We should be inexcusable if we omitted to notice the high importance of the labours of Laplace on the improvement of the lunar tables.  The immediate object of this improvement was, in effect, the promotion of maritime intercourse between distant countries, and, what was indeed far superior to all considerations of mercantile interest, the preservation of the lives of mariners.

Thanks to a sagacity without parallel, to a perseverance which knew no limits, to an ardour always youthful and which communicated itself to able coadjutors, Laplace solved the celebrated problem of the longitude more completely than could have been hoped for in a scientific point of view, with greater precision than the art of navigation in its utmost refinement demanded.  The ship, the sport of the winds and tempests, has no occasion, in the present day, to be afraid of losing itself in the immensity of the ocean.  An intelligent glance at the starry vault indicates to the pilot, in every place and at every time, his distance from the meridian of Paris.  The extreme perfection of the existing tables of the moon entitles Laplace to be ranked among the benefactors of humanity.[37]

In the beginning of the year 1611, Galileo supposed that he found in the eclipses of Jupiter’s satellites a simple and rigorous solution of the famous problem of the longitude, and active negotiations were immediately commenced with the view of introducing the new method on board the numerous vessels of Spain and Holland.  These negotiations failed.  From the discussion it plainly appeared that the accurate observation of the eclipses of the satellites would require powerful telescopes; but such telescopes could not be employed on board a ship tossed about by the waves.

The method of Galileo seemed, at any rate, to retain all its advantages when applied on land, and to promise immense improvements to geography.  These expectations were found to be premature.  The movements of the satellites of Jupiter are not by any means so simple as the immortal inventor of the method of longitudes supposed them to be.  It was necessary that three generations of astronomers and mathematicians should labour with perseverance in unfolding their most considerable perturbations.  It was necessary, in fine, that the tables of those bodies should acquire all desirable and necessary precision, that Laplace should introduce into the midst of them the torch of mathematical analysis.

In the present day, the nautical ephemerides contain, several years in advance, the indication of the times of the eclipses and reappearances of Jupiter’s satellites.  Calculation does not yield in precision to direct observation.  In this group of satellites, considered as an independent system of bodies, Laplace found a series of perturbations analogous to those which the planets experience.  The rapidity of the revolutions unfolds, in a sufficiently short space of time, changes in this system which require centuries for their complete development in the solar system.