Page:Catholic Encyclopedia, volume 12.djvu/84

 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