measured in terms of this unit. Delaunay, working independently, arrived at like conclusions, and shewed that tidal friction might thus be capable of producing just such an alteration in the moon's motion as had to be explained; if this explanation were accepted the observed motion of the moon would give a measure of the effect of tidal friction. The minuteness of the quantities involved is shewn by the fact that an alteration in the earth's rotation equivalent to the lengthening of the day by 110 second in 10,000 years is sufficient to explain the acceleration in question. Moreover it is by no means certain that the usual estimate of the amount of this acceleration—based as it is in part on ancient eclipse observations—is correct, and even then a part of it may conceivably be due to some indirect effect of gravitation even more obscure than that detected by Laplace, or to some other cause hitherto unsuspected.
288. Most of the writers on lunar theory already mentioned have also made contributions to various parts of planetary theory, but some of the most important advances in planetary theory made since the death of Laplace have been due to the French mathematician Urbain Jean Joseph Leverrier (1811-1877), whose methods of determining the distance of the sun have been already referred to (§ 282). His first important astronomical paper (1839) was a discussion of the stability (chapter xi., § 245) of the system formed by the sun and the three largest and most distant planets then known, Jupiter, Saturn, and Uranus. Subsequently he worked out afresh the theory of the motion of the sun and of each of the principal planets, and constructed tables of them, which at once superseded earlier ones, and are now used as the basis of the chief planetary calculations in the Nautical Almanac and most other astronomical almanacs. Leverrier failed to obtain a satisfactory agreement between observation and theory in the case of Mercury, a planet which has always given great trouble to astronomers, and was inclined to explain the discrepancies as due to the influence either of a planet revolving between Mercury and the sun or of a number of smaller bodies analogous to the minor planets (§ 294).
Researches of a more abstract character, connecting planetary theory with some of the most recent advances
