Mabch 28, 1913] 



SCIENCE 



467 



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 Vinci advo- 

 cates experiment : Galileo uses experiment. 



2. The second great achievement of Gali- 

 lei 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 dis- 

 cuss kinematical problems. 



Benedetti (1530-1590), one of the many 

 distinguished alumni of the University of 

 Padua, had not only expressed dissatisfac- 

 tion Avith the artificial distinction between 

 "violent" and "natural" motions, but had 

 gone farther and had paved the way for 

 mechanics and the differential calculus by 

 recognizing the fact of continuous varia- 

 tion in motion: Benedetti^" had in partic- 

 ular 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 able 

 to discover, pushed their study of moving 

 bodies beyond the mere consideration of 

 change of position. None of them had 

 recognized the inertia of the moving body 

 as a fundamental — perhaps the funda- 

 mental — fact of mechanics. Princes and 

 paupers, for ages, had stumped their toes 

 against bricks and stones: they were 

 doubtless quite as familiar as we with the 

 mere fact of inertia. But to Galileo it was 

 a cardinal fact, because he was the first to 

 see that the future history of a body de- 

 pends upon its possession of inertia. To 



"Lasswitz, " Atomistik, " Bd. 2, pp. 14-23, 

 gives a good description of Benedetti 's work. 



him the importance of a motion is, in gen- 

 eral, measured by the inertia involved, or, 

 as was then said — the weight involved. 

 Hence he assigned to the product of the 

 weight and velocity of a body the name 

 "momentum," which is merely the Latin 

 word for importance; as a synonym he 

 sometimes uses the word impetus, thus 

 emphasizing the impetuosity of motion. 



But Galileo never got beyond the point 

 where he measured inertia by weight, as, 

 indeed, engineers still do — all, at least, 

 except electric engineers. The invention 

 of the idea of mass was reserved for New- 

 ton. Even Huygens," who first mastered 

 the idea of centrifugal force, never got 

 beyond the point where he measured cen- 

 trifugal forces in terms of weight, thus 

 avoiding the conception of mass in all his 

 work. 



Those who wish to see just how clearly 

 Galileo conceived that the future behavior 

 of a body is connected with its inertia 

 should read those propositions in his 

 " Mechanics "^^ in which he calculates the 

 path of a projectile by assuming that the 

 horizontal speed of a shot, after it has left 

 the muzzle of a gun, continues to be uni- 

 form. His repeated use of this principle 

 makes it perfectly clear that he discovered 

 what we now call — and perhaps properly 

 call — Newton's first law of motion. Gali- 

 leo failed to generalize it by extending it 

 to all bodies, whether subject to the earth's 

 gravitation or not. This Newton did be- 

 cause he had acquired the new concept of 

 mass — that constant property which never 

 deserts a body in any position or condition. 



3. The next great step which Galileo 



" Huygens, ' ' Horologium Oseillatorium, ' ' Part 

 v., Prop. 13 ; or Hobart, ' ' School Science and 

 Matliematics, " Vol. 11, p. 692 (1911), for trans- 

 lation of Huygens 's paper. 



" Galileo, ' ' Dialogues on Motion, ' ' Fourth Day, 

 Problem I. et seq. 



