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



ent masses of matter, both of which conditions will be satis- 

 fied by the instrument now before you. 



A resisting force is to be understood as conveying pre- 

 cisely the same idea as the term moving force ; except so 

 far as regards the directions in which those forces act in re- 

 spect to the body's motion, these directions being contrary 

 to each other. 



If equal quantities of matter be projected in free space, 

 with any given velocity, and be resisted by different but in- 

 variable forces, the spaces described before the whole mo- 

 tion is destroyed, will be inversely as the resisting forces. 



Let the mass projected be 61 m, with a velocity of 18 

 inches in a second, and let it be resisted successively by the 

 forces m,2m,3 m ; the spaces described before the motion 

 of the body is destroyed will be ^ -^-fj | ; these spaces 

 being in the inverse proportion of the resisting forces. 



Make A equal 24 m, B equal 25^ m ; apply to the up- 

 per surface of A two rods, each equal to m ; then will the 

 weight, A, preponderate and descend by the action of a 

 moving force equal m, the whole mass moved being equal 

 to 63 m. Set the circular frame to 26.44 ; then the weight, 

 A, by describing from rest the space 26.44 inches, will 

 acquire a velocity = V ^ 4 + L93 -+26.44^ e q ua i to 18 inches 

 in a second ; and at that instant the two rods, each equal to 

 m, being removed, the weight will continue to descend with 

 a uniformly retarded motion, which will be precisely the 

 same as if a mass of 61 m were projected with a velocity 

 of 18 inches in a second, in free space, and a force of resist- 

 ance equal to m were opposed to its motion; wherefore A, 

 with the other parts of the system, will lose its motion 



gradually, and will describe a space equal to .' ^ 6 1 = 25.6 

 inches before its motion be entirely destroyed. You will, 

 therefore, have to descend as low as 52 inches, before it 

 begins to ascend by the superior weight of B. 



If any body, moving in a free space uniformly, be resisted 

 by a constant force, for any given time less than tJiat in which 

 the whole motion would be destroyed, the space described will 

 be the difference between the space which measures the initial 

 velocity of motion, multiplied into a number expressing the 

 given time, and that space which the body would describe, if 

 accelerated, during the given time, from quiescence, by a force 

 equal to that of resistance. 



