62 Eiiijt/iiy into the Nature and Effect t of the Curvature 



on the other. But if the tetnperature be diminiflied, the mod variable of the two metals, 

 by contracling more than tiic other, will form a concavity on its fide. 



It might afford data for intcreiling mathematical fpeculation to afcertain what would be 

 the nature of ilie curves formed by fuch a combination of materials in sU the aflumable 

 varieties of figure, tenacity, flexibility, and temperature. The confiderations wliich prcfcitt 

 themfelves in a loofc profpeil of the fuhjecl may be exemplified in two uniform bars of 

 brafs and fteel, differing oulv in thicknefs, meafured from the common face of contact. 



Metals arc eapablc of being lengthened or fliortened by mechanical force, as well as by 

 altering their temperature. Hence, if the temperature of a piece of metal be increafcd at 

 the fame time that its cxpaiifion is prevented, the confequencc mull be a contraClion or 

 change in the texture, of the nature of what workmen call hammer hardening. AnA the 

 contrary effect may be fuppofcd to t.ike place if a mechanical obftacle be oppofed to prevent 

 the contraction which would take place by cold. It is known from ;e\periment, that the 

 dilatations and contra£lions from change of temperature are made with an extremelv great 

 force ; but from other experiments it is alfo known, that the tenacities of bodies are fuf- 

 fjcient to oppofe and greatly diminiili the efieCt of thofe forces. / 



If a thifi bar of ftccI be foldered to a very thick bar of brafs, it may be inferred that the 

 greater expanfions and contrai£lions of the brafs will alternately rarefy and condenfe the ad- 

 herent fteel, at the fame time that the face of the brafs will probably undergo an oppofite 

 change of the fame nature, in the vicinity of the fteel. It may be imagined that the immediate 

 properties of the metals would in the courfe of time become changed by this continual effort ; 

 that is to fay, they might become more or lefs flexible, tenacious, hard, expanfible, denfe, &c. 

 Thus bell-wires become hard by pulling; gold, in the hands of the gold-beaters, becomes 

 foft by bending backward and forward ; brittlenefs is produced by twilling, and fo forth. 

 The power of the brafs to alter the texture of the fteel tiiuft be derived from two of its 

 qualities-, namely, its refift.ince to flexure, and Its ftrength or refiftance to change, of the 

 fame kind which was inferred to take place chiefly in the fmaller bar. Whenever, there- 

 fore, it is required that t!;c expanfions and contractions fruni temperature fliould be ex- 

 erted chiefly in bending the compound bar, it is ncceffary that the ftrengths and flexi- 

 bilities of the two bars (hould be fo proportioned 'that the texture of each ihould fuffer 

 aiike. 



The increafe of dimenfions in brafs and fteel in like elevations of temperature is nearly 

 ns two to one. The weight required to break a wire of fteel is about double that required 

 to produce the fame elTecb in brafs. If a bar of brafs be foldered to a bar of fteel of iialf 

 the thicknefs, their ftrengths will then be nearly equal ; and the yielding, except fo far 

 as depends on the mechanical difficulty of bending a thicker bar, will be nearly the fame 

 in both. Steel, being lefs flexible than brafs, diminidies the effect of the mechanical advan- 

 tage of the latter from its thicknefs, and renders it lefs ncceffary to take it into confideration. 



When the ftrengths of the two bars are nearly equal, and the flexibilities great, there 

 will moft probably be fome line within each bar which will poffefs the fame length as 

 that of the unconfined bar at the fame temperature. 



If a right line be .divided into any number of equal parts, and a number of equal per- 

 pendiculars be erected at the fcveral points of divifion, the diftances between the upper 

 extremities of the fcveral adjacent perpendiculars will be equal. But if thefe intervals be 



2 every 



