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small change in the time of oscillation has resulted in fixing two 

 seconds as the limit for any precision pendulum, as beyond this 

 point the instrumental errors would be increased in the same 

 ratio and would be difficult to overcome. The great Westmin- 

 ster pendulum vibrates in two seconds, and is probably the most 

 accurately compensated long pendulum in the world. The cor- 

 rection for errors of lateral and cubical dilatation, barometrical 

 error, long and short arcs of oscillation are all reduced to a 

 minimum. 



As we have said so much about seconds, it might be in order 

 to say there are two kinds, solar and sidereal, and they differ 

 from each other in length. 



The interval of time we call a second is reduced from the 

 solar day, which is the time between two successive returns of 

 the sun to the same meridian, and this interval divided into 

 86,400 parts. These solar days are not equal, but are made so 

 by the daily equation of time added to or subtracted from the 

 apparent solar day. 



The sidereal day is the interval between two successive 

 returns of a fixed star to the same meridian and is 3 minutes, 

 56.5 seconds shorter than the solar day, and this day divided 

 into hours, minutes and seconds furnishes us with the sidereal 

 seconds. The sidereal day represents the time of the rotation 

 of the earth on its axis, and is the most accurate observation of 

 time that can be made, as it requires no equation, and has not 

 changed as much as one-hundredth part of a second in over two 

 thousand years. Astronomers use astronomical clocks reading 

 24 hours on the dial, with pendulums vibrating sidereal seconds, 

 and by this time only do they find and locate celestial bodies. 



MUTUAL ATTRACTION. 



Another law governing the pendulum is this : The action 

 of gravity or the mutual attraction between bodies varies with 

 their masses, and inversely as the square of their distances. 

 Following from this, a pendulum will vibrate seconds only in a 

 given place. Our standard of measurement is taken from a 

 pendulum vibrating seconds in a vacuum at the level of the sea. 

 It also follows that the further a pendulum is removed from the 

 center of the earth the less it will be attached in its descent 

 toward the vertical. This explains why a pendulum loses on 



