COMMON THINGS CLOCKS AND WATCHES. 



as the range of the oscillations became more limited. This led 

 him to infer that property of the pendulum expressed by the 

 word isochronism, in virtue of which the vibrations, whether 

 in longer or shorter arcs, are performed in the same time. 



Although, however, as we shall presently show, pendulums 

 possess this property Vhen the arcs of vibration are very small, 

 they do not continue to manifest it when the range of vibration 

 becomes more considerable. 



13. To simplify the exposition of the important theory of the 

 pendulum, it will be convenient, in the first instance, to consider 

 it as composed of a heavy mass of small magnitude, suspended by 

 a wire or a string, the weight of which may be neglected. Thus, 

 let us suppose a small ball of lead suspended by a fine silken 

 string, the length of which is incomparably greater than the 

 diameter of the leaden ball. Such an arrangement is called the 

 simple pendulum. 



Let s, fig. 1, be the point of suspension; let s B be the fine 

 silken thread by which the ball B is suspended, and the 

 weight of which, in the present case, 

 is neglected. Let B be the position of 

 the ball when in the vertical under the 

 point of suspension s. In that posi- 

 tion the ball would remain at rest; 

 but if we suppose the ball drawn aside 

 to the position A, it will, if disengaged, 

 fall down the arc A B, of which the 

 centre is s, and the radius the length 

 of the string. Arriving at B, it will 

 have acquired a certain velocity, which, 

 in virtue of its inertia, it will have a 

 tendency to retain, and with this velo- 

 city it will commence to move through 

 the arc B A'. Supposing neither the 

 resistance of the atmosphere nor friction to act, the ball will rise 

 through an arc B A' equal to B A ; but it will lose the velocity which 

 it had acquired at B ; for it is evident that it will take the same 

 space, and the same time, to destroy the velocity which has been 

 acquired, as to produce it. Thus, the velocity at B, being acquired 

 in falling through the arc A B, will be destroyed in rising 

 through the equal arc B A'. 



Having arrived at A', the ball, being brought to rest, will 

 again fall from A' to B, and at B will have again acquired the 

 same velocity which it had obtained in falling from A to B, but 

 in the contrary direction ; and in the same manner it may be 

 explained that this velocity will carry it from B to A. Having 

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