178 REPORTS ON THE STATE OF SCIENCE.—1913. 
axles are under tension, compression, or bending 13:38 to —13-38, range 
26:76 ; 23 to 0, range 23. Shearing or torsion 10°5 to —10°5, range 21. 
18-2 to 0, range 18:2. These figures would approximately fit the maximum 
strain theory. It is evident that more work is required in this portion of 
our field. 
14. The Separation of Matervals. 
A distinction has been drawn between ductile and brittle materials. 
Frémont*® has arrived at the interesting conclusion that steel is brittle or 
tough according to whether the ratio of the elastic limits in tension and 
compression is less or greater than one. It is quite possible that the usual 
classification is not along correct lines, and this should be discovered when 
greater attention is paid to substances of an intermediate character. The 
latter appear likely to introduce considerable complexity. For com- 
pletely ductile and brittle materials it appeared possible that double limits 
would cover all the conditions, and these would be shear modified by fric- 
tion, and possibly the maximum stress in tension. The intermediate steels 
appear to show an intermediate behaviour, and then we cannot apply the 
two limits. Scoble® has suggested that a criterion might be found of the 
form 
P,+ mP, =c 
in which m depends on the degree of ductility of the material. This 
equation is a general expression for all the laws except that of maximum 
strain, which would require a P, term. For brittle materials m and ¢ have 
different values in tension and compression. A microscopic study is 
particularly desirable to discover the mechanism of failure for the inter- 
mediate materials, since it is possible that it is not of a simple character, 
but a combination of that exhibited by the extremes. It is further neces- 
sary to give each substance its correct position in a scale based on those 
standard properties which determine its behaviour under combined 
stresses. 
15. An Engineering View. 
Yield has been taken to denote failure in most tests of ductile materials 
under compound stress. The reason has sometimes been given that the 
yield stress, and of course certain other considerations, fixes the working 
stress. This is only partly correct ; the ultimate strength retains much of 
its old importance, and the relative bearing of the yield and maximum 
stresses depends on the conditions of the case under consideration. The 
real reason for the selection of the yield point appears often to have been, 
either that the scheme of the tests was such that they could not con- 
veniently be continued to fracture, or that the stress distribution varied 
from point to point and could be estimated only within the elastic range. 
Although a knowledge of the ‘ Law of Failure ’ is of great interest, it is 
not of great importance to the engineer in cases of simple static loading. 
He will prefer to fix his working stresses by tests which are modelled on the 
working conditions. When combined stresses are produced by the loading, 
the theories are liable to be misleading or of no assistance. ‘Two examples 
will illustrate this contention. 
The yield and maximum stresses are considered to fix a working stress 
for a sample of steel in tension. The yield stress should not be exceeded, 
and the excess of the maximum over the yield stress is a reserve of strength. 
