194 M. R. Thalen on the Determination of 



on the surface of the wire in each case, it is obvious that the amount 

 engendered on a square inch of s x is to the amount engendered on a 

 square inch of s 2 as d 2 3 : d x 3 , that is, in the inverse ratio of the cube 

 of the diameter, 



W W 1 }_ 



s x s 2 d* d 2 



XXV. On the Determination of the Limit of Elasticity in 

 Metals. By Robert Thalen*. 



[With a Plate.] 



HODGKINSON and Morin have been led by their investi- 

 gations to different results as regards the determination 

 of the limit of elasticity. The former thought he had found that 

 a body, when it has experienced any elongation or contraction, 

 never completely assumed its original dimensions. Hence it 

 follows that in stretching a metal, the least loading produces a 

 permanent elongation, that is, lowers the limit of elasticity. 

 Morin doubts the validity of this conclusion, and, in the cir- 

 cumstance that the bars used by Hodgkinson (15 metres in 

 length) were composed of smaller pieces, thinks he finds an 

 adequate explanation of the low position of the limit of elasticity. 

 The permanent elongations observed, Morin thinks, need not 

 necessarily depend on an actual elongation of the fibres, but 

 might rather arise from an alteration of the connecting joint, or 

 from a stretching of the bars themselves, Morinf found a con- 

 firmation in some new investigations which were made with 

 metal wires 24 metres in length : it was observed then that the 

 permanent elongation only occurred with greater loads, or, that 

 the limit of elasticity had a high position. Even if Morin's 

 explanation of Hodgkinson' s lower position of the limit of elas- 

 ticity is partly right, it cannot be extended to the conclusion 

 that the permanent elongation observed with small loads entirely 

 arises in this way. This is too much to object to so experienced 

 a man as Hodgkinson. Nor does it seem necessary, on the 

 basis of Morin's experiments, completely to reject Hodgkinson's 

 statements ; for the results of both experimenters, however dis- 

 crepant they appear, need not necessarily exclude one another, 

 but may be both true. 



To show the possibility of this, and also to furnish a contri- 

 bution to the important question of the elastic properties of 

 bodies, I venture to give here part of the results which I have 

 obtained in a similar investigation with iron or steel. And first, 



* From PoggendorfF's Annalen, April 1865. 



t Resistance des matfriaux, 2nd edit. p. 10. Comptes Rendus, vol. liv. 

 p. 235. 



