526 



SCIENCE 



[N. S. Vol. XXXI. No. 797 



lives suffice therefore to bridge the gap be- 

 tween Galileo and our contemporaries. 

 Back to Galileo is not therefore a far cry. 



Recognizing the limitations of his sci- 

 ence, and seeing that the search after causes 

 was futile, Galileo adopted the causal pos- 

 tulate and prepared to confess his ignor- 

 ance of gravitation, cohesion, muscular 

 tension, and to say that, when we see a 

 body changing its momentum, there is a 

 ' ' force ' ' at work upon it. Following is the 

 sentence, from his "Dialogues"^ in which 

 he introduces force as a synonym for any 

 of these unknown influences which pro- 

 duce acceleration: 



It does not appear to me worth while to investi- 

 gate the causes of natural motion concerning 

 which there are as many different opinions as 

 there are different philosophers. Some refer them 

 to an attraction towards the center; others assign 

 them to repulsion between the small particles of 

 a body, while still others would introduce a cer- 

 tain stress in the surrounding medium which 

 closes in behind the falling body and drives it 

 from one of its positions to another, Now all 

 these fantasies, and others too, must be examined; 

 but it is not really worth while. For all that is 

 needful is to see just how one investigates the 

 properties of accelerated motion and how these 

 are defined, without consideration of their cause, 

 in such a way that the momentum (of the body) 

 increases imiformly from the initial condition of 

 rest in simple proportionality to the time. 



The paragraph which I have just quoted 

 is, so far as I am able to learn, the earliest 

 expression and definition of that central 

 physical quantity which we now call 

 "force." Observe first of all the modesty 

 of the man ; twice within this definition he 

 inserts a distinct disavowal of any consid- 

 eration of the cause of motion. So far is 

 he in advance of our modern text-books, 

 that he declines to define force as a " cause 

 of motion" or a "tendency to produce 

 motion," but says it is not even worth 



' Ostwald's " Klassiker der Exakten Wissen- 

 schaften," No. 24, p. 15. 



while to consider the question from that 

 point of view. 



How clear these same ideas were to New- 

 ton will be evident from the following two 

 sentences from the first book of the ' ' Prin- 

 cipia." He says: 



For I here design only to give a mathematical 

 notion of those forces without considering their 

 physical causes or seats. 



And again : 



Wherefore the reader is not to imagine that by 

 those words I anywhere take upon me to define 

 the kind or the manner of any action, the cause 

 or the physical reason thereof. 



Having thus abandoned all considera- 

 tion of cause and having assigned our- 

 selves the simpler task of describing the 

 motions of bodies, we come back to the 

 definition of Galileo and Newton, namely, 

 the rate of change of momentum — as the 

 one perfectly correct, competent and com- 

 plete description of force. 



It remains only to show that Galileo had 

 a clear and modern conception of momen- 

 tum. This is sufficiently evident from the 

 following paragraph in the "Dialogues."^ 

 He says: 



It is clear that an impulse is not a simple 

 matter, seeing that it depends upon tioo important 

 factors, namely, the weights (il peso) of the col- 

 liding bodies and their velocities. 

 And again on the same page he says 



It is customary to say that the " momentum " 

 of a light body is equal to the " momentum " of a 

 heavy body when the velocity of the former bears 

 to the velocity of the latter the inverse ratio of 

 their weights. 



If then I have correctly stated the facts 

 of the case, force would appear to be a 

 pure concept of the intellect: but a pre- 

 cious concept; one which is well under- 

 stood, clear, definite, quantitative, and one 

 whose extraordinary usefulness has made 



" Ostwald's " Klasiker der Exakten Wissen- 

 schaften," No. 25, p. 44. 



