Ph'tlofoph'ical VJei af a common IJ'atch. 55 



that the leading one occupied at the commencement of the counting ; then thefe beats divided 

 fcy the beats per fecond marked on the watch-paper, will give the exa£l number of uncor- 

 re£ted feconds, by which the following ftar pafles later over the meridian than the leading one : 

 when thefe feconds and parts of a fecond are afcertained, we have the following analogy 

 for determining the angle, which includes alfo thfe correction, namely, as the time of a fidereal 

 rotation of the earth (which at a mean rate* may be taken at 23h. 56' ^"jOgS, but more or lefs 

 accordingly as the earth is near the aphelion or perihelion of its orbit), the daily error in the 

 rate of going, is to 360°, fo is the obferved number of feconds (of time) to the quantity of 

 the required angles. The watch is here fuppofed to be regulated to fhew folar time ; but if 

 it fhould be regulated exactly for fidereal time, inftead of 23h. 56' 4',098 we mud ufe exactly 

 24 hours in the analogy. 



As a fecond inftance, let it be required to afcertain the diftance of the nearer of two eleiSlri-^ 

 fied clouds from an obferver, when there are fucceflive peals of thunder to be heard : a little 

 time before the expe£ted repetition of a flafh of lightning place the watch at the ear, and com- 

 mence the numbering of the beats at the inftant the flafli is feen, as before direfted, and take 

 care to ceafe with the beginning of the report ; then the beats converted into feconds, with 

 the proportional part of the daily error added or fubtrafled, will give the difference of time 

 taken up by the motion of the light and found : if, laftly, we fuppofe light to be inftantaneous at 

 fmall diftanccs, the diftance of the nearer cloud will be had by multiplying the diftance that 

 found is known to pafs through in a fecond by the number of obferved feconds obtained from 

 the beats that were counted. 



Many more inftances might be here pointed out, in which the beats of a good watch would 

 be extremely ferviceable in the pradiical branches of philofophy ; but the occurrence of fuch 

 inftances will always point out the propriety of the application, when it is once known and 

 pradlifed. 



I fliall therefore only mention one further advantage which feems peculiar to this mode 

 of counting a limited number of feconds by a watch, which is, that it is free from any error 

 thatmightarife from the graduations of a dial-plate, or unequal divifions in the teeth of wheels 

 and pinions, where the feconds are counted by a hand. 



In order to introduce this method of meafuring fmall portions of time accurately, it is de- 

 firable that a watch be conftrufled fo as to make an exzGt number of beats per fecond 

 without a fradiion, for then the reduction of beats into feconds would be more readily made. 

 With a view of promoting thisobje£t, I have calculated numbers for a watch, which will 

 produce the defired eiFeft, and which, as they are equally practicable as thofe in ufe, I fliall 

 infert in this paper, in hopes of hearing at fome future period, that they have been adopted 

 by fome good workman. By the method of arrangement already given, the numbers proper 

 for fuch a watch, as will indicate hours, minutes, and feconds, by three hands, and alfo make 

 juft four beats per fecond, will ftand thus, viz. . ;! : ^ .. 



I am not aware of any ohfer-vnble variation in the time of tlie earth's rotation. In theory it may vary from 

 the variable diftutbing forces of fun and moon, as well as from other ca«fe« which may affeft its mean diameter, 

 iSee Phii«f. Journal, I. -.98.— II. 40.— and III, 30.--N. 



50 great 



