34 HISTORY OF MECHANICS. 



that I look upon the experiment as a very difficult 

 one to make accurately." Yet it is clear from the 

 Notion of a Constant Force that (omitting the re- 

 sistance of the air,) this equality must take place ; 

 for the Force which will gradually destroy the 

 whole velocity in a certain time in ascending, will, 

 in the same time, generate again the same velocity 

 by the same gradations inverted ; and therefore the 

 same space will be passed over in the same time in 

 the descent and in the ascent. 



Another difficulty arose from a necessary conse- 

 quence of the Laws of Falling Bodies thus esta- 

 blished ; the proposition, namely, that in acquiring 

 its motion, a body passes through every interme- 

 diate degree of velocity, from the smallest conceiv- 

 able, up to that which it at last acquires. When a 

 body falls from rest, it begins to fall with no velo- 

 city ; the velocity increases with the time ; and in 

 one thousandth part of a second, the body has only 

 acquired one thousandth part of the velocity which 

 it has at the end of one second. 



This is certain, and manifest on consideration; 

 yet there was at first much difficulty raised on the 

 subject of this assertion ; and disputes took place 

 concerning the velocity with which a body begins to 

 fall. On this subject also Descartes did not form 

 clear notions. He writes to a correspondent, "I 

 have been revising my notes on Galileo, in which I 

 have not said expressly that falling bodies do not 

 pass through every degree of slowness, but I said 



