XXII. W. H. WARREN. 
gives the percentage of elongation, which it is the custom to 
record in test reports on materials in ordinary commercial testing. 
The error in the method and the divergence in the results when 
made on test pieces of different lengths is now well understood, 
the percentage of elongations increasing as the length of the 
specimen decreases, for the same diameters. The method of 
expressing the true percentage of elongation has been investigated 
by Mr. J. H. Wickstead in 1890, also by Professors Dwelshauvers, 
Derry, and Tetmaier, and it is generally admitted that the elon- 
gation up to the point of maximum load supported by the test 
piece should be used, and the local elongation or ‘necking’ which 
occurs afterwards should be rejected as it has nothing whatever 
to do with the length of the specimen, increasing with the 
diameter in circular sections, and with the ratio of breadth to 
thickness in rectangular sections, In Plate 1 fig. 10, the exten- 
sion up to the point m is proportional to the length of the test 
piece, but the portion between m and r is the local extension or 
necking. The true extension per unit of length may however be 
obtained from the test piece in the following manner :— 
Let the local extension be denoted by Alo, the elongation per 
unit of length by Xo. Then for a test piece of length /=8" and 
total elongation A/, we have : 
Al, = Alo + B Adw....... (1) 
If now we measure the total elongation over a length of 4” in 
the same test piece (or over any other convenient length contain- 
ing the local elongation) we have : 
From these two equations we can find the two unknown quanti- 
ties A/o and Ao thus: 
The elongation at rupture is therefore for a length of 8” : 
Al = 8 Xo = 2 (Al, — Ad)......... (5) 
