MATTER IN MOTION 



89 



coveries regarding the lever he began with what 

 seemed to him the self-evident assumption that 

 "magnitudes of equal weight acting at equal 

 distances are in equilibrium." When we have, 

 as in Figure 15, two precisely similar bodies 



J 



Figure 15 

 Illustrating a Theorem of Archimedes 



suspended at equal distances from their mutual 

 point of support, it would have surprised Archi- 

 medes to learn that these might not be in equi- 

 librium, and that certain inequalities in the 

 earth's crust might cause one body to sink and 

 the other to rise. But if there is no dissymmetry 

 of external conditions it becomes evident that 

 there must be a state of balance, from what is 

 called the principle of sufficient reason, or in 

 mathematical parlance, the principle of sym- 

 metry. Suppose, however, that the two bodies 

 are not just alike, that they differ in chemical 

 substance or in shape or in color. What a priori 



