LAWS OF FALLING BODIES, 57 



feet, the sp<ace passed through by a falling body in one second, bemg taken 

 as the common multiple of distances and velocities. 



Thus, to ascertain the heiglit from which a body would fall in 5 seconds, 

 take in the fourth column of the table the number opposite 5 seconds, whith 

 is 25, and multiply it by 16; the product, 400, will be the height required. 

 Problems of this character may also be worked by the rule given (§ 107). 



In the same manner, if it be required to determine the space a falling body 

 would descend through in any particular second of its motion, as, for exam- 

 ple, the 5th second, we take in the second column of the table the number 

 opposite five seconds, which is 9, and multiply it by 16 ; the product, 14A, is 

 the space required. 



In like manner, if it be required to determine with what velocity a body 

 would strike the ground after falling during an interval of 5 seconds, we take 

 the number in the third column cf the table opposite 5 seconds, which we 

 find to be 10, and multiply this by 16. The product, 100 feet, will be the 

 Telocity required; and a body thus falling for 5 seconds would have, when 

 it strikes the ground, a velocity of 160 feet 



..^ , .„ ^ 112. If a body, instead of falling; perpen- 



What will l>e • ' ^ . \ 



the velocity of diculai'lv, be made to roll down an inclined 



a bodv falling « , p . , 



down an in- plane, free from friction, the velocity acquired 



cUaed plane? , . . p- i -Hi i 



at the termmation oi its descent, ■vsill be equal 

 to that it would acquire in falling through the perpen- 

 dicular height of the inclined plane. 



Fig. 28. Thus, the velocity acquired in rolling down the whole 



length of A B, Fig. 28, is equal to that it would acquire 

 by lalling down the perpendicular height A C. 



113. The great Itahan philosopher Gahleo, during the 

 .B ^^^^y P^^' of the ITth century, had his attention directed, 

 while in a church at Florence, to the swmging of the 

 chandeliers suspended from the lofty ceihng. He noticed tnat when they 

 How, and by ^^'^^® moved from theu- natural position t»y any disturbing 

 whom was the cause, they swung backward and forward m a curve, for a 

 covered" ^^°S time, and with great uniformity, nsmg and faUing alter- 



nately in opposite directions. His inquiry mto the cause of 

 thes3 motions led to the invention of the pendulum, the tneory of which may 

 be explamed as follows : 



Explain the ^^^- ^^^ bodies will have their motion as much accelerated 



theory of the whilst descending a curve, as retarded whilst ascendme. Let 

 pendulum. C A B be a curve, Fig. 29. If a 



ball be placed at C, the attraction of gravitation 

 will cause it to descend to A, and in so doing it 

 will acquire velocity sufficient to carry it to B, 

 all opposing obstacles being removed, such as 

 friction and resistance of the air. Gravitation 



3* 



Fig. 29. 



