28 ILLINOIS ACADEMY OF SCIENCE 



they may assure themselves that it is not in the pow- 

 er of professors of demonstrative sciences to change 

 their opinions at pleasure. 



Or witness the following paragraph from the "Saggia- 

 tore"(9) as illustrating the great weight which Galileo at- 

 tached to experimental evidence. He says 



We examine witnesses in things which are 

 doubtful, past, and not permanent, but not in things 

 which are done in our presence. 



If discussing a difficult problem were like carry- 

 ing a weight, then since several horses will carry 

 more sacks of corn than one alone, I would agree 

 that many reasoners avail more than one; but dis- 

 coursing is like coursing, and not like carrying; and 

 one barb by himself will run faster than a thous- 

 and Friesland horses. 



In all his thinking nothing is exempt from experiment. 

 Astronomy even, in his hands, ceases to be a purely observa- 

 tional science; for when he wishes to discover whether the 

 bright portions of the moon's surface are rough or smooth, 

 he sets up two surfaces, one rough and one smooth ; then 

 illuminates them with Italian sunlight. Desiring to learn at 

 what rate falling bodies gain speed, he devises a time meas- 

 uring machine, invents a method of "diluting gravity'' and 

 actually measures the rate at which speed is gained. His 

 discussions begin and end with experiment — a method so 

 familiar to us that we forget how recent and powerful it is. 

 His two great dialogues — one dealing with astronomy, 

 the other with mechanics — abound in experiments — most of 

 them apt and clever. Leonardo da \"inci advocates experi- 

 ment : Galileo uses experiment. 



2. The second great achievement of Galileo was his 

 seizure upon momentum as the fundamental quantity in the 

 science of mechanics, and his demonstration that velocity is 

 a factor in momentum. Galileo was by no means the first 

 to study and discuss kinematical problems. 



Benedetti (1530-1590), one of the many distinguished 

 alumni of the University of Padua, had not only expressed 

 dissatisfaction with the artificial distinction between "vio- 

 lent" and "natural" motions, but had gone farther and had 

 paved the way for mechanics and the difTerential calculus by 

 recognizing the fact of continuous variation in motion: Ben- 

 edetti (10) had in particular studied oscillatory motion and 

 had shown that such a motion is continuous even when the 

 vibrating particle is at rest at the end of its path. He had in 

 fact introduced the modern idea of continuous variation. But 

 none of the predecessors of Galileo had, so far as I have been 



