i06 Mr. J. J. Gkiest on the /Strength of 



discriminant then becomes 



Ui— v i<j> —0; 



I # 6 2— ^ 



and the principal strains have the values 



i{e 1 + 6 2 ± V(ei-e 2 ) 2 + ^) 2 }; e 3 > 



The maximum shear-strain, being the difference between the 

 greatest and least principal stresses, is 



In the case of the internal pressure experiments, the strains 

 have been calculated from the values of the principal stresses 

 and of the elastic constants. The results so obtained are always 

 less than the measured values of the strains would be; as in 

 the tension and internal pressure the axial strain is a principal 

 one, its measured volume in the column " Axial strain " can 

 be compared with its calculated value in the column t] 1 of the 

 principal strains. 



The maximum slides or shear-strains, being in value equal 

 to the difference between the greatest and least principal strains, 

 have also been tabulated ; these should be, but for the elastic- 

 limit effect, directly proportional to the maximum shearing- 

 stresses, and independent of the third stress. 



44. Maximum Shear and Slide are proportional. — For if 

 the principal stresses be vt x , ■s^,^, then the maximum shearing- 

 stress perpendicular to vr 3 is \fa\ — ux 2 ). The principal strains 



are ^ fa — (tvt 2 — <jw 8 ) , ^ fa — osj 3 — ctct-j) , ^ fa — cra^ — <tot 2 ) , 



and the corresponding maximum slide to ^(^i nr 2 ) is — p— 



X ( , st 1 — i*r 2 ). So that the maximum slide directly corresponds 

 to the maximum shearing-stress and is independent of the 

 stress normal to its plane. Thus the comparison of the 

 maximum shear and slide columns in the tables o£ results 

 will indicate the magnitude of the elastic- limit effect. 



45. Quantities tabulated. — Thus for the tests the values of 

 the principal stresses, of the principal strains, of the maximum 

 shear, and the maximum slide at the yield-point have been 

 tabulated ; a column has also been included giving the maxi- 

 mum principal strain as calculated from the elastic constants 

 and stresses, this being the yield-point strain on the supposition 

 that Hooke's law holds up to the yield-point. 



The values of E, Young's modulus, and 0, the modulus of 

 rigidity, have been calculated from the elastic ratio of stress 

 and strain in the tension and torsion experiments ; they have 



