COMMON THINGS CLOCKS AND WATCHES. 



disengaged that it shall commence its oscillation at the same 

 moment with the commencement of one of the oscillations of the 

 other ball. 



Let it, in short, be so managed, that when the one ball is at 

 A, the other shall be at c ; and that both shall commence their 

 descending motion towards B at the same moment. It will be 

 then found that their oscillations will be synchronous for a con- 

 siderable length of time, that is to say, the balls will arrive at A' 

 and c', respectively, at the same instant; and returning, will 

 simultaneously arrive at A and c respectively. 



If, in this case, the oscillation of the ball A were made through 

 an arc, even as great as 10, that is to say, 5 each side of the 

 vertical, the oscillation of the ball c being made through an arc 

 of 2, it would be found that 10001 oscillations of the latter 

 would be equal to 10000 oscillations of the former, so that the 

 actual difference between their times of oscillation would not 

 exceed the ten thousandth part of such time. 



15. In the practical application of the pendulum, however, 

 this departure from absolute isochronism, small as it is, becomes 

 unimportant ; for a power is always provided, by which the loss 

 of motion which would be produced by friction and atmospheric 

 resistance is repaired, and the magnitude of the oscillations is 

 maintained uniform, as we shall presently show. 



16. It might be expected that the time of oscillation of different 

 pendulums would depend, more or less, upon the weight of the 

 matter composing them, and that a heavy body would oscillate 

 more rapidly than a lighter one. Both theory and experience, 

 however, prove the result to be otherwise. The force of gravity 

 which causes the pendulum to oscillate acts separately on all the 

 particles composing its mass; and if the mass be doubled, the 

 effect of this force upon it is also doubled; and, in short, in 

 whatever proportion the mass of the pendulum be increased or 

 diminished, the action of the force of gravity upon it will be 

 increased or diminished in exactly the same proportion, and con- 

 sequently the velocity imparted by gravity to the pendulous mass 

 at each instant will be the same. 



It is easy to verify this by experiment. Let different balls of 

 small magnitude, of metal, ivory, and other materials, be sus- 

 pended by light silken strings of the same length, and made to 

 oscillate ; their oscillations will be found to be equal. 



17. If pendulums of different lengths have similar arcs of 

 oscillation, the times of oscillation of those which are shorter will 

 be less than the times of oscillation of those which are longer. Let 

 a, b, c, d, and e, fig. 2, be five small leaden balls, suspended 

 by light silken strings to the point of suspension s, and let all 



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