468 



SCIENCE 



[N. S. Vol. XXXVII, No. 952 



made was the discovery of the constant 

 factor in the motion of falling bodies. One 

 of his earliest experiments, performed 

 while stiU a young man at the University 

 of Pisa, was to allow a bronze ball to roll 

 down a carefully prepared inclined plane, 

 an experiment from which he cleverly in- 

 ferred that while the position and speed of 

 the ball were changing, the time-rate at 

 which it gained momentum remained con- 

 stant. It was with reference to these par- 

 ticular experiments that Goethe remarked 

 "dem Genie, ein Fall fiir tausend gelte." 

 The experiment is completed by showing 

 how one can compute the momentum (or 

 speed) of a body after it has been falling 

 for any given time or through any given 

 distance. In all these computations, the 

 unit of momentum employed is that which 

 a body acquires in falling freely through 

 an arbitrarily selected unit of distance. 



As illustrating how tenaciously he clings 

 to the idea of momentum, witness the fol- 

 lowing clear, exact and thoroughly modern 

 definition dating from the year 1604:^^ 



I oaU a motion uniformly accelerated when 

 starting from rest its momentum, or degree of 

 speed, increases directly as the time, measured 

 from the beginning of the motion. 



Observe that we have here, without any 

 mention of the word, precisely the dynam- 

 ical idea which we to-day use under the 

 name of a "constant force." There is, 

 indeed, no necessity for the name; for 

 Galileo attempts nothing more than to dis- 

 cover how the momentum of a body 

 changes, owing to the presence of another 

 body such as the earth in the neighborhood 

 (action at a distance) or owing to contact 

 with an elastic body such as the hot gases 

 of exploding gunpowder in the barrel of a 

 gun (action through a medium). Later 

 generations had not yet beclouded the idea 

 of force with ' ' tendencies to motion ' ' ; they 



""Nat. Ed.," Vol. II., p. 166. 



had not yet identified it with that vastly 

 more complex "muscular sensation"; they 

 had not yet made it over in the form of a 

 "man"; they had not yet named it an 

 "agent"; they had not yet identified it 

 with a state of stress or strain which one 

 elastic body exhibits when held perma- 

 nently at rest by another elastic body ; still 

 less had there been any attempt to con- 

 vince people — principally high-school lads 

 and college students — that all these various 

 things are one and the same, since, for- 

 sooth, at various times we call them by one 

 name, "force." Some of Galileo's most 

 worthy successors, such as Clifford,^* Poin- 

 care^^ and Hertz, have pointed out our 

 inconsistent definitions of force, and have 

 advocated in the most outspoken manner, 

 a return to the simple methods of this 

 Italian academician. 



The best known of all his experiments 

 is, of course, that in which he proves that 

 the time of fall is independent of weight, 

 an experiment which completes to a first 

 approximation the laws of falling bodies 

 practically as we have them to-day. He 

 accomplishes a second approximation by 

 eliminating the buoyant force of the me- 

 dium. He is prevented from making a 

 third approximation only because he meets 

 the barrier of viscosity, a barrier which 

 still renders impossible the solution of any 

 but a few simple cases in fluid motion. 



The one remaining fundamental phe- 

 nomenon of falling bodies is that the ac- 

 celeration of gravity is independent of the 

 substance of which the falling body is com- 

 posed. This Galileo^" proved by swinging, 

 side by side, two pendulums, having bobs 



"Clifford, Nature, Vol. 22, p. 122 (1880). 



" Poincarg, lecture before the Wissenschaftlich 

 Verein in Berlin, p. 116 (Teubner, 1912). 



"'<Nat. Ed.," Vol. 8, pp. 128-130, First Day, 

 translated into German by von Oettinger, Ost- 

 Tval's Wiss. Klassiker, No. 11, p. 76 



