56 OUTLINES OF NATUllAL PHILOSOPHY, 



which they act ; v the velocity at the beginning of 

 the action, tf at the end of it, 



F s + F' sf -f- F'' s + F" s"' == + V* + t/. 



And if v"' = 0, then 

 F s -f FV + I 1 " *" -f tf '" *"> === 2 . 



103. If the force which accelerates or retards in 

 the last proposition j be uniform, the distance to 

 which the body will go before it acquire or lose a 

 given velocity* will be as the square of that velo- 

 city. 



. Oil this is founded that estimation of the force of 

 moving bodies, which is known by the name of the 

 vis VIVA, and which makes that force proportional 

 to the square of the velocity. The truth is, that 

 the effect of a body in motion may be measured 

 either by the distance it goes to, or by the time that 

 elapses before a resistance of uniform intensity re- 

 duce it to rest. If the effect be measured in the 

 first of these ways, it will be found to be as the 

 square of the velocity ; if in the second, as the ve- 

 locity simply. Both these measures may be consi- 

 dered as correct, and are not inconsistent when light- 

 ly understood. The former makes the effect F S, 

 the latter F t, retaining the significations already 

 given to these letters. The same term, however, 

 ought not to be indiscriminately applied to two things 

 so essentially different. It is mdst conformable to 

 the use made of the word Force, in the fundamen- 

 tal investigations of Dynamics, to t&ke the quantity 



