ON ACCZLERATIXG FOUCES. <>9 



knowledge our total ignorance of the intimate nature of forces of every kind; 

 and we are first to examine the eftect offerees, considering only their magni- 

 tude and direction, without any regard to their origin. 



It was truly asserted by Descartes, that the state of motion is equally na- 

 tural with that of rest. When a body is once in motion, it requires no fo 

 reign power to sustain its velocity. If therefore a moving body is subjected 

 to the influence of any force, which acts upon it in the line of its direction, its 

 motion will be either accelerated or retarded, accordingly as the direction of 

 the force coincides with that of the motion, or is opposed to it. A ston*, for 

 instance, beginning to fall, or projected downwards, by uo means retains the 

 same velocity throughout its. descent, but acquires more and more motion every 

 instant. We well know,, that the greater the height from which a body falls, 

 the more danger there is of its destroying whatever opposes its progress. In 

 the same manner, when a ball is thrown upwards, it gradually loses its motion 

 by the operation of gravitation, which is now a retarding force, and at last 

 begins again to descend. 



It may here be proper to inquire what is the precise meaning of the term ve- 

 locity; we appear indeed to understand sufficiently the common, use of the 

 word, but it is not easy to give a correct definition of it. The velocity of a 

 body may be said to be the (juantity or degree of its motion, independently of 

 any consideration of its mass or magnitude ; and it might always be measured 

 by the space described in a certain portion of time; for instance a second, if 

 there were no other motions than undisturbed or uniform motions : but the ve- 

 locity may vary very considerably within the second, and we must therefore 

 have some other measure of it than the space actually described in any finite 

 interval of time. If however the times be supposed infinitely short, the ele- 

 ments of space described may be considered as the true measures of velocities. 

 These elements, although smaller than any assignable quantity, may yet be 

 accurately compared with each other ;. and the reason that they afford a true 

 criterion of the velocity, is this, that the change produced in the velocity, 

 tluring so short an interval of time, must be absolutely inconsiderable in com- 

 parison with the whole velocity, and the element of space becomes a true mea- 

 sure of the temporary velocity, in the same manner as any larger portion of 

 space may be the measure of a uniform velocity. 



