■ <^ Experinunt or, Cmipouml Bars. The Expanfion BjLmce. 



-of Fahrenheit, both bars touched ; but upon immerGng the whole in boiling water, the 

 compound bar bended, and puflied the clip through the Ipacc of 0.16 inch. This fpacc 

 is the vcrfcd fine of the circular arc AC, produced by raifing the temperature from ^o" to 

 2i2°, namely 172°. Uut as the vcrfcd fine 0.16 is to the fine 6. 35, fo is the fine 6.35 to a 

 fourth number 252 ; wliich added to the verfed fine gives the diameter 252.23 inches of 

 the circle into which the upper face of the fteel bar had bended, and its circumference 792 

 inches. But the diifcrence between the diameter of the circle, mcnfurcd on tlie brafs 

 convex outer face, and that bounded by the interior or concave face of the l\ccl, was twice 

 the thicknefi of the bar, or 0.132 inch. But it feems fair to meafurc th.e real lengths of 

 the bars through the middle of their folidilies. The dilTcrence of diameter of two circles 

 paffing through the bars in this manner would confcqucntly be no' more thjn 0.066 inch ; 

 and of their circumfercMices 0.207, which is the expanfion of the whole circle of brafs 

 beyond the fteel. Whence the whole periphery 792 inches is to the length of the bar (nc- 

 gletling the expanfion endways) O.35 as the whole difference of the circumferences 0.207- 

 inch is to tlic cxcefs of expanfion in the brafs beyond the fteel c.oot66 inch. Now as the 

 motion of the end of the compound, bar by flexure was 0.16 inch, it was nearly one hun- 

 dred times as great as the linear diiTerenee of expanfion in the two metals. 



Since the verfed fines of very fmall arcs may be taken to be as the fquarcs of the lengths 

 of the arcs themfelves, and in fimilar arcs they are as the diameters, the quantities of de- 

 fledtion mcafured by the verfed fines of equal fmall arcs in circles of diliercnt diameters 

 will be invcrfcly as the fquares of the diameters, and dire£lly as the diameters, or more 

 fmiply in the inverfe ratio of the diameters themfelves. And as the fteel made ufe of in 

 this experiment was about five times the thicknefs of ordinary watch-fpving, it will follow, 

 that a compound bar made of wateh-fpring and brafs of the fame tliickncfs would have been 

 deflected five hundred times as much as the mean excefs of expanfion of the brafs beyond 

 the ftccl. 



Fig. 10, Plate V, reprcfcnts the balance contlrucled on tliis principle, and known by tlic 

 name of the expanfion balance. The outer part of the rim is brafs, aiid the inner fteel. 

 After this compound rim is brought to its figure by turning, it is cut through in three 

 places A, B, C, which fels one end of each third part of the periphery at liberty to move 

 outwards when the temperature is diminiflied, or inwards when it is increafed. D, E, F 

 are three fimilar and equal mafles of metal fitted upon the circular bars in a proper m.in- 

 iier to adniit of their being fixed at any required diftance from t!ic extremity, where the 

 motion is moft confiderable. G, H, I are three icrews, the heads of which tray be fct 

 nearer to or farther from the centre, and ferve as weights to effect the adjuftments for po- . 

 fiiion and rate. The peculiar advantage of this balance may be explained as follows: 

 When an increafc of heat dimlniflies the elaftic force of the pendulum-fpring K, the outer 

 brafs rim being lengthened more than the fteel, muft throw the weights UEF nearer to the 

 auls, and diminifii the effect of tire inertia of tlie balance, which confiquently is as fpeedily 

 carried through its vibration as before. And on the contrary, wlien cold weather adds ro 

 the elaftic force of tlie fpring, the fame weights are alfo thrown farther out, and prevent 

 the acceleration which would have followed. The exaiSl adjuftment of the weights is 

 found by trial of the going of the machine. If it gain by heat, the weights compcnfate too 

 ruuch, and muft be moved fartlicr from the extreme ends of tlic circular compound bars; 



but 



