THE AUTHOR'S PREFACE

the same reciprocal proportion as the power of the striker has to the resistance of the struck body; for the power of the striker can be greater or less than the resistance of the struck body, even while their velocities are always equal to one another.

Excited by these difficulties, as I conjecture, Galileo devised and performed those two famous experiments related by Mersenne in Physical-Mathematical Reflections, Chapter 23, which the most famous and learned man, Michael Angelo Ricci, communicated to him. They are as follows:

In the middle of an arch's string, he attached a cord a cubit long, at the lowest end of which hung a lead ball of 2 ounces, and he lowered this from the summit of the arch, and noted its flexion and the traction of the string. Then he placed ten pounds in the middle of the same arch's string, by which the string was held in the same state of flexion. When he had later taken a stronger arch, whose string was brought to a lesser space by the same falling weight, he tested that the string could not be held by 10 pounds in that place to which it had been brought by the force of 2 falling ounces, but that 20 pounds were required. From which he concluded that an arch could be made so robust that not even 100 pounds could retain it in that position to which it had been brought by 2 ounces falling as before, and therefore that the force of percussion is in some way infinite. He brings forward another observation about a lead globe, which a falling hammer thins out from the height of one arm, for example; which thinning, even if 10 pounds pressing on an equal globe accomplish it the first time, if the hammer strikes its lead globe again from the same height with a repeated blow, it will make a new depression, which another 10 pounds—that is, 20 pounds—cannot accomplish. And if you urge the same again, the force of percussion will finally be concluded to be infinite.

That Galileo himself frequently communicated these same experiments to friends, and from them deduced that the force of percussion is infinite, Raphael Magiotti, Bonaventura Cavalieri, Famiano Michelini, and other intimate friends of Galileo have testified many times. Furthermore, at the end of the fourth dialogue of Galileo's On the Motion of Projectiles, he hints that the theory of the energy of percussion is very obscure, and that none of those who have treated this subject have penetrated its recesses, which are wrapped in shadows and entirely removed from first human imaginations; and among other conclusions, he offers one that is undiscovered: namely, that the force of percussion is interminable, if we do not wish to call it infinite, and that he finally wishes to defer the dissertation of this argument to another more opportune time.