involved in the Construction 0/ Artillery. 293 



but, as has been already remarked (chap. 10), all writers on Physics have copied 

 each other in the error of inexact physical conception involved in equation 3, 

 sect. 88, which properly applies only to absolutely rigid and perfectly elastic 

 solids, to which even iron in its cold state only approximates. Iron softened, 

 and rendered ductile, by a high temperature, however, is no longer in the same 

 condition. 



290. For example, the contraction of a wrought-iron bar of an inch square 

 is about -j-oJuro of its length for a change of temperature of 15° Fahr., and a 

 mechanical strain of one ton produces about a like extension ; and this C9ntinues 

 nearly true for both, throughout whatever range of temperature and of strain, 

 while the molecular structure of the bar remains the same ; but if the bar be 

 heated 900°, or 60 x 15°, it will expand, and in cooling again contract, through 

 rather a greater range than yo'-Suu °^ i'^ length ; yet it does not follow, that 

 after its cooling and contraction, a strain of 60 tons will remain upon the bar 

 at its extremities, if their approach be prevented: it is impossible, — for the total 

 power of the bar (1 inch square) to resist rupture, is only from 14 to 30 tons, 

 at most. 



291. What, then, does happen ? The bar, heated until its molecular condi- 

 tion is altered, and part of its rigidity gone, and replaced, by a new state of duc- 

 tility and softness, amounting in the extreme case almost to plasticity, is no longer 

 in a condition to transmit the force of its own contraction, and the latter is 

 expended, not in labouring force at the extremities, but in work done in elon- 

 gating the bar itself, whose length becomes permanently increased, and in 

 altering its form, and the effort finally expended upon the extremities, is only 

 the residual strain., or difference between the total force of contraction, and that 

 already expended in altering the length (and with it the other dimensions) of 

 the bar. Thus, the experiments of the Franklin Institute upon the tenacity of 

 wrought-iron at various temperatures proved that — 



At 800° to 900° Fahr J 



1050° „ 4 



1240° „ I 



1317° „ T^j 



of the maximum tenacity of the metal, at ordinary atmospheric temperatures, 

 were destroyed ; while at 3945°, its fusing point, according to Clement and 

 VOL. xxni. 2 Q 



