LESSONS IN PHYSICS. 51 



AE, acting at right angles to AD, will pull the ball toward the 

 point M. If the ball is allowed to fall to M, its inertia will carry 

 it beyond that point; but when it passes the point M, gravita- 

 tion begins to pull backward, with just the same power it exerted 

 to pull the ball from A to M. The ball will rise from M to N, a 

 distance just as far beyond M as it has fallen to reach M. It will 

 there stop and gravitation will bring it back to M, while its 

 inertia will carry it up to A again. The resistance of the air and 

 friction of the cord will finally make it stop at M. 



The time of one vibration at any given place varies as the 

 square root of the length of the pendulum, and varies inversely 

 as the square root of the force of gravity. In general, the am- 

 plitude or extent of vibration does not affect the time. The truth 

 of the first law may be shown by experiments with pendulums of 

 different lengths, when it will be found that a pendulum one foot 

 long vibrates twice, while a pendulum four feet long vibrates 

 once. The pendulum is used to measure time. If the wire sus- 

 pending the pendulum ball is of steel or any single substance, it 

 varies in length with the temperature during the year, so that the 

 pendulum will vibrate more rapidly in some seasons of the year 

 than in others; usually the movement will be more rapid in win- 

 ter and slower in summer. Compensation pendulums are some- 

 times made by using different metals, so that the contraction 

 of one balances the expansion of the other. 



The pendulum? is also used to determine the figure of the earth. 

 The rate of the vibrations of the pendulum depends upon the force 

 of gravity. If at any place the pendulum vibrates more rapidly, 

 other conditions being the same, it shows an increase of the 

 force of gravity. If it vibrates more slowly, then the force of 

 gravitation must be less, indicating that in the one case the 

 pendulum was nearer the center of gravity of the earth than in 

 the other, which would indicate variations from a true spherical 

 form. The vibrations of the pendulum are more rapid toward 

 the poles, and vary somewhat in other directions. 



Let a stone be thrown into the water of a lake or pond and 

 the tranquil surface will be carved into a series of circular ridges 



