^3 PhllofophiCalVfts of acommott JVaUh. 



Now, omitting the great wheel and its pinion of 12, we have 54X48x48x15X2 = 

 3732480 for double the product of the fpecified wheels, and 6 X 6x6 = 216 for the produ£t 



of the fpecified pinions; alfo ■ "' " ■ =17280 are the number of beats inan hour, and ^ — =4»8 



theexaft number of beats per fecond : accordingly, Mr. Emerfon fays that this watch makes 

 ^ about 4| beats in a fecond." The number of fpirals on the fufee is 7 ; therefore, 7 K 



- =28 is the number of hours that the watch will go at one winding up : likewife the dial- 

 work 1" X — = = 1 2 fliews that whilft the firft drivins; pinion of 10 eoes twelve times 



10 II 120 3 r t> 



round, the laft wheel of 36 goes only once ; whence the angular velocity of two hands carried 

 by their hollow axles are to each other as 1 2 to i . 



For 3 fecond example, I will take a watch which is in my own pofTefljon, the numbers of 

 which in the calculation of beats per fecond will be thus : 60 X 60 X 60 X 13 X 2 = 5616000, 

 double the product of the wheels ; and 8x8x6 = 384 the produd of the pinions ; then 



— -J — = 14625 will be me beats in an hour, and —^ =54,0625, thebeats per fecond. 



Befides this I have examined two other common watches, one of which requires this cal- 

 culation :54XS2X52Xi3Xa = 379641 6 for double the produ£l: of the wheels, and 6 X 6 X 6= 



216 for theproduftof the pinions; therefore^ g— =17576 arc the beats in an hour, and 



-T— =4,882, the beats per fecond by this watch : alfo double the produft of the wheels of 

 the other, viz. 56 X 51 X 50 X 13 X 2 is 37 12800, and the produ£l of the pinions, as in the 

 laft, 6x6x6=216; confequently — ^^-^ gives 17188 beats in an hoyr, which divided by 



3600 gives 4)7746 for the beats per fecond. 



Thefe four examples, it is prefumed, will render the method of afcertaining the beats per 

 fecond in any watch fufficiently eafy for any perfon who is acquainted with common arithmetic. 



It remains now for an inftance or two to be adduced for the application of the beats of a 

 watch to philofophical purpofes, in order to fhew the practical utility of the method here 

 propofed of meafuring very fmall portions of time. 



Let us fuppofe, for one inftance, with Dr. Herfchel, that the annual parallax of the fixed 

 (lars may be afcertained by obferving how the angle between two ftars, very near to each 

 other, varies in oppofxte parts of the year. For the purpofe of determining an angle of this kind, 

 where an accurate micrometer is wanting, let a telefcope that has crofs-wires be dire£led to the 

 ftars when paffing the meridian, in fuch a manner that the upright wire may be perpendicular 

 to the horizon, and let it remain unmoved as foon as the former of the two ftars is juft com- 

 ing into the field of view ; then fixing the eye to the telefcope and the watch to the ear, repeat 

 the word one along with every beat of the watch before the ftar is arrived at the perpendicular 

 hair, until it is in conjundlion with it, from which beat go on two, three, four-, Sec. putting 

 down a finger of either hand at every twfntp till the fecond ftar is feen in the fame fituation 



that 



