This may be otherwise expressed by saying that the length of the month diminishes by about one-thirtieth of a second in the course of a century. Moreover, as Laplace shewed (§ 245), the eccentricity of the earth's orbit will not go on diminishing indefinitely, but after an immense period to be reckoned in thousands of years will begin to increase, and the moon's motion will again become slower in consequence.
Laplace's result agreed almost exactly with that indicated by observation; and thus the last known discrepancy of importance in the solar system between theory and observation appeared to be explained away; and by a curious coincidence this was effected just a hundred years after the publication of the Principia.
Many years afterwards, however, Laplace's explanation was shewn to be far less complete than it appeared at the time (chapter xiii., § 287).
The same investigation revealed to Laplace the existence of alterations of a similar character, and due to the same cause, of other elements in the moon's orbit, which, though not previously noticed, were found to be indicated by ancient eclipse observations.
241. The third volume of the Mécanique Céleste contains a general treatment of the lunar theory, based on a method entirely different from any that had been employed before, and worked out in great detail. "My object," says Laplace, "in this book is to exhibit in the one law of universal gravitation the source of all the inequalities of the motion of the moon, and then to employ this law as a means of discovery, to perfect the theory of this motion and to deduce from it several important elements in the system of the moon." Laplace himself calculated no lunar tables, but the Viennese astronomer John Tobias Bürg (1766-1834) made considerable use of his formulae, together with an immense number of Greenwich observations, for the construction of lunar tables, which were sent to the Institute of France in 1801 (before the publication of Laplace's complete lunar theory), and published in a slightly amended form in 1806. A few years later (1812) John Charles Burckhardt (1773-1825), a German who had settled in Paris and worked under Laplace and Lalande, produced a new set of tables based directly on the formulae
