THE SCIENTIFIC METHOD 119 



The continuity of space and time is generally accepted ; 

 without this belief it is impossible to establish the 

 geometrical laws of figure founded on the point, line, 

 and surface or the analytical laws of motion derived 

 from the calculus. The only exception I know to 

 this postulate is Professor Planck's theory of quanta, 

 in w 7 hich motion may occur in jumps. But the divisi- 

 bility of matter is not usually supposed to be infinite. 

 Indeed, the denial of this assertion is the foundation 

 of all atomic theories. Yet it is difficult to see how 

 mathematics can be anything but abstract logic, or how 

 it can be applied to physical problems unless this third 

 fundamental quantity, which is, as it were, the con- 

 necting link between the abstract and the concrete, be 

 also indefinitely divisible. It is only by the postulate 

 of the indefinite divisibility of mass that we may pass 

 from the mathematical laws of pure motion (kine- 

 matics) to the physical laws of the motion of bodies 

 (dynamics). How, otherwise, can we replace finite 

 bodies by mathematical centers of inertia? In this 

 connection Sir Joseph Larmor says : " The difficulty of 

 imagining a definite uniform limit of divisibility of 

 matter will always be a philosophical obstacle to an 

 atomic theory, so long as atoms are regarded as dis- 

 crete particles moving in empty space. But as soon as 

 we take the next step in physical development, that of 

 ceasing to regard space as mere empty geometrical 

 continuity, the atomic constitution of matter (each 



