the Limit of Elasticity in Metals. 205 



the curve has a more ascending direction than in the other kinds. 

 See, for instance, figs. 1 and 4. In general it may be said that 

 the radius of curvature is smaller the softer the material ; hence 

 it is least in iron. 



§ 9. On the Point of the Maximum of Curvature. 



It is perhaps superfluous to remark that the quality of a ma- 

 terial may be judged, not merely by the position of the two points 

 of the curve which indicate the limit of elasticity and the tear, 

 but that the curve must be considered in its totality. But since 

 the form of the curve is very complicated, and its equation can- 

 not probably be determined without much trouble, it is only 

 possible in each case to reproduce it graphically. 



Yet if in comparative experiments of this kind, for ascertain- 

 ing the greater or less applicability of different ores for a given 

 purpose, it is necessary to choose a determinate point of the 

 curve as point of comparison, I do not hesitate to propose that 

 at which the greatest curvature takes place. In my experiments 

 with rolled bars, those of the same kind have exhibited a special 

 agreement precisely in reference to the position of this point, 

 which cannot be said of the limit of elasticity. 



To determine practically the position of greatest curvature 

 from the figure is extremely easy, the more so since the curve 

 has the remarkable property, that in the neighbourhood and on 

 both sides of the said point it is symmetrical. On the axis 

 about which symmetry takes place is the least radius of cur- 

 vature. 



The point in question has, too, over the so-called limit of elas- 

 ticity, the advantage that it is indicated by the curve itself, and 

 has, we may say, a physical significance, which is not the case 

 with the point of the limit of elasticity. From what has been 

 said, it is obvious that just after passing through the point of 

 greatest curvature the permanent elongations are of real signifi- 

 cance; and, it may be added, these elongations are so marked 

 that, at any rate with bars 5 feet in length, they may be observed 

 with the greatest ease with the naked eye ; from which it is clear 

 that at a time when the permanent elongation was indeed known, 

 but the measuring-instruments had only a small degree of pre- 

 cision, the point in question at which the curvature is a maxi- 

 mum must have been designated as the point at which the per- 

 manent elongations begin — that is, as the limit of elasticity. 



From the important significance which I have sought to attach 

 to the point of maximum curvature, and from the preference 

 which I would give to it above that of the limit of elasticity, the 

 conclusion must not be drawn that I consider this point free 

 from all the errors which are incidental to the limit of elasticity. 



