1 70 Dynamics. 



ing a uniformly accelerating force, is strictly applicable to gravity, 

 it being well understood at the same time, that the resistance of 

 the air and obstructions of every kind are oat of the question. 



In order to determine, therefore, with respect to the motion 

 of heavy bodies, the spaces described and the velocities acquired, 

 we require only one single effect of gravity for a determinate 

 time. For the equations v gt, s = |g 2 , enable us to calcu- 

 late each of the particulars above enumerated, when the value of 

 g is known. 



It must be recollected that by g we have understood the 

 velocity which a body acquires by gravity in one second of 

 26<7 - time. Now we know by actual observation, that a body, not 

 impeded by the resistance of the air or other obstacle, falls at 

 the surface of the earth through 16,1 feet in one second. We 

 shall see hereafter how this is determined. 



But we have shown that with the velocity acquired by a 

 series of accelerations, the body would describe with a uniform 

 266. motion double the space in the same time. Hence the veloc- 

 ity acquired by a heavy body at the end of the first second of 

 its fall is such, that if gravity ceased to act, it would describe 

 twice 16,1 feet, or 32,2 in each succeeding second. Therefore 

 g = 32,2 feet. 



274. Now of the two equations v = g t, and s = g t 2 , the 

 first teaches us, that in order to find the velocity acquired by a 

 heavy body, falling freely, during a number t of seconds, it is 

 necessary to multiply the velocity acquired at the end of the 

 first second by the time f, or number of seconds. 



Hence, when a heavy body has fallen during a certain number 

 of seconds , the velocity acquired is such, that if gravity ceased to act, 

 the body would describe in each second as many times 32,2y*ee, as 

 there were seconds elapsed. 



Thus a body that has fallen during 7 seconds, will move at 

 the end of the 7 seconds, with a velocity equal to 7 times 32,2 or 

 225,4 feet in a second without any new acceleration. 



275. From the second of the above equations, namely. 



