MOTION, MECHANICS, ETC. 183 



If any body, equal to 64 m, fall freely, or be acted upon 

 by its own natural weight, it will describe 192 inches in the 

 first second of its fall ; but if the same mass be impelled by 

 only _i_ of its accelerating force, or I m, it will describe only 

 a 64th part of the former space ; that is, only three inches, 

 a proportional effect. 



To prove this, let A and B be each made equal to 25 m, 

 then will A and B be equal to 50 m ; to this add 1 1 for the 

 inertia of the wheels, and we have 61 m ; now put 2 m on 

 A, and 1 m on B, and the mass moved will be 64 m, and 

 the moving force 1 m. 



Set the stage to three inches, and let the weight descend 

 as before, and you will find it strike the stage at the first 

 second. 



If the same force impel different quantities of matter for any 

 given time, the spaces described from rest will be inversely as 

 the quantities of matter moved. 



Let the force be m, and the mass 64 m, then the space 

 described, during one second, will be three inches. 



Let the force be m, and the mass 32 m, then the space 

 described in the same time will be six inches. 



If the, force be increased or diminished in the same propor- 

 tion with the mass moved, the spaces described from rest in the 

 same time, ivill be equal. 



Let m, 2 m, and 4 m, be the moving forces which impel 

 the quantities of 32 m, 64 m, 128 m, respectively ; then m 

 will impel 32m through six inches in a second, 2 m will im- 

 pel 64 m, and 4 m will impel 128 m through the same space 

 in the same time. 



From hence you may infer, that when different quantities 

 of matter describe equal spaces in equal times, being accele- 

 rated from quiescence, the forces must be in the same pro- 

 portion with the quantity of matter moved. 



If a body be moved from quiescence during any given time, 

 it will, at the end of that time, have acquired such a velocity, 

 as will, if continued uniform, carry it through double the space 

 which the body has already described to acquire that velocity. 



Let the mass moved be 64 m, the force, m , but let m, 

 which is applied to A, as the moving force, be one of the 

 flat rods, m, Fig. 176. Place the circular frame so that A 

 may, in descending, pass through it, and its height be such, 

 that the instant the lower surface of A arrives at 12 inches, 

 the rod, m, may be intercepted by the surface of the circular 



