﻿Manchester Memoirs, Vol. xlix. (1905), No. 1. 5 



bar sufficiently great to produce permanent set, the bar was 

 taken out of the machine and a new arc d, e Fig. 2, 

 struck from the same centre, the dividers having still the 

 same radius. The distance between the first and the second 

 arcs, measured along a line parallel to the axis of the bar 

 gave the diminution of length caused by the imposed 

 stress. The actual measurements between the arcs were 

 made with a micrometer microscope. As the lines were 

 very fine and were scribed on clean metal, it was found 

 that the measurements could be made with a considerable 

 degree of precision. 



After each application of the load a new arc was 

 struck with the original radius and a micrometer observa- 

 tion taken. . In some of the tests two sets of readings 

 were taken, one on each side, while in others three sets 

 were taken. 



If / is taken as the original length, and /' as the 

 shortened length, then : — 



(the permanent strain) = e = —j— 



The corresponding stress is p, which is the load on 

 the bar divided by its area at the moment when it is 

 sustaining the load in question ; this is calculated from 

 the length between the gauge lines on the assumption 

 that the volume of the bar remains constant. It is known 

 that the variation in the density of metals under stress is 

 small and may be neglected for the present purpose. 

 If / is the original length and a the original area, then 

 the initial volume is Ixa. Similarly I' and d are the 

 corresponding values for the load in question, and I'xa 

 the volume. These two being assumed to be equal 



, a. I 

 a =-T' 



