96 THE ANATOMY OF SCIENCE 



It was Newton, as you know, who welded to- 

 gether the results of these two investigators into 

 a great law which for over two centuries stood 

 as one of the really exact laws of nature. Indeed, 

 the whole of mechanics as left by Newton, while 

 it gained something of generalization and of 

 elegance in presentation, remained without 

 essential change until the recent remarkable dis- 

 coveries of Einstein. 



I shall not dwell upon the laws of classical 

 mechanics which are familiar to all of you, but 

 shall proceed at once to show how these funda- 

 mental laws may be displayed with remarkable 

 simplicity in our four-dimensional geometry of 

 space and time, or, for the sake of easier visuali- 

 zation, in the three-dimensional geometry char- 

 acteristic of the motion of balls upon a billiard 

 table, and the two-dimensional geometry which 

 shows the motion of beads upon a string. 



Let us represent in Figure 18 the space-time 

 paths of two bodies which, when they are near 

 together, exercise an action (in this particular 

 case a repulsive action) upon one another. The 

 masses of the two particles we may represent 

 by the length of arrows drawn along the paths. 

 Thus the mass to the right is twice as great as 

 that on the left. Newton's first law of motion, 



