THE PRESIDEXT"S ADDRESS 31 



the substance of which the falling body is composed. This 

 Galileo (15) proved by swinging, side by side, two pendu- 

 lums, having bobs of lead and cork, respectively. When the 

 suspension fibers had equal lengths and the pendulums 

 swung through equal amplitudes, they had equal velocities at 

 each point of their path. It is difficult to find in Xewton's hol- 

 low pendulum experiment much more than a second approxi- 

 mation in which he eliminates the air resistance from this ex- 

 periment of Galileo. 



4. The fourth advance which we owe to Galileo is the 

 observation that the momentum communicated to a body in 

 one direction does not alter its momentum in a direction at 

 right angles. This independence of components of momenta, 

 now known as Xewton's second law of motion, was in the 

 hands of Galileo no mere philosophical theorem, no vague 

 guess, but a practical rule of action to be empolyed in me- 

 chanical operations. It is by compounding a uniform hori- 

 zontal velocity with an accelerated vertical velocity that he 

 proves, for the first time, that the path of a projectile is a 

 parabola. It was by means of this principle that he prepared 

 a range-table for gunners. The fact is then that Galileo dis- 

 covered and employed the first two of Xewton's laws essen- 

 tiallv as we use them today. 



It requires more than sheer strength to climb a difficult 

 mountain peak : one must start in on the right trail. More than 

 mere intellectual ability is needed to make an important dis- 

 covery in physical science : one must start in with the correct 

 viewpoint. This viewpoint is precisely what Aristotle 

 lacked and exactly what Galileo possessed. It is Gomperz.(16) 

 the distinguished historian of Greek thought, who says: 

 The physical doctrines of Aristotle are a disa}>- 



pointing chapter in the history of science. They dis- 



plav to us an eminent mind wrestling with problems 



to which it is in no wise equal. 



5. As a minor achievement of Galileo allow me to men- 

 tion some discoveries to which he blazed a part of the road. 



In a letter to a friend he says he had spent more years in 

 the study of philosophy than weeks in mathematics. It i-^ 

 therefore, extraordinarily surprising to find set forth in his 

 ".Dialogues on Motion" (17) all the detailed facts and ideas 

 which are involved in the modern definition of an infinite 

 quantity developed by Boltzano. Cantor, and Dedekind. viz., 

 an assemblage containing a part which may be put into one- 

 to-one correspondence with the whole. 



Again he paves the way, in a very distinct manner, for the 

 differential calculus, in pointing out that the definitions (18) 

 of constant velocitv and constant acceleration hold onlv whe-i 



