Electronic edition published by Cultural Heritage Langauge Technologies (with permission from Charles Scribners and Sons) and funded by the National Science Foundation International Digital Libraries Program. This text has been proofread to a low degree of accuracy. It was converted to electronic form using data entry.
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