290. The lunar tables of Hansen and Professor Newcomb, and the planetary and solar tables of Leverrier, Professor Newcomb, and Dr. Hill, represent the motions of the bodies dealt with much more accurately than the corresponding tables based on Laplace’s work, just as these were in turn much more accurate than those of Euler, Clairaut, and Halley. But the agreement between theory and observation is by no means perfect, and the discrepancies are in many cases greater than can be explained as being due to the necessary imperfections in our observations.
The two most striking cases are perhaps those of Mercury and the moon. Leverrier’s explanation of the irregularities of the former ([§ 288]) has never been fully justified or generally accepted; and the position of the moon as given in the Nautical Almanac and in similar publications is calculated by means of certain corrections to Hansen’s tables which were deduced by Professor Newcomb from observation and have no justification in the theory of gravitation.
291. The calculation of the paths of comets has become of some importance during this century owing to the discovery of a number of comets revolving round the sun in comparatively short periods. Halley’s comet (chapter XI., [§ 231]) reappeared duly in 1835, passing through its perihelion within a few days of the times predicted by three independent calculators; and it may be confidently expected again about 1910. Four other comets are now known which, like Halley’s, revolve in elongated elliptic orbits, completing a revolution in between 70 and 80 years; two of these have been seen at two returns, that known as Olbers’s comet in 1815 and 1887, and the Pons-Brooks comet in 1812 and 1884. Fourteen other comets with periods varying between 3-1∕3 years (Encke’s) and 14 years (Tuttle’s), have been seen at more than one return; about a dozen more have periods estimated at less than a century; and 20 or 30 others move in orbits that are decidedly elliptic, though their periods are longer and consequently not known with much certainty. Altogether the paths of about 230 or 240 comets have been computed, though many are highly uncertain.
Fig. 87.—The path of Halley’s comet.
292. In the theory of the tides the first important advance made after the publication of the Mécanique Céleste was the collection of actual tidal observations on a large scale, their interpretation, and their comparison with the results of theory. The pioneers in this direction were Lubbock ([§ 286]), who presented a series of papers on the subject to the Royal Society in 1830-37, and William Whewell (1794-1866), whose papers on the subject appeared between 1833 and 1851. Airy ([§ 281]), then Astronomer Royal, also published in 1845 an important treatise dealing with the whole subject, and discussing in detail the theory of tides in bodies of water of limited extent and special form. The analysis of tidal observations, a large number of which taken from all parts of the world are now available, has subsequently been carried much further by new methods due to Lord Kelvin and Professor G. H. Darwin. A large quantity of information is thus available as to the way in which tides actually vary in different places and according to different positions of the sun and moon.
Of late years a good deal of attention has been paid to the effect of the attraction of the sun and moon in producing alterations—analogous to oceanic tides—in the earth itself. No body is perfectly rigid, and the forces in question must therefore produce some tidal effect. The problem was first investigated by Lord Kelvin in 1863, subsequently by Professor Darwin and others. Although definite numerical results are hardly attainable as yet, the work so far carried out points to the comparative smallness of these bodily tides and the consequent great rigidity of the earth, a result of interest in connection with geological inquiries into the nature of the interior of the earth.
Some speculations connected with tidal friction are referred to elsewhere ([§ 320]).
293. The series of propositions as to the stability of the solar system established by Lagrange and Laplace (chapter XI., [§§ 244], 245), regarded as abstract propositions mathematically deducible from certain definite assumptions, have been confirmed and extended by later mathematicians such as Poisson and Leverrier; but their claim to give information as to the condition of the actual solar system at an indefinitely distant future time receives much less assent now than formerly. The general trend of scientific thought has been towards the fuller recognition of the merely approximate and probable character of even the best ascertained portions of our knowledge; “exact,” “always,” and “certain” are words which are disappearing from the scientific vocabulary, except as convenient abbreviations. Propositions which profess to be—or are commonly interpreted as being—“exact” and valid throughout all future time are consequently regarded with considerable distrust, unless they are clearly mere abstractions.