LAWS OF FALLING BODIES. 61 



is tho center of attraction, or when carried to the bottom of a mine, -where 

 it is attracted both bj matter above it and below it. 



•What is the ^-1- The length of a pendulum that wi 1 

 o'irdf^°pcndu.' describe sixty oscillations in a minute, each 

 '"™' oscillation having the duration of a second, 



is, in the latitude of Greenwich, England, 39.1393 inches 

 in length ; one to vibrate in half seconds must measure 

 1.7848, or rather more than 9^ inches. 



At the pole it would require to be somewhat longer ; at the equator somo- 

 what shorter. A pendulum that ■s^ibratcd seconds at Paris, was found to re- 

 quire lengthening .09 of an inch iu order to perform its vibrations in the same 

 time at Spitzbergen. 



How may the 122. The Icugth of B pcndulum vibrating 

 In'lfs'^^pe^du- seconds being always invariable at the same 

 L"?ti'ndard^ of P^^ce, siuco thc attraction under the same 

 measure? circumstances is always the same, it may be 



used as a standard of measure. 



This application has already been described underthe section "Weight (§ 67). 



The duration of the oscillation of a pendulum is not aflected by altering tho 

 ■weight of the baU, since all bodies moving over the same space, under tho 

 influence of gravitation, acquire equal velocities. 



How do the 1-3. The lengths of diiferent pendulums, 

 dThmis vibi^a't- vibrating in unequal times, are to each other 

 tiSiscl^mpar"'? ^^ *^^ squarcs of the times of their vibration. 



Thus a pendulum, to vibrate once in two seconds, must 



have four times the length of one that vibrates once in one second ; to vibrato 



once in three seconds, it must have nine tunes the length, etc. — the duration 



of the oscillation bemg as the whole numbers, 



1, 2, 3, 4, 5, 6, 7, 8, 9. 



The length of the pendulum will be as their squares. 



1, 4, 9, 16, 25, 36, 49. 64, 81. 



. A pendulum, therefore, that will vibrate once in nine seconds, must have 



t length of 81 times greater than one vibrating once in one second. 

 •» 



\ 



PRACTICAL PROBLEMS ON THE THEORY OF FALLING 



BODIES. 



1. A stone let fall from the top of a tower struck the earth in two seconds ; how high 

 ■was the tower ? 



2. How far will a body acted upon by gravity alone, fall in ten seconds? 



3. How deep is a well, into which a stone bcin;? dropped, reaches the surface of the 

 water in two seconds, the depth of the water in the well being ten feet ? 



