174 Oh the Power of Expanfton-hars as Firji-movers, 



of verfed fines of finall arcs, that the diftance A B, fig. 2, wil), ceteris paribus, be as^ the- 

 fquare of C A; and it fhould feem as if a confiderable advantage might be derived from ufing 

 the whole length of the bar, as in that figure, 2, inftead of the tv/o half-lengths in fig. 3. But 

 It muft be confidered, that the effect of hammer-hardening the lower part, and wire-drawing 

 the upper, of the compound bar C A, is twice as great at C, fig. 2, as it is at C, in fig. 3, 

 and is fhewn in the greater fpring, or yielding of the parts ; and that the aflion at A, in this 

 figure, is doubled at the oppofite extremity of the bar : — fo that upon the whole, the adtion at A, 

 on account of the fhort lever A C, fig. 3, being twice as powerful as that at A, in fig. 2, and 

 being exerted through the fpace A B,iig. 3, of one-fourth part of the fpace A B, in fig. 2,. 

 will be half the a6tion at the end of fig. 2. But as both extremities of the bar are made to 

 aft in fig. 3, the whole of its a6tion will be precifely equal to that in fig. 2. The combi- 

 nation, fig. 3, appears, therefore, to be preferable on account of its convenient figure only. 



It may alfo be queftioned, whether thefe bars fliould be made extremely thin, or the contrary. 

 If they be very thin, the efFeft of the readion being equivalent to a pull, or pufh endways 

 upon the bar, which is greater than the reaftion itfelf, in the proportion of the length of the 

 bar to its half thicknefs, it may eafily be imagined, that the texture and cohefion will be moft 

 ftrongly affedted ; but, on the contrary, if the bar be very thick, the effect from change of 

 temperature may refolve itfelf intirely into an aftion upon the parts near the contiguous 

 furfaces without producing any flexure at all. It appears, therefore, that there is a thicknefs 

 which is practically better than any other ; but what this thicknefs may be, remains to be 

 determined by trials. As the quantity of motion is inverfely as the thicknefs (Philof. 

 Journal, I. 576), and the force direftly as that thicknefs, it muft follow, that the quantity of 

 mechanic efFe£t in all fimilar bars, neither extremely thick, nor extremely thin, will be the 

 fame upon equal changes of temperature. I fhould give the preference to thin bars, not fo 

 much reduced as to have any perceptible fpring. ^ 



If the fig. 4. be fuppofed of fuch dimenfions, as that the circular arc flruck through the 

 sniddle parts of all the bars might be three feet in length, and the bars were each fix inches 

 long in the-radial direaion, with a thicknefs nearly equal to that of the fecond experiment 

 related at the laft-quoted article of our Journal ; the fpace moved through, by each bar, upon- 

 an alteration of 146 degrees, would be about 0,05 inch, or half a tenth: but 300 of thefe bars, 

 might, with eafe, be contained in the circular fpace of three feet, and thefe would produce a 

 motion of fifteen inches by the fame change of temperature, or one-tenth of an inch for 

 every, degree of Fahrenheit. In order to determine the force with which this change of 

 pofition would be affefted, we are in want of fome experiments on the expaniions of metals. 

 It is generally fuppofed that a rod, or wire, will contraft or dilate, by change of temperature,. 

 in the fame manner, whether it be at perfeft liberty to move horizontally, or be made, to 

 fupport a weight hung from its extremity, or placed on its upper end. This is, in.fadt, fup- 

 pofed to be the cafe in the eftimates for conftrudting gridiron pendulums, and if it were 

 ftridtiy true, the power of this wheel would be conflantly equal to the reaction againft which it 

 fliould be exerted. But it would be to little purpofe to inftitute a. calculation upon data affumed 



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