PHYSICS
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PHYSICS
glory lay in his discoveries in hydrostatics; and the
determining of the extent and point of application
of the pressure on the slanting inner side of a vessel
by the liquid contained therein was in itself sufficient
to entitle this geometrician from Bruges to a foremost
place among the creators of the theory of the equi-
librium of fluids. Benedetti was on the point of
enunciating the principle known as Pascal's Law, and
an insignificant addition permitted Mersenne to
infer this principle and the idea of the hydrauhc
press from what the Italian geometrician had written.
Benedetti had justified his propositions by using as
an axiom the law of the equilibrium of liquids in
communicating vessels, and prior to this time Vinci
had followed the same logical proceeding.
XVI. Dynamics in the Sixteenth Century. — The geometricians who, in spite of the stereotyped methods of Averroism and the banter of Humanism, continued to cultivate the Parisian dynamics of impetus, were rewarded by splendid discoveries. Dissipating the doubt in which Albert of Saxony had remained enveloped, Vinci had declared the velocity acquired by a falling body to be proportional to the time occupied by the fall, but he did not know how to determine the law connecting the time consumed in falling with the space passed over by the falling body. Nevertheless to find this law it would have sufficed to invoke the following proposition: in a uniformly varied motion, the space traversed by the mo\-ing body is equal to that which it would traverse in a uniform motion whose duration would be that of the preceding motion, and whose velocity would be the same as that which affected the preceding motion at the mean instant of its duration. This proposition was known to Oresme, who had demon- strated it exactly as it was to be demonstrated later by Galileo; it was enunciated and discussed at the close of the fourteenth century by all the logicians who, in the University of Oxford, composed the school of William of Heytesbury, Chancellor of Oxford in 1375; it was subsequently examined or invoked in the fifteenth century by all the Italians who became the commentators of these logicians; and finally, the masters of the University of Paris, contemporaries of Vinci, taught and demonstrated it as Oresme had done.
This law which Vinci was not able to determine was pubUshed in 1545 by a Spanish Dominican, Domingo Soto (1494-1560), an alumnus of the Uni- versity of Paris, and professor of theology at Alcald, de Henares, and afterwards at Salamanca. He for- mulated these two laws thus:
The velocity of a falling body increases propor- tionally to the time of the fall.
The space traversed in a uniformly varied motion is the same as in a uniform motion occupying the same time, its velocitj' being the mean velocity of the former.
In addition Soto declared that the motion of a bodj' thrown vertically upward is uniformly retarded. It should be mentioned that all these propositions were formulated by the celebrated Dominican as if in relation to truths generally admitted by the mas- ters among whom he lived.
The Parisian theory, maintaining that the accel- erated fall of bodies was due to the effect of a continual increase of impetus caused by gravity, was admitted by Julius Ca-sar Scaliger (14S4-155S), Benedetti, and Gabriel Vasquez (1551-1604), the celebrated Jesuit theologian. The first of these authors presented this theory in such a way that uniform acceleration of motion seemed naturally to follow from it.
Soto, Tartaglia, and Cardano made strenuous efforts, after the manner of Vinci, to ex-plain the motion of projectiles by appealing to the conflict between impetus and gravity, but their attempts were frustrated by a Peripatetic error which several
Parisian masters had long before rejected. They
believed that the motion of the projectile was acceler-
ated from the start, and attributed this initial acceler-
ation to an impulse communicated by the vibrating
air. Indeed, tlvroughout the sixteenth century, the
Italian Averroists continued to attribute to the am-
bient air the very transportation of the projectile.
Tartaglia empirically discovered that a piece of
artillery attained its greatest range when pointed at
an angle of forty-five degrees to the horizon. Bruno
insisted upon Oresme's explanation of the fact that
a body appears to fall in a vertical line in spite of the
Earth's motion; to obtain the trajectory of this
body it is necessary to combine the action of its
weight with the impetus which the Earth has im-
parted to it. It was as follows that Benedetti set
forth the law followed by such an impetus. A body
whirled in a circle and suddenly left to itself will
move in a straight line tangent to the circle at the
very point where the body happened to be at the
moment of its release. For this achievement Bene-
detti deserves to be ranked among the most valuable
contributors to the discovery of the law of inertia.
In 1553 Benedetti advanced the following argument:
in air, or any fluid whatever, ten equal stones fall
with the same velocity as one of their number; and
if all were combined they would still fall with the
same velocity; therefore, in a fluid two stones, one
of which is ten times heavier than the other, fall with
the same velocitj'. Benedetti lauded the extreme
novelty of this argument with which, in reality,
many scholastics had been familiar, but which they
had all claimed was not conclusive, because the resis-
tance which the air offered to the heavier stone
could certainly not be ten times that which it opposed
to the lighter one. Achillini was one of those who
clearly maintained this principle. That it might
lead to a correct conclusion, Benedetti's argument
had to be restricted to the motion of bodies in a
vacuum, and this is what was done by Galileo.
XVII. Galileo's Work.— Galileo Galilei (1564- 1642) had been in youth a staunch Peripatetic, but was later converted to the Copernican system, and devoted most of his efforts to its defence. The tri- umph of the system of Copernicus could only be secured by the perfecting of mechanics, and espe- cially by solving the problem presented by the fall of bodies, when the earth was supposed to be in motion. It was towards this solution that many of Galileo's researches were directed, and to bring his labours to a successful issue he had to adopt cer- tain principles of Parisian dynamics. Unfortunately, instead of using them all, he left it to others to ex- haust their fecundity.
Galilean statics was a compromise between the incorrect method inaugurated in Aristotle's "Mechan- ical Questions" and the correct method of virtual displacements successfully applied by the School of Jordanus. Imbued with ideas that were still intensely Peripatetic, it introduced the consideration of a certain impeto or momenta, proportional to the velocity of the moving body and not unlike the impetus of the Parisians. Galilean hydrostatics also showed an imperfect form of the principle of virtual displacements, which seemed to have been suggested to the great Pisan by the effectual re- searches made on the theory of running water by his friend BenedettoCastelli, the Benedictine (1577-1644). At first Galileo asserted that the velocity of a falling body increased proportionally to the space traversed, and afterwards, by an ingenious demonstration, he proved the utter absurdity of such a law. He then taught that the motion of a freely falling body was uniformly accelerated; in favour of this law, he con- tented himself with appealing to its simplicity with- out considering the continual increiise of impetus under the influence of gravity. Gravity creates, in
