rg Expanf.^n of Bodies hy Hfat and Cold. EffcEi on Time-Pieces. 



dimenfions with regard to the centre of ofeillation. But heat and cold alter the dimeiifion* 

 of all the fubftances we know, though not equally in each. The remedy is derived from 

 this inequality, and conflllutes the I'ubjecl of the prefent memoir. 



Since the dimenfions of all bodies increafe with their temperature, it naturally follows 

 that the pendulums of decks are longer in hot weather than in cold ; and will therefore 

 make their vibrations in longer times. As, far, therefore, as this caufc of irregularity ex- 

 tends, every time-piece, regulated by a pendulum or balance, will go (lower in fummcr and 

 fafter in winter. In the pendulum for feconds, the quantity required to be added to, or 

 fubtraded from, the length, to caufe a gain or lofs of one minute per day, is 0.0545 inch 

 at a medium, which does not differ from either extreme more than the half of unity in the 

 fail figure. Hence the mean variation of length anfwering to one fecond is o.ooogo8 inch. 

 And by General Roy's experiments, in the feventy-fifth volume of the Thilofophical 

 Tranfaflions, the expanfions of five feet of the undermentioned fubftances, I y a variation 

 of temperature of J 80 Jegrees of Fahrenheit, namely from 32° to 212° arc, 



Inch. 

 Rod of F.nglifti plate brafs — — — o.i 13568 



Rod of fteel — ~ . — ~ c. 068684 



Prifm of call- iron — — — — 0.066563 



Glafs tube _ _ _ _ 0,046569 



Solid glafs rod made long before — — — 0.04S472 



Hence it is feen that, in a clock with a fimple pendulum, having the rod of fteel, every 

 difference of temperature of four degrees will caufe a variation of one fecond per day. 



That the variation with a brafs rod is nearly twice as much. 



And with a glafs rod, not much more than half the quantity. 



The difference between the mean heights of the thermometer within, at the Royal So- 

 ciety's apartments, in fummcr and winter, is about 25°. Hence the difference of rate be- 

 tween tlie going of a clock with a fimple pendulum in fummer and in winter, will be about 

 fix feconds per day, or one minute in ten days. 



The difference of length in ftraight grained deal wood is ^found to be very fmall ; 

 whence it is a general opinion, tliat in clocks of the common conftructions, in which the 

 pendulum is without internjjffion connected with the train, and the parts of the efcapement 

 are oiled, the errors from expanfion in fuch a pendulum are much lefs than thofe which 

 arifc from the unequal tranfmiffion of the maiiitaining power. 



But the beft method, in praftice as well as in theory, for correding the effects of heat 

 find cold in pendulums, confifts in oppofing the expanfions and contraiStions of different 

 kinds of metal to each other. The celebrated George Graham was, as far as I am in- 

 formed, the firit who applied this expedient to clocks. His account is in fome of the 

 earlier volumes of the Philofophical Tranfaftions, vvhich I have not at hand, and there- 

 fore make reference to it from memory. Having afcertained that the expanfion of mer- 

 cury greatly exceeds that of iron, he formed a pendulum confifting of an iron tube 

 filled with mercury to a certain height. In this compound pendulum it is clear that, if 

 the whole had been iron, the centre of ofeillation would have defcendcd by heat; and it 

 is equally clear that, if the iron tube could be deprived of all expanfibility whatever, the 

 mercury fupportcd beneath would be lengthened upwards by increafe of temperature ; and 



