The direct services of permanent value that Galileo rendered to astronomy are virtually summed up in his telescopic discoveries. His name is justly associated with a vast extension of the bounds of the visible universe, and his telescopic observations are a standing monument of his ability. Within two years after their discovery, he had constructed approximately accurate tables of the revolutions of Jupiter's satellites and proposed their frequent eclipses as a means of determining longitudes on land and at sea. The idea, though ingenious, has been found of little use at sea. His observations on sunspots are noteworthy for their accuracy and for the deductions he drew from them with regard to the rotation of the Sun and the revolution of the Earth.

A puzzling circumstance is Galileo's neglect of Kepler's laws, which were discovered during his lifetime. But then he believed strongly that orbits should be circular (not elliptical, as Kepler discovered) in order to keep the fabric of the cosmos in its perfect order. This preconception prevented him from giving a full formulation of the inertial law, which he himself discovered, although it usually is attributed to the French mathematician René Descartes. Galileo believed that the inertial path of a body around the Earth must be circular. Lacking the idea of Newtonian gravitation, he hoped this would allow him to explain the path of the planets as circular inertial orbits around the Sun.

The idea of a universal force of gravitation seems to have hovered on the borders of this great man's mind, but he refused to entertain it because, like Descartes, he considered it an "occult" quality. More valid instances of the anticipation of modern discoveries may be found in his prevision that a small annual parallax would eventually be found for some of the fixed stars and that extra-Saturnian planets would at some future time be ascertained to exist and in his conviction that light travels with a measurable although extremely great velocity. Although Galileo discovered, in 1610, a means of adapting his telescope to the examination of minute objects, he did not become acquainted with the compound microscope until 1624, when he saw one in Rome and, with characteristic ingenuity, immediately introduced several improvements into its construction.

A most substantial part of his work consisted undoubtedly of his contributions toward the establishment of mechanics as a science. Some valuable but isolated facts and theorems had previously been discovered and proved, but it was Galileo who first clearly grasped the idea of force as a mechanical agent. Although he did not formulate the interdependence of motion and force into laws, his writings on dynamics are everywhere suggestive of those laws, and his solutions of dynamical problems involve their recognition. In this branch of science he paved the way for the English physicist and mathematician Isaac Newton later in the century. The extraordinary advances made by him were due to his application of mathematical analysis to physical problems.

Galileo was the first man who perceived that mathematics and physics, previously kept in separate compartments, were going to join forces. He was thus able to unify celestial and terrestrial phenomena into one theory, destroying the traditional division between the world above and the world below the Moon. The method that was peculiarly his consisted in the combination of experiment with calculation--in the transformation of the concrete into the abstract and the assiduous comparison of results. He created the modern idea of experiment, which he called cimento ("ordeal"). This method was applied to check theoretical deductions in the investigation of the laws of falling bodies, of equilibrium and motion on an inclined plane, and of the motion of a projectile. The latter, together with his definition of momentum and other parts of his work, implied a knowledge of the laws of motion as later stated by Newton. In his Discorso intorno alle cose che stanno in su l'acqua ("Discourse on Things That Float"), published in 1612, he used the principle of virtual velocities to demonstrate the more elementary theorems of hydrostatics, deducing the equilibrium of fluid in a siphon, and worked out the conditions for the flotation of solid bodies in a liquid. He also constructed, in 1607, an elementary form of air thermometer.

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