The Galileo Project > Science > On MotionOn MotionDuring the time he taught the mathematical subjects at the university of Pisa(1589-1592), Galileo began a book, De motu ("On motion"), which was never published.In it, we can trace the early development of his ideas concerning motion.One of the fundamental propositions of Aristotelian philosophy is that there is no effectwithout a cause. Applied to moving bodies, this proposition dictates that there is nomotion without a force. Speed, then is proportional to force and inversely proportional toresistance. This notion is not at all unreasonable if one takes as ones defining case ofmotion, say, an ox pulling a cart: the cart only moves if the ox pulls, and when the oxstops pulling the cart stops. For falling bodies, the force is the weight pulling down abody and the resistance is that of the medium, air or water. As the science of motionbecame somewhat more quantitative in the sixteenth century, some people began toinvestigate the motion of falling bodies more carefully. Galileo was one of these.If weight determines the speed of fall, then when two different weights are dropped froma high place the heavier will fall faster and the lighter slower, in proportion to the twoweights. A ten pound weight would reach the Earth by the time a one-pound weight hadfallen one-tenth as far.One approach was to speculate: suppose one connected the two weights with a string,what would be the speed of fall? Suppose one tied them together? In the first case thelighter weight would slow down the heavier one and therefore the time of fall would begreater than that of the heavier weight; in the second case there now was a compositebody weighing eleven pounds, whose time of fall would be less than that of the ten-poundweight. Perhaps weight was not the determiner of the speed of fall.But there was another approach, one of experience. Why not drop bodies of differentweights and see whether Aristotles prediction was correct. As early as 1544, the historianBenedetto Varchi referred to actual tests, which showed that it was not. In a tract writtenin 1576, Giuseppe Moletti, Galileos predecessor in the chair of mathematics at theuniversity of Padua, reported that bodies of the same material but different weight, aswell as bodies of the same volume but different material, dropped from a height arrived atthe Earth at the same time.Galileos approach to this problem was somewhat different. In De motu he proposed thatin free fall bodies dropped with a characteristic uniform speed determined not by theirweight but by their specific gravity (not his term). He put this theory to the test bydropping bodies from heights and found that the experiments did not confirm his theory.He states that, in fact, the lighter body (i.e. that of the lower specific gravity) will moveahead of the heavier body at the start of the fall, and that the heavier body then overtakesit and arrives at the bottom slightly earlier.
Scholars have pointed to such passages to support their argument that Galileo did notperform such experiments and that his references to experiments were only rhetoricaldevices. After all, we all know that in a vacuum all bodies would fall with the same speedand in a medium such as air the heavier body (assuming the two bodies are of the sameshape) will fall slightly faster: at no time will the lighter body be ahead of the heavierone. But when Galileos supposed experiment was repeated, the results showed that hehad described a real experiment. Students dropped spherical balls of wood and iron ofequal diameter and the wooden balls invariably moved ahead of the iron balls. Theexplanation lies in the fact that the heavier iron ball must be clasped in the hand withmore force and is therefore released slightly later than the wooden ball.Obviously, then, Galileo was performing experiments at the very beginning of hisinvestigations into motion, and he took his experimental results seriously. Over the nexttwo decades he changed his ideas and refined his experiments, and in the end he arrivedat the law of falling bodies which states that in a vacuum all bodies, regardless of theirweight, shape, or specific gravity, are uniformly accelerated in exactly the same way, andthat the distance fallen is proportional to the square of the elapsed time.Sources: Thomas B. Settle, "Galileo and Early Experimentation," in Springs of ScientificCreativity: Essays on Founders of Modern Science, ed. Rutherford Aris, H. Ted Davis,and Roger H. Stuewer (Minneapolis: University of Minnesota Press, 1983), pp. 3-20;idem, "Experimental Research and Galilean Mechanics," in Galileo Scientist: His Yearsat Padua and Venice, ed. Milla Baldo Ceolin (Padua: Istituto Nazionale di FisicaNucleare; Venice: Istituto Veneto di Scienze, Lettere ed Arti; Padua: Dip artimento diFisica, 1992), pp. 39-57.http://galileo.rice.edu/sci/theories/on_motion.html