170 REPORTS ON THE STATE OF SCIENCE.—1913. 
Too frequently the complexity of our subject has not been realised, 
and confusion has followed the omission of conditions and limitations. 
This is particularly noticeable in early statements of theories, and has not 
been eliminated in some of the most important modern contributions. 
2. Failure. 
The laws of failure for materials are important to elasticians, experi- 
mentalists, theorists, and engineers, and we must inquire whether one 
definition of failure can be generally acceptable. The theory of elasticity 
is based on Hooke’s Law which holds to the elastic limit, consequently the 
elastic limit is the fail point for the elastician, and also for the experimenter 
who calculates his stresses from formule based on Hooke’s Law. But 
the elastic limit is not a well-defined point even under the most favourable 
conditions,* and many materials extensively used in engineering practice 
have no elastic range. In the case of steel the yield point has been taken 
for experimental purposes instead of the elastic limit, and modern tests 
under simple loading indicate that these points coincide for some steels 
initially in a state of ease. Engineers are justified in considering fracture 7° 
because in many structures the yield point is exceeded locally (as in riveted 
joints), and where the stress intensity varies through the mass of the 
material the distribution at rupture is entirely different from that within 
the elastic range of the material. 
These considerations lead to the suggestion that for the purpose of the 
present investigation experiments should be arranged with uniform distri- 
bution of stress, and then important data will be obtained at elastic failure 
and at fracture. Experiments which employ non-uniform stress distribu- 
tions will give useful results at the elastic limit and possibly at the yield 
point of the material, but the data obtained at fracture or other complete 
failure in such cases is of no value for the present purpose. 
3. Materials. 
We have to consider materials with widely different mechanical pro- 
perties,j and it is certain that all materials do not behave similarly when 
tested under identical conditions. To the present the distinction appears 
to have been between ductile and brittle materials,2?: “1 which is better 
than the frequent neglect of this consideration ; but this is not a complete 
definition, and, furthermore, it does not readily enable the physical pro- 
perties of a material to be defined with exactness. It is possible that 
Mallock’s suggestions will lead to more accurate scales, and consequently 
to a knowledge of the relation between the elastic constants and the 
behaviour under any system of combined stresses. 
4. The Systems of Stress. 
The stresses may be referred to the three principal stresses. Each 
principal stress may be either a tension or a compression. In cases of 
simple tension or compression two of the principal stresses are zero. With 
two-dimensional stress one principal stress is absent, and we can have 
combinations of two tensions, two compressions, or one tension and one 
compression. There are corresponding combinations for three-dimensional 
* The correspondence on this point should be consulted. 
+ Mallock”’ suggests relations between the unclassified mechanical properties, 
brittle, ductile, tough, &c., and the measurable constants of the substances to which 
they are applicable. 
