MOTION, MECHANICS, ETC. 



185 



twelve inches, the moving forces must be as 4 to 3. The 

 following experiments will illustrate this truth. 



You may infer, from the two last sets of experiments, 

 that the moving forces, which impel bodies through the 

 same spaces, are in the joint ratios of the quantities of 

 matter moved, and the squares of the velocities generated. 



If a given quantity of matter be impelled from rest through 

 different spaces by tlie action of the same force, the velocities 

 generated will be in a subduplicate ratio of the spaces described. 



Let the quantity of matter be 64 m, the force m, the 

 spaces 3 inches and 2V inches, the velocities will be in the 

 ratio of 1 to 3 ; for it will descend in the first experiment 

 through six inches in a second ; in the next you will find it 

 go through 18 inches in a second. Now the spaces are 3 

 and 27, or as 1 to 9 ; the velocities acquired as 6 to 18, or 

 as 1 to 3. 



Experiment* on uniformly retarded Motion. The laws 

 observed during the motion of uniformly accelerated bodies, 

 having been made evident to the senses by the preceding 

 experiments, I shall now proceed to illustrate the properties 

 of uniformly retarded motion. 



When a body is thrown perpendicularly upwards from 

 the earth's surface, it is continually resisted by a force 

 which is equal to the body's weight ; and the weights of all 

 substances being proportional to the quantity of matter they 

 contain, it follows, that the force which retards the perpen- 

 dicular ascent of any body, being measured by its weight 

 divided by the ascending mass, is the same, being such as 

 destroys a velocity of 32 feet in each second of the body's 

 motion. But in order to illustrate, by experiment, the 

 general laws according to which bodies are retarded by the 

 action of constant forces, such methods should be made use 

 of as will enable us to apply different resisting forces to the 

 same mass of matter, and the same resisting force to differ- 



