the Limit of Elasticity in Metals. 197 



determining experimentally the limit of elasticity thus defined, 

 there are in certain cases exceptionally great difficulties. 



In his first paper on the elasticity of bodies, Wertheim* says 

 that before beginning the actual observations a stretching of 

 the bar must take place ; but the stretching is never complete, 

 he adds, for even in the first loads small permanent elongations 

 are observed, which, as he then maintains, depend on the stretch- 

 ing. He therefore loaded the wire with a weight sufficiently 

 great for the stretching, which he now allowed to serve as start- 

 ing-point for the subsequent measurements, whereby the pre- 

 sent length of the wire was considered the original length. 



This method, applicable perhaps in wires, is inadmissible, it 

 seems to me, in bars of greater section. A rolled bar is never 

 completely straight, but has a number of bendings. If by load- 

 ing the bar it is to be stretched straight, this cannot be done 

 without the bar undergoing at the same time a permanent elon- 

 gation ; for it is evident that it is only when the bar is so con- 

 siderably stretched that a permanent elongation results, and the 

 particles assume a new position of equilibrium, that a return of 

 the crooked part of the bar to its old form is no longer possible. 

 But the elongation observed consists of the straightening of the 

 bendings, as well as of the permanent elongation necessary for 

 this stretching ; and these cannot be separated. It is therefore 

 impossible with perfect accuracy to determine the original posi- 

 tion of the bars, and therefore also to find accurately the limit 

 of elasticity. The error in the determination becomes greater 

 in proportion as the load for stretching the bar is great; for 

 then, as I shall show, the limit of elasticity can by stretching be 

 raised not merely beyond its original value, but, in short, to any 

 extent. 



§ 4. Raising the Limit of Elasticity by Stretching, 



The subsequently adduced observations show that a succes- 

 sive stretching of a bar can actually raise the limit of elasticity. 

 In the Tables, 



P = the load in Swedish pounds upon the unit of surface (a 

 Swedish decimal line square). 



AL = the permanent elongation produced (in a bar 5 feet in 

 length), expressed in parts of the measuring-scale. 



L is the original length of the bar. 



A its original section. 



E the loading of the bar after passing the limit of elasticity. 



Using now Wertheim's definition of the limit of elasticity 

 (permanent elongation =0 # 0005 of the unit of length), in the 



* Recherches sur V elasticity premier memoire, p. 19.* 



