376 POPULAR LECTURES AND ADDRESSES. 



vibrate round a vertical axis always in opposite 

 directions. The effect of suspension in this in- 

 stance is to make the watch go faster than 

 when its case is held perfectly fixed, but this 

 effect is smaller the nearer the upper points of 

 support are. The circumstances of the extreme 

 case when they arc as close as possible arc best 

 realised by hanging the chronometer, as in Archi- 

 bald Smith's experiment, by a long single cord, 

 from a fixed point, by means of a sling or 

 three short cords tied round the watch and so 

 adjusted as to keep its face horizontal, thus 

 giving the watch as a whole perfect freedom to 

 move round a vertical axis. The permanent 

 effect is then such, that the balance-wheel and 

 the rest of the chronometer oscillate in opposite 

 directions through ranges inversely as their mo- 

 ments of inertia. The period of this vibration 

 is the same as that which the balance-wheel 

 would have if the length of the hair-spring were 

 diminished to the same proportion to its whole 

 length that the moment of inertia of the chrono- 

 meter (with the balance-wheel ideally free on 



