History of the inductive sciences, from the earliest to the present time

by William Whewell

[68] Lal. 1459.

[69] Mr. Baily* says that Mayer’s Nouvelles Tables de la Lune in 1753, published upwards of fifty years after Gregory’s Astronomy, may be considered as the first lunar tables formed solely on Newton’s principles. Though Wright in 1732 published New and Correct Tables of the Lunar Motions according to the Newtonian Theory, Newton’s rules were in them only partially adopted. In 1735 Leadbetter published his Uranoscopia, in which those rules were more fully followed. But these Newtonian Tables did not supersede Flamsteed’s Horroxian Tables, till both were supplanted by those of Mayer.

*Supp. p. 702.

But Halley had long proposed a method, different from that of Newton, but marked by great ingenuity, for amending the Lunar Tables. He proposed to do this by the use of a cycle, which we have mentioned as one of the earliest discoveries in astronomy;—the Period of 223 lunations, or eighteen years and eleven days, the Chaldean [436] Saros. This period was anciently used for predicting the eclipses of the sun and moon; for those eclipses which happen during this period, are repeated again in the same order, and with nearly the same circumstances, after the expiration of one such period and the commencement of a second. The reason of this is, that at the end of such a cycle, the moon is in nearly the same position with respect to the sun, her nodes, and her apogee, as she was at first; and is only a few degrees distant from the same part of the heavens. But on the strength of this consideration, Halley conjectured that all the irregularities of the moon’s motion, however complex they may be, would recur after such an interval; and that, therefore, if the requisite corrections were determined by observation for one such period, we might by means of them give accuracy to the Tables for all succeeding periods. This idea occurred to him before he was acquainted with Newton’s views.[70] After the lunar theory of the Principia had appeared, he could not help seeing that the idea was confirmed; for the inequalities of the moon’s motion, which arise from the attraction of the sun, will depend on her positions with regard to the sun, the apogee, and the node; and therefore, however numerous, will recur when these positions recur.

[70] Phil. Trans. 1731, p. 188.

Halley announced, in 1691,[71] his intention of following this idea into practice; in a paper in which he corrected the text of three passages in Pliny, in which this period is mentioned, and from which it is sometimes called the Plinian period. In 1710, in the preface to a new edition to Street’s Caroline Tables, he stated that he had already confirmed it to a considerable extent.[72] And even after Newton’s theory had been applied, he still resolved to use his cycle as a means of obtaining further accuracy. On succeeding to the Observatory at Greenwich in 1720, he was further delayed by finding that the instruments had belonged to Flamsteed, and were removed by his executors. “And this,” he says,[73] “was the more grievous to me, on account of my advanced age, being then in my sixty-fourth year: which put me past all hopes of ever living to see a complete period of eighteen years’ observation. But, thanks to God, he has been pleased hitherto (in 1731) to afford me sufficient health and strength to execute my office, in all its parts, with my own hands and eyes, without any assistance or interruption, during one whole period of the moon’s [437] apogee, which period is performed in somewhat less than nine years.” He found the agreement very remarkable, and conceived hopes of attaining the great object, of finding the Longitude with the requisite degree of exactness; nor did he give up his labors on this subject till he had completed his Plinian period in 1739.

[71] Ib. p. 536.

[72] Ib. 1731, p. 187.

[73] Ib. p. 193.

The accuracy with which Halley conceived himself able to predict the moon’s place[74] was within two minutes of space, or one fifteenth of the breadth of the moon herself. The accuracy required for obtaining the national reward was considerably greater. Le Monnier pursued the idea of Halley.[75] But before Halley’s method had been completed, it was superseded by the more direct prosecution of Newton’s views.