208

HISTORY OF PHYSICAL ASTRONOMY.

period were therefore mainly directed to the improvement of the transcen-dental analysis, the only instrument that could be expected in future toafford any efficient aid in the abstruse researches relating to the system ofthe world, its applications being confined to problems of pure mechanics—the branch of science which forms the connecting medium betweenanalysis and physics. The prodigious mass of original matter that hadbeen presented in the Principia in a synthetic form supplied geometerswith an inexhaustible field of delightful speculations of this nature, andgave birth to a multitude of analytical inventions which proved of incalcu-lable service in the future development of the theory of gravitation.

The second period in the history of physical astronomy extends fromthe commencement of the labours of Euler and his contemporaries on thelunar theory to the close of the eighteenth century. Less fertile inoriginal ideas than the period to which we have been referring, it notwith-standing exhibits a refinement of conception in fundamental principles,combined with a power of generalization in the methods of research, towhich no scientific investigations in any other age can offer a parallel.These brilliant efforts of genius, when applied to Celestial Mechanics , con-ducted the geometer to new solutions of all the great problems of thesystem of the world, more comprehensive in design, and more fertile indetail, than those derived from the synthetic methods of the Principia.Formulas were assigned exhibiting the oscillations of the planetary move-ments throughout indefinite ages both past and future. The sublimetruths relating to the stability of the planetary system were established byLagrange and Laplace upon the basis of a rigorous analysis. The accuratecomputation of the motion of the lunar apogee, the equally satisfactoryaccount of the hitherto inexplicable irregularities of Jupiter and Saturn, andof the secular acceleration of the moon’s mean motion, the solution of thegreat problem of the precession of the equinoxes by the strictest principlesof mechanical science, and the complete establishment of the theory ofJupiter ’s satellites, may be ranked among the most brilliant conquestsachieved during this period. The actual state of astronomical sciencewas also now y brought into more intimate connexion with the researches ofthe geometer than it had been in the preceding period. The phenomenaof the celestial motions discovered by Hipparchus and his successors downto Kepler inclusive, were too broadly traced out in the heavens to exciteany doubts respecting their real character. It only remained, therefore,to explain their dependence upon physical principles, a task which devolvedexclusively on the geometer. But when the latter proceeded to considerthe more recondite parts of the theory of gravitation, it became indis-pensable, in order to obtain a confirmation of his results by an appeal toobservation, that the corresponding phenomena of the heavens should beexhibited in a clear form by the astronomer. The objects of research,being now, however, of a more minute character than those hithertoaccounted for by theory, were appreciable to the astronomer only by a closerscrutiny of facts and greater delicacy of observation. It was thus thatastronomy and abstract science reflected a light upon each other’s paths,which conduced materially to their mutual progress. The results achievedby the critical acumen of Halley, the sagacity of Bradley, and the unrivalledpractical skill of Maskelyne, advanced at an equal pace with the analyticalresearches of the geometers on the Continent , and are imperishably asso-ciated with them in the magnificent triumphs which illustrate the historyof physical astronomy during this period. The latter aptly closes with thepublication of the Mecanique Celeste , a work embodying many of the most