EFFECT5 OF GRAVITY ON TIMEPIECES. ] 35 



both being to regulate the motion of the respective instru- lance hitherto 

 ments, similar methods have been adopted in each for com- 

 pensating the effects of heat and cold. But the difference 

 of latitude which has been so fully recognized as affecting 

 the pendulum has not yet, as far as I know, been considered 

 to have any influence on the balance. 



(b) The time of the fall of the pendulum is in the inverse Gavity should 

 subduplicate ratio of the force of gravity. In the watch, on motfo^oVa* 

 the other hand, the time of the vibration of the pendulum watch, 

 spring is in the direct subduplicate ratio of the weight of 



the balance. It appears to me, therefore, that any ap- 

 proach toward the equator, by diminishing the gravity of 

 the balance, must tend to accelerate the motion of the 

 watch in the same ratio by which it retards that of the 

 qjock. 



(c) Suppose the diminution of gravity at the equator T ^ Difference of 



= 0*004367. Let the weight of a balance vibrating mean rate at the pole 

 ; . & *> & the equator, 



time at the pole be denominated 1. Being removed to the 



equator, its weight will be 1 — 0*004367 rz 0*995633, and 



the time of one vibration at the pole, to the time of one 



vibration at the equator, will be as */ 1 to y 0*995633, or 



as 1 to 0*997814; consequently the number of vibrations 



in ope day at the equator will be to those at the pole as 



\ — 1*002191; which reduced to time eives 24 b 3' 



9*3". That is, the watch will go too fast 3' 9*3". If the 



diminution be taken at T fa, agreeing with a printed table 



of the variation of the pendulum to every fifth degree of 



latitude, then by the same process, the errour of the watch 



will be 3' 48*3" daily. 



(d) The errour here is so great, that in proceeding from Experiments 

 this latitude to the line, it is not possible, that it could have with the P en * 

 escaped observation, with the almost numberless experi- j U ff um f S10U 

 ments that are now made with watches; but if the reasons those with thf 

 for the variation of the balance be found just, these experir balanc *- 

 ments will stand in opposition to those that have been made 



with the pendulum. With respect to the latter, they have 

 been conducted by men of such eminence, that we should 

 have no reason to doubt their accuracy, if they did not dif- 

 fer so widely from one another. 



(*) Mr. Richer found by experiments, that a pendulum, 



which 



