504 PHYSIOLOGICAL PHYSICS. [Chap. XLII. 



acted. Suppose the body were not acted on by any 

 other force, such as friction, resistance of the air, etc., 

 it would go on moving with the velocity it had ac- 

 quired, and this would be uniform motion. It would 

 never cease moving. But various forces, resistance, etc., 

 oppose its uniform motion, so that in the end it comes 

 to rest. If, however, the force acts for a longer time, 

 the motion is uniformly accelerated, and the velocity 

 will be in proportion to the length of time during 

 which the force acts. Gravity is a constantly acting 

 force, so a falling body will have a uniformly accele- 

 rated motion. A body falling from rest is found at 

 the end of one second to have in London a velocity 

 equal to 32-1889 feet, 32-2 approximately. The in- 

 tensity of gravity in London is then 32 -2, expressed 

 by saying g = 32 -2. But the intensity of gravity 

 varies in different places, being least at the equator, 

 so that the amount must be experimentally found for 

 each place. The acceleration being uniform, the 

 velocity at the end of a given number of seconds will 

 be 3 2 -2 x by the number of seconds. Let v = the 

 velocity, and t = the number of seconds, then 



The velocity at the end of 10 seconds will be 32 -2 

 X 10, expressed in feet per second. 



It was found that the actual space traversed by 

 a body falling from rest was 16'1 feet at the end of 

 the first second. (Distinguish between the space 

 traversed during the second, and the velocity at the 

 end of the second.) At the end of two seconds the 

 space traversed is 64-4 feet ; at the end of three 

 seconds it is 144-9. During 1 second IG'l feet, 2 

 seconds 64*4, 3 seconds 144'9, these figures give the 

 proportions for time 1, 2, 3, and for the space tra- 

 versed 1, 4, 9 ; that is to say, the space traversed the 

 first second (which = 1 6' 1 feet, i.e. ^ of 32, i.e. ^ g) 



