136 THE REALITIES OF MODERN SCIENCE 



falling for twice the time of the other, will acquire twice 

 the velocity, he formulated the necessary relations for 

 s and t. He had to deal with s and t instead of v and t 

 because he had no means for measuring instantaneous 

 velocities. His reasoning has been followed in the 

 preceding analysis, where it was shown that the 

 total distance traversed should be proportional to 

 the square of the time during which motion occurs. 



This conclusion from his fundamental assumption 

 he set himself to test. Clocks and chronographs were, 

 of course, unknown and only water clocks or sand- 

 glasses were available. With such crude devices it 

 would ordinarily be impossible to determine the time 

 of descent of a freely falling body with sufficient 

 accuracy to check the conclusion. He sought first, 

 therefore, to retard the descent so that it might be 

 more accurately observed. For this reason he studied 

 the motion of balls rolling down grooves in an in- 

 clined plane. A further assumption was therefore 

 required to the effect that the form of the relation- 

 ship between s and t would not be altered. Measuring 

 distances from the upper extremity of the plane he 

 marked off lengths of 1, 4, 9, and 16 arbitrary units. 

 The corresponding times of descent should be found 

 to be as 1, 2, 3, and 4. 



He next sought an improvement in methods of 

 timing. For the means he used a vessel of water, 

 with a large transverse area, in the bottom of which 

 there was a minute orifice which he could close by his 

 finger. Such a vessel will have a practically constant 

 " pressure head" while a small amount of water is 

 being discharged, and hence the weights of water 



