198 Mr. Mallet on the Physical Conditions 



Franklin Institute, on tension at high temperatures, equally unnoticed by 



him. 



119. Poncelet has devised a coefficient to express the relation of the work 

 done by the force balancing this resistance, at each of these limits: the one T„ 

 which he calls that of" resistance vive d'elasticite ;" the other, Tr-, that of " resist- 

 ance vive de rupture." They express respectively the work done by the force 

 P moving tlirough the space z, up to the limit where elasticity is lost or materially 

 altered, and up to that of rupture or crushing ; in both cases as the nearly 

 immediate results of application of the force. 



For the resistance vive of elasticity, as P = ez, we have 



Te=hPiovieP; (15) 



and a similar expression applies to Tr, increasing the values of P and i in either 

 case for each special substance. 



120. The force P is variable between the limits o and i — 



i=-^andP=^i (16) 



eA L 



If X be any small extension or compression the n" part of f, the P, corre- 

 L 



eA 

 spending to or = -y^x, the work done in extending or compressing through the 



eA 

 infinitely small additional space Ax (assumed uniform) = -j^xAx, and the whole 



work done, 



Tt = -^j^\xdx — ^-F-i^ or |ei^ for unit of L and A as above. (17) 



Ij Jo Lj 



121. Kthe strain P, due to z, the extension or compression, be brought at 



once upon the bar, then the work done upon the bar will be double the former 



eA . 

 = -^ i^ and the extreme extension or compression will be 2i, and the end of 



the bar i, will oscillate from o to 2j, making equal excursions at either side of i. 

 If between equations i — —j and T^ — \-y-v^ i be eliminated, we have 



