the tables would not be at all afiected by tte circumstance : hts con-^ elusion, therefore, in regard to my rule is incorrect^ £9r I do not determine the s^e of any system of astronomy by a single item, as he thought proper to assume on this occasion, to give the greater plausibility to his assertions; I make use of as many as appear to be the most connect, because the errors counteract each other. Why did he not apply the rule to some tables, the age of which was known to him, the same as I have done in respect of the system of Aryabhatta, in the third section of the second pait of my essay, the author of which gives his own date? I have also applied the same rule to the Brakma SUdhanta, the first of the mo- dem astronomical works introduced in AD. 538, to which the reader may refer, and where he will find the method by which the system was cbn- structed explamed at length. The application of liie rule, in both these instances, when we had the actual dates c^ the system before us, demonstrate that it is perfectly just, so far at least as we require Digitized by Google xu PREFACE. it. I shall, however, for the sake of exposing the fallacy of such arguments, apply the rule to the determination of the age of certam well knowni modem tables, which 1 hope will put this cavilling at rest, or expose the author of them to the censure he deserves. A set of astronomical tables being put into my hands, to determine their antiquity, I accordingly compaied them with the third edition of La Lande's, which is supposed to be correct, and find the errors gradually diminishing from the Christian era down to about the year A.D. 1744, as in the following TABLE. Planets, &c. A.D. 0 A. D. 1000 A. D. 1500 A. D. 1700 Year when no Error. Yearn Se- lected. A B Sqd, + Qo 1^26'' 60 0'42''5 0 0' 19^7 0° O'U" 1948 Sim*s apogee— 1 37 2 0 41 8 0 13 11 0 1 59 1737 1737 Moon, _ 0 6 38 0 2 48 0 0 53 0 0 7 1730 1730 — Apogee, + 0 0 68 0 0 58 0 0 58 0 0 58 — Node, + 0 0 51 0 0 51 0 0 51 0 0 51 Mercury, 2 18 29 10 9 0 20 59 0 5 20 1768 1768 — Aphel. *^ 6 69d7 3 0 17 1 0 42 0 12 54 1754 1764 — Node, 0 49 2 0 20 42 0 6 32 0 0 53 1731 1731 Veaos, 4 0 12 81 0 4 31 0 0 31 -.0 15 1565 — Aphel. 49 0 8 20 50 8 6 45 8 17 8 1740 1740 — Node, 0 0 0 0 0 0 0 0 0 0 0 0 Mars, + 0 0 30 0 0 30 0 0 30 0 0 30 ^ Aphel. 0 0 0 0 0 0 0 0 0 0 0 0 — Node, 5 46 15 2 29 35 0 51 15 0 11 55 1761 1761 Jiq>iter, 2 23 17 0 53 49 0 4 5 + 0 15 40 1541 — Apbel. _ 2 32 14 1 4 24 0 20 29 0 2 55 1733 1733 — Node, — 11 27 6 4 42 6 1 19 30 +0 1 23 1606 Satom, + 4 17 53 1 26 49 0 1 17 -0 32 56 1507 — Aphel. 9 52 35 3 13 45 + 5 40 1 25 26 1486 — Node, + 0 47 7 0 21 17 0 8 22 0 2 12 1823 Sum of til e years in the two last colou divided by the number of iU ans, •.•.•••..••...*• A 25520 B 13954 itns, the mean results are The same 1701 1744} Digitized by Google PREFACE. Xin To make my meaning better understood, I have selected into the last column all those years that agree near to each other, and the result from thence comes out 1744, the s^e of the astronomical tables : but to show how far the ernurs in the years in the other column would affect this result, I have cast them up as they stand, and they give then 1701 years. The notion of the reviewer is here shown in the item of 1948, at the beginning of the column under A, in order to show his error; for that item is balanced by others on the contrary side: — but is not the idea of using an erroneous result, when we have so many others to choose from, truly ridiqulous ? Surely the astronomer must be at liberty to employ those results he finds most correct, and not those that appear erroneous. . The reviewer's ideas in this respect are totally unscien- tific, and rest upon nothing but sophistry, misrepre-* sentation, and deception. No result can be drawn when the motions are the same by both tables, as in the moon's apogee and node, the node of Venus, Mars and his* aphelion; for the errors neither increase, nor diminish. The tables here given as an example to the rule, are those of La Lande^ first or second edition; but the title-page and date are wanting. The reason why the mean result makes the tables older than the epoch, which I believe was 1770, is, that the Digitized by Google •XIV PREFACE. observations on whidi they are founded are anterior to it. None of the Hindu artificial systems are ancient: they are all since A. D. 538, the year in which the modem astronomy commenced, and not at the beginning of the Kali Yuga, as imagined by Bailly or others ; for they had no astronomy then, as I have fully proved in the Essay, v^here I have brought forward all the astronomical facts and ob- servations that could be collected relative to their ancient astronomy, showing that it did not go further back than about 1425 before Christ, which was only the dawn of astronomy in India. The reviewer naust be greatly mistaken, if he imagines that the motions of the planets in Hindu artificial systems, were drawn from two actual ob- Bervations, as in the j^urppean methods, and '' that their merit, and their claim to antiquity, was de- cided"— " by the accurs^cy of the mean motions, as contained in the tables." Now the assertion thus boldly made is not correct ; for the Hindu artificial systems, and tables drawn from them, which give the motions alluded to, are not ccmstructed on the European principle.