66 Metbd f>f adjujlir.g Compamd Bars for Tinie-Plects. 



When the pendulum N, Fig. 3, becomes lengthened by heat, it is evident that it would go 

 flovi-cr if the greater expnnfion of the brafs in the compound bar EE did not at the fame 

 time render the whole bar more convex above, and raife the fcrew and its nut, and with it 

 the pendulum itfclf, which is by that means correfpondently fliortened at O. If the com- 

 mon rate of going from day to day diiTer from mean time, the adjuftment muft be made 

 by the fcrcw A. But if this rate, beinp (leady while the temperature continues unaltered, 

 (hould be found to change when the tf mpcrature is changed, the adjuftment muft be made 

 by the fcrew FF. That is to fay, the bridges HH are to be moved further afunder, if the 

 pendulum lofes by heat ; but if, on the contrary, heat caufes it to gain, the efFe£t of the 

 *ompenfation in the bar E£ is too confiderable, and the remedy will confift in moving the 

 bridges nearer to each other. 



Thus it is fcen that an adjuftablc compenfation for temperature may be applied by this me- 

 thod with the fame facility as the adjuftment for rate. It only remains to be obferved, for 

 the inftruclion of ackual workmen, by what method it is afccrtaincd that the bar EE fhall 

 poflefs fufficient variation in its flexure to produce the defired effeft within the limits of the 

 bridge-pieces. For this purpofe it is advifable to make a compound b;ir of brafs and fteel, 

 faftened together by riveting, foft-foldering, or brazing ; the latter method of which is mod 

 advifable. The length of this bar may be fix or eight inches, and the thicknefs of each metal 

 may be between the twentieth and thirtieth part of an inch. After reducing the two bars 

 in their conjoined ftate to an uniform thicknefs by filing and calipering as much as may 

 be requifite, the whole flexure of the bar, by a confiderable number of degrees alteration 

 of temperature, may be afcertained in the method defcribed by reference to Fig. 2. The 

 fpace run through by the clip C will be the verfcd fine of the arc of flexure ; whence the 

 verfed fines or deviations from the right line may be deduced in fhorter lengths ; for thefc 

 are very nearly in the prefent cafe as the fquares of the lengths of the bar. The efl^eftive 

 length of the compound bar EE muft be meafured from one of the bridges E to the middle 

 point •, that is to fay, it will be equal to half the diftance between the bearing edges when 

 drawn as far as poffible from each other. The proportion will therefore be: as the fquare 

 of the whole bar is to the fpace moved through by the clip, fo is the fquare of the effeifiive 

 bar of tha apparatus to its flexure by expanfion. From the length of the intended pendulum, 

 and the nature of the metal of its rod, its direct expanfion for the number of degrees in 

 queftion may be known from various tables, or by experiments. The rates of expanfion in 

 brafs and fteel have already been quoted in this paper. It is taken for granted that the 

 compound bar here fpoken of has been made fufficiently thick, and that the deviation by 

 flexure in the efTeclive bar, deduced from the proportion of the fquares, will prove lefs 

 than the dire£l expanfion of the pendulum. If it fliould prove greater, the bar is too thiny 

 and there is no remedy but to make a thicker. We may however proceed on the fuppofi- 

 tion that the quantity of deviation in the effeiSlive bar is confiderably lefs. It will be mod 

 convenient that this deviation (hould be about one-third lefs. If the difTercnce do not ex- 

 ceed this quantity, a piece of the long bar may be cut, and fitted to the apparatus. If it 

 do exceed, the flexibility of the bar from temperature will be increafed by reducing it 

 on both fides with the file. The quantity of deviation will be nearly in the inverfe pro- 

 portion of the thicknefs, as has already been ftated. Whence it is obvious, that the re- 

 quifite thicknefs may. be deduced and acquired from the original experiment of flexure by 

 change of temperature. But it is fafer and better to take the fmall additional trouble of 



4 afcert^ining 



