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



descending order of magnitude, may be written in the form 



( a i a )(«'+y+'i+(«i- a j 5 )'+ =, ?*-.i 



(since the invariants are the same), it is clear that any state 

 of stress can be represented by the coexistence of a shearing- 

 stress, a volumetric uniform stress, and a stress perpendicular 

 to the plane of the shear ; and the yield-point occurs when 

 the shearing-force together with a small fraction of the volu- 

 metric stress reaches a certain amount : the volumetric stress 

 being reckoned positive when tensile. 



That the coefficient of the volumetric stress for steel is 

 small has been shown by these tests, and that it has some 

 value greater than zero seems probable, as volumetric tension 

 would ultimately reduce the material to the liquid or gaseous 

 form and cause the necessary shear to evanesce. No value 

 cau be directly deduced from such considerations owing to 

 lack of knowledge of ultimate molecular action. It may be 

 noted that Bauschinger's experiments on the yield-point in 

 tension and compression, in which the effect of X would be 

 most marked, would point to zero as its value. 



57. The Copper and Brass Tests, and Diagrams. — In the 

 case of the copper and brass tests the yield-point is more 

 difficult to locate ; the shearing-stress law still appears to be 

 that one of the simple laws nearest to the truth. Taking into 

 account the volumetric stress effect, the coefficient A, is larger 

 than in the case of steel, but so few tests have been made that 

 conclusions should be drawn with hesitation, especially as the 

 yield-point stress tends to rise with the successive tests. 



In the copper tests the yield-points were very indefinite, 

 and 1 have plotted out types of the unusual tests from which 

 the stresses and resulting strains and the mode of their varia- 

 tion can be seen at a glance, and their values at points con- 

 sidered to correspond to the elastic limit or yield-point in the 

 various tests readily compared. These curves are given in 

 figs. 21-24. 



In fig. 21 is shown a test under internal pressure only, the 

 stresses parallel to the axis being one-half of the simultaneous 

 circumferential stresses; the values of the internal pressure 

 are laid off along the central line, and the values of the 

 corresponding axial and circumferential strains given on the 

 right and left hand respectively of the figure. The readings 

 of the axial and diametral (fig. 14, p. 93) extensometers are 

 given along the base line, and the corresponding strains along 

 the top of the diagram. The axial strain is laid off positively 

 (extension) towards the right, and the circumferential strain 

 (from the diametral extensometer) positively towards the left. 



