30 ILLINOIS ACADEMY OF SCIENCE 



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 dis- 

 tance. 



As illustrating how tenaciouly he clings to the idea of 

 momentum, witness the following clear, exact and thoroughly 

 modern definition dating from the year 1604: (12) 



I call a motion uniformly accelerated when start- 

 ing from rest its momentum, or degree of speed, in- 

 creases directly as the time, measured from the be- 

 ginning of the motion. 



Observe that we have here, without any mention of the 

 word, precisely the dynamical idea which we today 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 neighbor- 

 hood (action at a distance) or owing to contact with an elas- 

 tic body such as the hot gases of exploding gunpowder in 

 the barrel of a gun (action through a medium). Later gen- 

 erations had not yet beclouded the idea of force with ''ten- 

 dencies to motion" ; they 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 

 ])ermanently at rest by another elastic body; still less had 

 there been any attempt to convince people — principally high 

 school lads and college students — that all these various things 

 are one and the same, since, forsooth, at various times we 

 call them by one name, "force." Some of Galileo's most 

 worthy successors, such as Clififord,(13) Poincare(14) 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 

 is which he proves that the time of fall is independent of 

 weight, an experiment which completes to a first approxima- 

 tion the laws of falling bodies practically as we have them to- 

 day. He accomplishes a second approximation by eliminating 

 the bouyant force of the medium. He is prevented from making 

 ing a third approximation only because he meets the barrier 

 of viscosity, a barrier which still renders impossible the so- 

 lution of any but a few simple cases in fluid motion. 



The one remaining fundamental phenomenon of falling 

 l)odies, is that the acceleration of gravity is independent of 



