78 Mr. J. J. Guest on the Strength of 



volume under a simple tension (else it would decrease volu- 

 metrieally under three orthogonal tensions). 



It is hardly conceivable that a should be negative, but it 

 cannot be less than — 1 ; otherwise the material would be 

 unstable under torsion as the energy of a simple shear, 



%r (1 + 0") j would be negative should 1 -t-<r be negative. 



The values of a met with in the course of experiments 

 undertaken will be found in Table V. They are not determined 

 by a method possessing much accuracy, being' found from the 

 values of E and C ; they are, however, sufficiently accurate 

 for the purpose in view. 



17. The Maximum Strain Theory not disproved by published 

 experiments. — Upon the maximum strain theory of strength 

 the yield-point stress under torsion to that under tension 

 should be 0*80 for cases in which <7 = 0*25. The least value 

 of this ratio will occur when a is a maximum, i.e. when <r = 0"5, 

 the value then being 0'66. As the experimental results quoted 

 above place this ratio, for steel, between 0625 and 0'735, it 

 will be seen that, taking into consideration the effect of flaws 

 upon a torsion test and the difficulty of locating the yield- 

 point, the experimental results cannot be held to disprove the 

 theory, although they militate against it. 



In discussing the phenomena of torsion, Tresca separates 

 the state of the material into three stages : the elastic state, 

 the plastic stage, and an intermediate condition. These 

 correspond to the portions OA, BC. and AB respectively in 

 a stress-strain curve such as fig. 1. St. Venant, followed by 

 many elasticians, does not recognize the intermediate stage, 

 and considers that Hooke's law holds up to the point at which 

 plasticity begins ; he adopts Tresca's results that in the plastic 

 stage the shearing-force is constant, and upholds a specific 

 maximum strain as the condition of limiting elasticity. 



I fail to understand how a material could have one con- 

 dition for the commencement of plasticity and an entirely 

 different one for its existence; perhaps users of these con- 

 ditions tacitly admit the existence of the intermediate stage, 

 but neglect it for the simplification of calculation and because 

 the physical difference between the elastic and plastic states 

 is so great ; or perchance they do not admit the rigour of the 

 deduction of the plastic law from Tresca's experiments. 

 [St. Venant/s proof (Comptes Rendus, lxx., and Todh. & 

 Pearson's ' History of Elasticity/ vol. ii. § 236) that in the 

 plastic stage the resistances to slide (shearing-strain) and 

 elongation have the same value, consists in equating the work 

 done in similar changes under a simple shear q and a com- 



