30 LECTURE nr. 



Wlieu the increase or diminution of the velocity of a moving body is uni- 

 form, its cause is called a uniform force: the spaces which would be described 

 in any given time, with the actual velocity uniformly continued, being always 

 equally increased or diminished by the action of such a force. For example, if 

 the velocities, at the beginning of any two separate seconds, be such, that the 

 1)ody Avould describe one foot and ten feet in the respective seconds, if undis- 

 turbed, and the spaces actually described become two feet and eleven feet, each 

 being increased one foot, the accelerating force must be denominated uniform. 



• The power of gravitation, acting at or near the earth's surface, may, with- 

 out sensible error, be considered as such a force. Thus, if a body begins to 

 fall from a state of rest, it describes about 16 feet, or more correctly l6-fV, 

 in tile first second ; if it begins a second with a velocity of SSI feet, it describes 

 .'32 and] 6, or 4 H feet, in this second. The decrease of the force of gravitation 

 in proportion to the squares of the distances from the earth's centre, is barely 

 fj^iteptible, iit any heights within our reach, by the nicest tests that we can 

 employ. . 



The velocit}' produced by any uniformly accelerating force, is proportional 

 to the magnitude of the force, and the time of its operation conjointly. When 

 tlie forces are the same, a little consideration will convince us that, since every 

 equal portion of time adds equally to the velocity, the whole velocity produced 

 or destroyed must be in proportion to the whole time; and when the forces 

 diifer, the velocities differ in the same ratio; for the forces are only measured 

 by the velocities which they generate. Thus a double force, in a double time, 

 produces a quadruple velocity. That a force producing a double velocity is 

 properly called a double force, may be shown from the laws of the composition 

 of motion; for when the equal sides of a parallelogram representing two se- 

 parate forces or motions, approach to each other, and at last coincide in direc- 

 tion, the diagonal of the parallelogram, representing their joint effect, becomes 



equal to the sum of the sides, (Plate I. Fig. 10.) 



./<:'• DV -Mi n't -: ^ 



The machine invented by Mr. Atwood furnishes us with a very convenient 

 mode of making experiments on accelerating forces. The velocity, produced 

 by the undiminished force of gravity, is much too great to be conveniently sub- 

 mitted to experimental examination; but by means of this apparatus, we can 



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