Uniform Stress and Permanent Strain. 5 



by the time duration of previous stress. For this purpose a 

 bar of wrought-iron of very soft quality was cut up into nine 

 lengths of 20 inches, and the 20" bars turned parallel. 



Each bar was placed in the testing machine and a given 

 stress applied, the full stress being attained in about one 

 minute. The load was kept constant for thirty minutes, 

 when the permanent strain was observed and the bar taken 

 out of the machine. The results of these experiments when 

 combined show that the relation between the stress and 

 permanent strain is given by the formula 



p = Ce*, 



where p = stress in tons per square inch on the reduced 



section of the bar. 



. I'-l 

 e = permanent strain = — j— > 



where /= initial length, /' = stretched length, C = constant. 



This relation is clearly seen in Fig. <?, in which 

 Professor Reynolds'* method of logarithmic plotting is 

 used. Thus, if points whose ordinates and abscissae are 

 respectively the logarithms of p and e are plotted ; these 

 points are found to lie on a straight line, the inclination of 

 which will give the value of k, which in the above experi- 

 ments was found to be '25. 



Assuming the above formula, then in the case of the 

 nine bars, the maximum variation in the value of the con- 

 stant C is from 39*25 to 39/49, or 0'6%. 



It seemed probable that the permanent strains produced 

 in testing a single bar by successive loads would not be 

 given by the above formula ; but in Fig. 2, where the results 

 for bars No. 2 and 7 are plotted, it is seen that the same 

 relation holds approximately for cases where the time 

 duration of the stress does not exceed 30 minutes. 



In the case of bar No. 13, where the second stress 



Phil. Trans. Roy. Soc, 1879 — p. 753. 



