MECHANICS AND PHYSICS 197 



replace the two weights by a single weight equal to 

 4 lbs. and fixed at a distance of 6 inches. The moment 

 of the force acting on the pendulum in a horizontal 

 position is still equal to 24, i.e., the product of 6 by 4. 



Under these conditions it would seem that if we 

 allow the pendulum to oscillate, we must obtain the 

 same result in both cases and find that the duration 

 of the oscillations is the same. But in fact it is not 

 so. Why ? Because the conditions of symmetry for 

 a system in motion are not the same as for a system 

 in equilibrium. By changing the compound pendulum 

 into a simple pendulum we certainly have not changed 

 the static moment of the system but we have modified 

 its moment of inertia, and for this reason the times 

 of oscillations can no longer be equal. 1 



Thus from the logical principle of symmetry one 

 cannot a priori deduce consequences before making 

 any experiment. It is experience alone which can 

 teach us in what way this principle works in nature, 

 for a mass of unknown factors may interfere and 

 confuse its application just where the latter might 

 rightly be expected. Concerning the lever, we know 

 for example that to maintain equilibrium, it is im- 

 material to hang the arrangement of two weights 

 higher or lower than the weight it replaces, and to 

 place this arrangement parallel or perpendicular to 

 the direction of the lever. 



If, notwithstanding, the demonstration of Archi- 



1 The moment of inertia I is the sum of the masses m 

 multiplied by the squares of their distances r from the axis 

 of suspension. The time of oscillation is then equal to 



T «= 2 n\/ — when M represents the static moment. 



If the calculations in the chosen numerical example be 

 made, it will be found that I for the compound pendulum is 

 equal to 2 x 4* + 2 x 8 ! = 160, while for the simple pendu- 

 lum it is only equal to 4 x 6 2 = 144. 



