GALILEI, GALILEO (b. Pisa, Italy, 15 February 1564; d. Arcetri, Italy, 8 January 1642), physics, astronomy.

    Yet Galileo was not only familiar with the weight of air; he had himself devised practicable methods for its determination, set forth in this same book, giving even the correction for the buoyancy of the air in which the weighing was conducted.

Phenomena of the pendulum occupy a considerable place in the Two New Sciences. The relation of period to length of pendulum was first given here, although it probably represents one of Galileo's earliest precise physical observations. Precise isochronism of the pendulum appears to have been the one result he most wished to derive deductively. In discussing resistance of the air to projectile motion, he invoked observations (grossly exaggerated) of the identity of period between two pendulums of equal length weighted by bobs of widely different specific gravity. He deduced the existence of terminal constant velocity for any body falling through air, or any other medium, but mistakenly believed increase of resistance to be proportional to velocity.

Like the pendulum, the inclined plane plays a large role in Galileo's ultimate discussion of motion. The logical structure of his kinematics, as presented in the Two New Sciences, is this: He first defines uniform motion as that in which proportional spaces are covered in proportional times, and he then develops its laws. Next he defines uniform acceleration as that in which equal increments of velocity are acquired in equal times and shows that the resulting relations conform to those found in free fall. Postulating that the path of descent from a given height does not affect the velocity acquired at the end of a given vertical drop, he describes an experimental apparatus capable of disclosing time and distance ratios along planes of differing tilts and lengths; finally, he asserts the agreement of experiment with his theory. The experiments have been repeated in modern times, precisely as described in the Two New Sciences, and they give the results asserted. Following these definitions, assumptions, and confirmation by experiment, Galileo proceeds to derive a great many theorems related to accelerated motion.

In the last section Galileo deduces the parabolic trajectory of projectiles from a composition of uniform horizontal motion and accelerated vertical motion. Here the concept of rectilinear inertia, previously illustrated in the Dialogue (“Second Day”), is mathematically applied but not expressly formulated. This is followed by additional theorems relating to trajectories and by tables of altitude and distance calculated for oblique initial paths. Because of air resistance at high velocities, the tables assumed low speeds and hence were of no practical importance in gunnery. But like Galileo's theory of fracture, they opened the way for rapid successive refinements at the hands of others.

Last Years.

Galileo lived four years, totally blind, beyond the publication of his final book. During this time, he had the companionship of Vincenzio Viviani, who succeeded him (after Evangelista Torricelli) as mathematician to the grand duke and who inherited his papers. Viviani wrote a brief account of Galileo's life in 1654 at the request of Leopold de' Medici, which, despite some demonstrable errors, is still a principal source of biographical information, in conjunction with the voluminous correspondence of Galileo that has survived and with the autobiographical passages in his works. Near the end of his life, Galileo was also visited by Torricelli, a pupil of Castelli and the ablest physicist among Galileo's immediate disciples. Galileo's son, Vincenzio, also assisted in taking notes of his father's later reflections, in particular the design of a timekeeping device controlled by a pendulum.

Galileo died at Arcetri early in 1642, five weeks before his seventy-eighth birthday. The vindictiveness of Urban VIII, who had denied even Galileo's requests to attend mass on Easter and to consult doctors in nearby Florence when his sight was failing, continued after Galileo's death: The grand duke wished to erect a suitable tomb for Galileo but was warned to do nothing that might reflect unfavorably on the Holy Office. Galileo was buried at Santa Croce in Florence, but nearly a century elapsed before his remains were transferred, with a suitable monument and inscription, to their present place in the same church.

Sources of Galileo's Physics.

The habitual association of Galileo's name with the rapid rise of scientific activity after 1600 makes the investigation of his sources a matter of particular interest to historians of science.

All agree that Archimedes was a prime source and model for Galileo, who himself avowed the fact. The work of Aristotle and the pseudo-Aristotelian Questions of Mechanics were likewise admitted inspirations to Galileo, although often only as targets of criticism and attack. The astronomy of Copernicus and the magnetic researches of William Gilbert were obvious and acknowledged sources of his work. Beyond these, there is little agreement.

Among sixteenth-century writers, Galileo probably drew chiefly on Niccolò Tartaglia, Girolamo Cardano, and Guidobaldo del Monte. Parallels between his early unpublished work and that of Benedetti are very striking, but the establishment of a direct connection is difficult. As with the case of Stevin, the parallels in thought may result from the Archimedean revival