184 BENJ. PIKE'S, JR., DESCRIPTIVE CATALOGUE. 



frame, and thereby be prevented from the further accelera- 

 tion of the system. Let the other stage be set at 36 inches, 

 that is, 24 from the circular frame. 



Now, let the weight begin to descend from o, on the 

 scale at any beat of the pendulum ; at the end of the second 

 beat, you will hear the rod strike the circular frame, having 

 described twelve inches with a uniformly accelerated motion ; 

 and at the fourth beat of the pendulum, it will strike against 

 the square stage at 36, having described 24 inches with a 

 uniform motion. 



If the same force act on the same mass for different times, 

 one second, two seconds, and three seconds, the velocities gene- 

 rated will then be six inches, 6x2 inches, and 6x3 inches in a 

 second respectively, being in the same proportion with the times 

 wherein the given force acts. 



Set the circular frame to three inches, and the stage to 

 nine inches, let the mass moved be 64 m, the moving force, 

 m ; the weight, A, beginning its descent at any beat of the 

 pendulum, the rod will strike the circular frame at the next 

 beat : here the rod is removed, and A describes the next 

 six inches uniformly in one second, striking the stage at nine 

 at the second beat. By trying the apparatus in other in- 

 stances, you will constantly find the experiments coinciding 

 with theory. 



These experiments show, that if the force by which bodies 

 are accelerated be the same, the velocities generated will 

 be in the same proportion as the times wherein the given 

 force acts. 



If a body be moved from rest through the same space by 

 different forces, the velocities generated will be in a subdupli- 

 cate ratio of the forces. 



Let the mass be 64 m, and the force m, you will find 

 the velocity acquired in describing twelve inches in two 

 seconds, will, when the force is removed, carry it through 

 twelve inches in one second. Now, let the mass be 64 m, 

 and the force 4 m, and you will find that the body, in de- 

 scribing twelve inches, will acquire a velocity of twenty-four 

 inches, being in the ratio of 1 to 2 ; whereas the accelerating 

 forces are in the ratio of 1 to 4. 



If different quantities of matter be impelled through the 

 same space, and acquire the same velocity, the moving forces 

 must be in the same ratio as the quantities of matter moved. 



Let the quantities of matter be 64 m and 48 m, the space 



