152 WHAT IS SCIENCE? 



of the work of Newton. We should never think it really 

 necessary to-day to confirm by experiment the results 

 of calculation based on that assumption ; indeed if 

 experiment and calculation did not agree, we should 

 always maintain that the former and not the latter was 

 wrong. But the assumption is there, and it is primarily 

 suggested by the aesthetic sense of the mathematician, 

 not dictated by the facts of the external world. Its 

 certainty is yet one more striking instance of the 

 conformity of the external world with our desires. 



And now let us glance at an example in which such 

 calculation becomes of real importance. Let us take a 

 pendulum, consisting of a heavy bob at the end of a 

 pivoted rod, draw it aside and then let it swing. We 

 ask how it will swing, what positions the bob will occupy 

 at various times after it is started. Our calculation 

 proceeds from two known laws, (i) We know how the 

 force on the pendulum varies with its position. That we 

 can find out by actual experiments. We hang a weight 

 by a string over a pulley, attach the other end of the 

 string to the bob, and notice how far the bob is pulled 

 aside by various weights hanging at the end of the string. 

 We thus get a numerical law between the force and the 

 angle which the rod of the pendulum makes with the 

 vertical. (2) We know how a body will move under a 

 constant force. It will move in accordance with Table II, 

 the distance travelled being proportional to the 

 " square " of the time during which the force acts. Now 

 we introduce the Newtonian assumption. We know the 

 force in each position ; we know how it would move in 

 that position if the force on it were constant ; actually 

 it is not constant, but we assume that the motion will be 

 the same as it would be if, in that position, the force were 

 constant. With that assumption, the general Newtonian 

 rule (of which the application to velocity is only a special 

 instance) enables us to sum up the effects of the motions 



