loO WHAT IS SCIENCE? 



can ; and in this way. When the velocity is constant 

 and we can measure it without ambiguity, then we can 

 establish laws between that velocity and certain properties 

 of the moving body. Thus, if we allow a moving steel ball 

 to impinge on a lead block, it will make a dent in it deter- 

 mined by its velocity ; and when we have established by 

 observations of this kind a relation between the velocity 

 and the size of the dent, we can obviously use the size of 

 the dent to measure the velocity. Suppose now our 

 falling body is a steel ball, and we allow it to impinge 

 on a lead block after falling through different distances ; 

 we shall find that its velocity, estimated by the size of 

 the dent, agrees exactly with the velocity estimated by 

 Newton's rule, and not with that estimated by any other 

 rule (so long, of course, as the other rule does not give the 

 same result as Newton's). That, I hope the reader will 

 agree, is a very definite proof that Newton's rule is right. 

 On this account only^ Newton's rule would be very 

 important, but it has a wider and much more important 

 application. So far we have expressed the rule as giving 

 the velocity at any instant when the relation between 

 time and distance is known ; but the problem might be 

 reversed. We might know the velocity at any instant 

 and want to find out how far the body has moved in any 

 given time. If the velocity were the same at all instants, 

 the problem would be easy ; the distance would be the 

 velocity multiplied by the time. But if it is not the same, 

 the right answer is by no means easy to obtain ; in fact 

 the only way of obtaining it is by the use of Newton's 

 rule. The form of that rule makes it easy to reverse it 

 and, instead of obtaining the velocity from the distance, 

 to obtain the distance from the velocity ; but until that 

 rule was given, the problem could not have been solved ; 

 it would have baffled the wisest philosophers of Greece. 

 Now this particular problem is not of any very great 

 importance, for it would be easier to measure by experi- 



