]38 EFFECTS OF GRAVITY ON TIMEPIECES. 



Enlarging a ba- («) Again, every thing remaining as before ; suppose I beat 



mUar effect! 1 " out tllis & old balance ^Xi its diameter be just doubled, or, 

 more accurately, till its diameter of percussion is just dou- 

 ble: here the inertia is quadrupled, for now it will require 

 eight springs equally strong with the first to make it vibrate 

 in the same time, and, generally* let D be the diameter of 

 percussion, and W the weight, the power of any balance 

 will always be as D*xW, for the strength of the spring 

 must be in this proportion to make it vibrate in the same 

 time. If the number of vibrations are changed, that is 

 more or less in the minute, the velocity in similar parts of 

 each vibration will be as this number, and if it be denoted 

 by N, the power of any balance will be as N* x £>* X W, 

 the spring being in this proportion. 



(o) Mr. dimming goes on to say, that " the vibrations of a 

 «« balance, whose centre of gravity coincides with its centre 

 ** of motion, have not the least dependence on gravitation.*' 

 Surely this cannot mean, that balances of different 

 weights, having their spring or motive force the same, will 

 vibrate in equal time; but either this must be the case, or 

 he must consider a variation in the power of gravity as not 

 altering the weight of any thing. 

 Variations of ip) * nave near d ** remarked, that timekeepers do not go 

 timekeepers so well at sea as they are found to do on land. But as all 

 considerable changes of place are made by sea, it is possi- 

 ble, that the influence of latitude on gravitation may be the 

 unsuspected cause of some part at least of this deviation. 

 If the principle I have suggested be not erroneous, it will 

 be of more importance than ever, to ascertain the exact 

 variation of this influence. But as I am veiy conscious, 

 that my attainments in science are not such as to entitle me 

 to be positive in a matt* r of this magnitude, however plain 

 it may appear to my own mind, I am solicitous to be fa- 

 voured with your judgment upon it, or that of any of your 

 correspondents. 



I am, Sir, 



Your most obedient humble servant, 



X. 



ANNO- 



at sea. 



