RATES 137 



discharged will be proportional to the time of flow. 1 

 With this apparatus he confirmed his assumptions. 



Further studies by Galileo of the kinematics of 

 uniformly accelerated bodies contributed much to that 

 base of accumulated knowledge upon which his suc- 

 cessors, and especially Newton, built the classical 

 system of mechanics. The modern concept of energy 

 upon which science rests to-day was frequently ap- 

 proached but apparently never firmly grasped by these 

 natural philosophers. For example, Galileo studied 

 the relations which must subsist between free descent 

 and motion on an inclined plane. As he had shown 

 previously, the velocity of a freely falling body is 

 increased proportionally to the time of descent. He 

 therefore reasoned that if its direction of motion should 

 be reversed at any instant, as by a reflection, the 

 velocity would then be diminished proportionally 

 to the time of ascent. The body should, therefore, 

 rise through the same distance as it had previously 

 fallen. If, then, a body is allowed to roll down an 

 inclined plane and up another it cannot rise to a point 

 higher than that from which it started. In the limiting 

 case it will just attain this height. If it could exceed 

 this height it would be possible to arrange inclined 

 planes so as to effect the elevation of bodies by gravity 

 alone. The velocity acquired in frictionless descent 

 along an inclined plane depends, then, only upon the 



1 It was Torricelli, somewhat later, who perceived the analogy 

 between freely falling bodies and the flow of liquids under a gravity 

 feed. He showed that, neglecting all frictional resistances, the 

 velocity of efflux from an orifice, a distance of h below the surface, 

 is given by v* = 2gh. Hence if the head, h, is constant the velocity 

 is constant and the discharge is proportional to the time. 



