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

by William Whewell

[74] Phil. Trans. 1731, p. 195.

[75] Bailly, A. M. c. 131.

We have already remarked, in the history of analytical mechanics, that in the Lunar Theory, considered as one of the cases of the Problem of Three Bodies, no advance was made beyond what Newton had done, till mathematicians threw aside the Newtonian artifices, and applied the newly developed generalizations of the analytical method. The first great apparent deficiency in the agreement of the law of universal gravitation with astronomical observation, was removed by Clairaut’s improved approximation to the theoretical Motion of the Moon’s Apogee, in 1750; yet not till it had caused so much disquietude, that Clairaut himself had suggested a modification of the law of attraction; and it was only in tracing the consequences of this suggestion, that he found the Newtonian law of the inverse square to be that which, when rightly developed, agreed with the facts. Euler solved the problem by the aid of his analysis in 1745,[76] and published Tables of the Moon in 1746. His tables were not very accurate at first;[77] but he, D’Alembert, and Clairaut, continued to labor at this object, and the two latter published Tables of the Moon in 1754.[78] Finally, Tobias Mayer, an astronomer of Göttingen, having compared Euler’s tables with observations, corrected them so successfully, that in 1753 he published Tables of the Moon, which really did possess the accuracy which Halley only flattered himself that he had attained. Mayer’s success in his first Tables encouraged him to make them still more perfect. He applied himself to the mechanical theory of the moon’s orbit; corrected all the coefficients of the series by a great number of observations; and in 1755, sent his new Tables to London as worthy to claim the prize offered for the discovery of longitude. He died soon after [438] (in 1762), at the early age of thirty-nine, worn out by his incessant labors; and his widow sent to London a copy of his Tables with additional corrections. These Tables were committed to Bradley, then Astronomer Royal, in order to be compared with observation. Bradley labored at this task with unremitting zeal and industry, having himself long entertained hopes that the Lunar Method of finding the Longitude might be brought into general use. He and his assistant, Gael Morris, introduced corrections into Mayer’s Tables of 1755. In his report of 1756, he says,[79] that he did not find any difference so great as a minute and a quarter; and in 1760, he adds, that this deviation had been further diminished by his corrections. It is not foreign to our purpose to observe the great labor which this verification required. Not less than 1220 observations, and long calculations founded upon each, were employed. The accuracy which Mayer’s Tables possessed was considered to entitle them to a part of the parliamentary reward; they were printed in 1770, and his widow received 3000l. from the English nation. At the same time, Euler, whose Tables had been the origin and foundation of Mayer’s, also had a recompense of the same amount.

[76] Lal. 1460.

[77] Bradley’s Correspondence.

[78] Lal. 1460.

[79] Bradley’s Mem. p. xcviii.

This public national acknowledgment of the practical accuracy of these Tables is, it will be observed, also a solemn recognition of the truth of the Newtonian theory, as far as truth can be judged of by men acting under the highest official responsibility, and aided by the most complete command of the resources of the skill and talents of others. The finding the Longitude is thus the seal of the moon’s gravitation to the sun and earth; and with this occurrence, therefore, our main concern with the history of the Lunar Theory ends. Various improvements have been since introduced into this research; but on these we, with so many other subjects before us, must forbear to enter.

Sect. 3.—Application of the Newtonian Theory to the Planets, Satellites, and Earth.

The theories of the Planets and Satellites, as affected by the law of universal gravitation, and therefore by perturbations, were naturally subjects of interest, after the promulgation of that law. Some of the effects of the mutual attraction of the planets had, indeed, already attracted notice. The inequality produced by the mutual attraction of Jupiter and Saturn cannot be overlooked by a good observer. In the [439] preface to the second edition of the Principia, Cotes remarks,[80] that the perturbation of Jupiter and Saturn is not unknown to astronomers. In Halley’s Tables it was noticed[81] that there are very great deviations from regularity in these two planets, and these deviations are ascribed to the perturbing force of the planets on each other; but the correction of these by a suitable equation is left to succeeding astronomers.