COMMON THINGS CLOCKS AND WATCHES. 



and disengaged so as to commence one of its oscillations with an 

 oscillation of the ball 9 ; and in the same manner let the ball 

 1 be started simultaneously with one of the 

 Fi 3 oscillations of the ball 9. 



ft will be found that two oscillations of 

 the one-foot pendulum are made in exactly 

 the same time as a single oscillation of the 

 four-foot pendulum; consequently, the 

 time of each oscillation of the latter will be 

 double that of the former, while its length 

 is fourfold that of the former. 



In the same manner, while the one-foot 

 pendulum makes three oscillations, the 

 nine-foot pendulum will make one, and, 

 consequently, the time of oscillation of the 

 latter will be three times that of the 

 former, while its length is nine times that 

 of the former, 



By this principle, the length of a pendulum which would 

 oscillate in any proposed time, or the time of oscillation of a 

 pendulum of any proposed length can be ascertained, provided 

 we know the length of a pendulum which oscillates in any 

 given time. 



18. We have hitherto supposed that the pendulous body is a 

 heavy mass of indefinitely small magnitude, suspended by a wire 

 or string having no weight. These are conditions which cannot 

 be fulfilled in practice. Every real pendulous body has a defi- 

 nite magnitude, its component parts being at different distances 

 from the point of suspension ; the rod which sustains it is of con- 

 siderable weight, and all the points of this rod, as well as those of 

 the pendulous mass itself, are at different distances from the point 

 of suspension. In estimating, therefore, the effect of pendulums, 

 it is necessary to take into account this circumstance. 



Let us suppose a, 6, c, d, e, f, g (fig. 4), to be as many small 

 heavy balls connected by independent strings, the weight of 

 which may be neglected, with a point of suspension s, and let 

 these seven balls be supposed to vibrate between the positions 

 s M and s M'. Now if these balls were totally independent of 

 each other, and connected with the point of suspension by inde- 

 pendent strings, they would all vibrate in different times, those 

 whicb are nearer the point s vibrating more rapidly than those 

 which are more distant from it. If, therefore, they be all dis- 

 engaged at the same moment from the line s M, those which are 

 nearest to s will get the start of those which are more distant, 

 and at any intermediate position between the extremes of their 

 12 



