INFLUENCE OF SUSPENSION ON WATCH. 377 



its pivots) bears to the sum of this moment 

 of inertia and the moment of inertia of the 

 balance-wheel round its own axis. The period of 

 vibration will be diminished according to square- 

 root of this ratio. Thus, if the moment of inertia 

 of the chronometer is 649 times that of the 

 balance-wheel, the period will be v / if, or about 

 iEw f the proper rate ; or the chronometer 

 will gain one second in 1299, or about 67 seconds 

 in the twenty- four hours. This was the result ob- 

 served by Mr. Smith, from which he inferred the 

 moment of inertia of the pocket chronometer 

 referred to above. 



If, on the other hand, the upper points of sup- 

 port are put very wide apart, the vibration main- 

 tained is of the same character as that illustrated 

 in Fig. 3, and the watch goes slower than its 

 proper rate. The farther apart the points of sup- 

 port are the less is this effect, as the circumstances 

 approach more nearly to a perfect fixing of the 

 frame. 



If now, commencing with the upper points of 

 support very close together, we gradually increase 



