Sect. 2.—Application of the Newtonian Theory to the Moon.
The Motions of the Moon may be first spoken of, as the most obvious and the most important of the applications of the Newtonian Theory. The verification of such a theory consists, as we have seen in previous cases, in the construction of Tables derived from the theory, and the comparison of these with observation. The advancement of astronomy would alone have been a sufficient motive for this labor; but there were other reasons which urged it on with a stronger impulse. A perfect Lunar Theory, if the theory could be perfected, promised to supply a method of finding the Longitude of any place on the earth’s surface; and thus the verification of a theory which professed to be complete in its foundations, was identified with an object of immediate practical use to navigators and geographers, and of vast acknowledged value. A good method for the near discovery of the longitude had been estimated by nations and princes at large sums of money. The Dutch were willing to tempt Galileo to this task by the offer of a chain of gold: Philip the Third of Spain had promised a reward for this object still earlier;[63] the parliament of England, in 1714, proposed a recompense of 20,000l. sterling; the Regent Duke of Orléans, two years afterwards, offered 100,000 francs for the same purpose. These prizes, added to the love of truth and of fame, kept this object constantly before the eyes of mathematicians, during the first half of the last century.
[63] Del. A. M. i. 39, 66.
If the Tables could be so constructed as to represent the moon’s real place in the heavens with extreme precision, as it would be seen from a standard observatory, the observation of her apparent place, as seen from any other point of the earth’s surface, would enable the observer to find his longitude from the standard point. The motions of the moon had hitherto so ill agreed with the best Tables, that this method failed altogether. Newton had discovered the ground of this want of agreement. He had shown that the same force which produces the Evection, Variation, and Annual Equation, must produce also a long series of other Inequalities, of various magnitudes and cycles, which perpetually drag the moon before or behind the place where she would be sought by an astronomer who knew only of those principal and notorious inequalities. But to calculate and apply the new inequalities, was no slight undertaking. [435]
In the first edition of the Principia in 1687, Newton had not given any calculations of new inequalities affecting the longitude of the moon. But in David Gregory’s Elements of Physical and Geometrical Astronomy, published in 1702, is inserted[64] “Newton’s Lunar Theory as applied by him to Practice;” in which the great discoverer has given the results of his calculations of eight of the lunar Equations, their quantities, epochs, and periods. These calculations were for a long period the basis of new Tables of the Moon, which were published by various persons;[65] as by Delisle in 1715 or 1716, Grammatici at Ingoldstadt in 1726, Wright in 1732, Angelo Capelli at Venice in 1733, Dunthorne at Cambridge in 1739.
[64] P. 332.
[65] Lalande, 1457.
Flamsteed had given Tables of the Moon upon Horrox’s theory in 1681, and wished to improve them; and though, as we have seen, he would not, or could not, accept Newton’s doctrines in their whole extent, Newton communicated his theory to the observer in the shape in which he could understand it and use it:[66] and Flamsteed employed these directions in constructing new Lunar Tables, which he called his Theory.[67] These Tables were not published till long after his death, by Le Monnier at Paris in 1746. They are said, by Lalande,[68] not to differ much from Halley’s. Halley’s Tables of the Moon were printed in 1719 or 1720, but not published till after his death in 1749. They had been founded on Flamsteed’s observations and his own; and when, in 1720, Halley succeeded Flamsteed in the post of Astronomer Royal at Greenwich, and conceived that he had the means of much improving what he had done before, he began by printing what he had already executed.[69]
[66] Baily. Account of Flamsteed, p. 72.
[67] P. 211.