APPARATUS FOP MEASURING STRAIN AND APPLYING STRESS. 271 



state to the other in a solid specimen requires a certain range of stress, so that the 

 diagram at the point a exhibits a well-marked rounding. 



If we call q the maximum shear at the outer surface, 



r = radius of the specimen. 



r p = radius to which plasticity extends. 



Then the resistance of the bar to torque is the sum of the resistances due to ( 1 ) the 

 still elastic core, (2) the semi-plastic shell, and may be represented by 



T = 27rq, 



o—l r' A dr + 2irq I r 2 dr 

 J o J r p 



where v = any radius 



= 2 1 " 



up to the point where perfect elasticity prevails r = r p and 



but when the specimen is wholly plastic 



r P = 0, 

 and we get 



which is ^ of the value at the elastic limit. 



It would therefore appear that if the bar changes from the elastic to the plastic 

 condition at the yield-point, the maximum torque will be four thirds of that value at 

 which the first-marked deviation from perfect elasticity occurs. 



The result of experiment shows a fair agreement with this conclusion. In the 

 example of a wrought-iron specimen quoted in the next section, Table III., col. I., the 

 first-marked deviation occurs below 375 inch pounds, while the material failed at 

 525 inch pounds, giving a ratio of 1 "4. 



Taking another case for the steel specimen quoted in the same section, Table IV., 

 col. I., the first deviation occurred below 675 inch pounds, and failure took place at 

 870 inch pounds, corresponding roughly to a ratio of 1"29, which is very close to f. 



Having regard to the difficulty of observing exactly the first sign of failure, it seems 

 probable that the conditions assumed are not far from the truth. 



VI. — Eecovery of Elasticity with Time. 



If a bar of iron or steel be subjected to a torque causing a permanent strain in it, the 

 condition of the bar becomes quite different ; it no longer obeys Hooke's law, and the 

 strain for a given stress is now greater than before the increase, being more marked 

 at the higher loads. As an example we may take that of a turned wrought-iron bar 



VOL. XL. PART II. (NO. 14). 2 S 



