Maech 28, 1913] 



SCIENCE 



469 



of lead and cork, respectively. When the 

 suspension fibers had equal lengths and the 

 pendulums swung through equal ampli- 

 tudes, they had equal velocities at each 

 point of their path. It is difficult to find, 

 in Newton's hollow pendulum experiment, 

 much more than a second approximation in 

 which he eliminates the air resistance from 

 this experiment of Galileo. 



4. The fourth advance which we owe to 

 Galileo is the observation that the momen- 

 tum communicated to a body in one direc- 

 tion does not alter its momentum in a 

 direction at right angles. This indepen- 

 dence of components of momenta, now 

 known as Newton's second law of motion, 

 was in the hands of Galileo no mere philo- 

 sophical theorem, no vague guess, but a 

 practical rule of action to be employed in 

 mechanical operations. It is by com- 

 pounding a uniform horizontal 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 discovered and employed the first 

 two of Newton's laws essentially as we use 

 them to-day. 



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 discovery in physical science; 

 one must start in with the correct view- 

 point. This viewpoint is precisely what 

 Aristotle lacked and exactly what Galileo 

 possessed. It is Gomperz,^' the distin- 

 guished historian of Greek thought, who 

 says: 



The physical doctrines of Aristotle are a dis- 

 appointing chapter in the history of science. They 



""Greek Thinkers," Vol. 4, p. 108, Berry's 

 translation. 



display 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 mention 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 philos- 

 ophy than weeks in mathematics. It is, 

 therefore, extraordinarily surprising to find 

 set forth in his "Dialogues on Motion"^* 

 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 dis- 

 tinct manner, for the differential calculus, 

 in pointing out that the definitions^" of 

 constant velocity and constant accelera- 

 tion hold only when the times considered 

 are "all whatsoever." If, therefore, one 

 wishes to employ these definitions in the 

 discussion of variable motion he must take 

 his time intei-vals indefinitely small. 



The invention of the well-known thermo- 

 scope which Galileo employed in his lec- 

 tures at Padua also belongs here ; for while 

 it is not a true thermometer it doubtless 

 led immediately to those exquisite sealed 

 instruments shortly afterwards constructed 

 by the Accademia del Cimento and still 

 preserved in the Tribuna di Galileo at 

 Florence. The theory of "dimensions," 

 first stated by Fourier, was led up to in 

 the First Day of the Dialogues on Motion. 

 The principle employed in his measure- 

 ment of the density of air=" is one which is 

 not only faultless in principle, but one 

 which makes it plainly evident that Gali- 

 leo had properly conceived that idea of 

 atmospheric pressure which, in the hands 



« First Day, "Nat. Ed.," Vol. 8, p. 78. 

 "Third Day, "Nat. Ed.," Vol. 8, p. 191. 

 =»"Nat. Ed.," Vol. 8, p. 124, First Day. 



