On the Trains of Clocks and Watches. ipi 



f^lus or mlnlis the <JaiJy error in the rate of going : are to 360° : :,fo is the number of ob- 

 ferved feconds of time : to the quantity of the horizontal angle required. 



Thefe are ail the additional obfervations which feem neceflary to make, refpefting the num- 

 bers of a new watch calculated for philofophical ufes, and the method of applying it ; but 

 there is another inftrument frequently to be met with, which is capable of various construc- 

 tions, that will meafure fmallcr portions of time, than it is ufually made to meafure ; and 

 which is fuffiqiently portable for being carried fmall diftances : I mean the fpring clock, the 

 vibrations of which are regulated by a ftiort pendulum^ Out .of the many inftruments of 

 this kind which I have noticed, I do not remember any one which meafures, or, at leaft, 

 which indicates feconds : I fliall, therefore, fubjoin fuch numbers as are proper for a fprino- 

 clock, that (hall indicate feconds, and alfo make a given number of vibrations in a fecond. — 

 If 39,2 inches be taken as the tru- length of a pendulum, to fwing feconds in our climate, 

 which varies not one-tenth of an inch from the refult of Mr. Whitehurft's and George 

 Graham's experiments on the lengths of pendulums, the error in the length of fmall pendu- 

 lums, calculated therefrom, will fall within the threads of the adjuding fcrew at the inferior 

 end of the rod ; on which account the lengths, fo deduced, may be put down as the true 

 lengths without impropriety : thus, 



4 vibrations in a fecond will require a pendulum - 2,45; inches long, 



3 <io- . ^ - _ . 4,35 



2i: do. - - - - - 6,27 



2ido. - -■ - - -^ - 7,74. 



2 do. - - - - - 9,8 



The two firil of thefe pendulums appear to be too (hort-to perform with fteadinefs, and 

 confequently will be confidered as unworthy of further notice. The iirft portion of a train,, 

 fuitable for any of the three laft pendulurris, for a fpring clock to go upwards of a week, may 



1 84 L i- /• 84 06 



be -g X17 '^"^"S on the fufee, or — X15 turns, or ^Xi2 turns, or indeed any other 



Cmilar numbers producing a like refult : for the fecond portion, any one of the formulae given 

 for a watch in the former part of this article, will be proper ; but for the laft portion, each, 

 different pendulum will require different numbers : a pendulum to make 7.\ vibrations on a 

 fecond, may have the contrate wheel 24, its pinion 8, and the crown wheel 25 ; or, other- 

 wife, the contrate wheel 40, with a pinion of 8, and the crown wheel 15 : where, the vibra- 

 tions are l\ in a fecond, the contrate wheel may be 36, with a pinion of 8, and the crown 

 wheel, as before, 15 : and for exaftly two vibrations in a fecond, the contrate wheel will be 

 required to be 32, with a pinion of 8, and the crov/n. wheel 15, as in the two lafl inflances. 

 In all thefe calculations, a hand, placed on the axle of the contrate wheel,. will indicate fe- 

 conds without apparent, recoil ; and the trains, compofed of any of the various portions laid 

 down, will be equally accurate, and admit of many varieties. 



If a fpring clock is to be ufed for meafuring fmall portions of time, by the vibrations of its 

 pendulum, which falls not under the defcription of any of thofe conftrudtious, the vibrations 



C c 2; and. 



