12 MR J. MUIR ON THE KKCOVERY OF IRON F1IM OVERSTRAIN. 



The "Shearing Back" of the Curves. 



It will have been noticed that, owing to the extensions being plotted to an 

 unusually large scale, the curves occupy an inconvenient amount .of space. This 

 may te avoided by adopting a geometric artifice, suggested by Professor EWING, ot 

 "shearing back" the curves; that is, retaining the same scale of measurement, 

 an amount is deducted from each extension proportional to the load producing 

 it. F..r example, if extensions of 120, 240, 360 were produced by loads of 4, 8, and 

 I-J tons IHT square inch respectively, the extensions might be diminished by, say, 100 

 units per 4 tons of load, and plotted as 20, 40, and 60. Another way of expressing 

 this is t. say that in the diagram the axis from which extensions are measured may 

 .simply be considered as tilted back in the manner shown below by fig. 2. Fig. 1 

 shows a curve drawn with ordinary rectangular axes, and fig. 2 the same curve 

 " sheared back." 



Extension Extension. 



Referring again to Diagram No. I HA., the process of " shearing back" is performed 

 graphically on the single Curve No. 6 by adopting an oblique base line, OY', the 

 distance from which of each point of the curve is measured horizontally and re-plotted 

 from the vertical base line. Curve No. 6' being obtained. Besides the convenience of 

 space gained, this foreshortening of the curves by diminishing the rates of extension 

 renders a more obvious comparison of similar, but slightly different, curves, and 

 emphasises any irregularities there may be in the extensometer readings. It should 

 thus be remembered that in a stress-strain curve which has been " sheared back " 

 inequalities in extension are exaggerated, since the relations they bear to the total 

 extensions are not shown. 



In Diagram No. Illn. all the curves of Diagram No. IIlA.* are shown sheared back 

 by the method just explained, and in all similar diagrams to be shown in this paper 

 the curves will be subjected to the same treatment. In all cases the amount of 

 shearing of the curves is the same the extensions are always diminished by y^^ths 

 of an inch for e\vry 1 tons of stress. The scale for the measurement of extensions 



Since Diagram H!A. has been reproduced one-half full size, while Diagram Ills, (and all other 

 diagrams in the paper) have been reproduced to a two-thirds scale, the two Diagrams IIlA. and IIIu. are 

 not absolutely comparable. Besides this difference due to reproduction, the scale for the measurement of 

 load in IIIn. was originally only half that in IIlA. 



