174 REPORTS ON THE STATE OF SCIENCE.—1913. 
copper tubes subjected to torque and a uniform bending moment. The 
maximum shear stress again varied, being greater in bending than in 
torsion, but this deviation from the law is in the contrary direction to that 
required by Theories (a) and (0b). 
Turner's *°: ® early experiments were modelled on those of Guest. He 
tested steel tubes in simple tension, and under simple torque, and included 
a few tests under combined tension and internal pressure. The shear 
stress theory was confirmed at elastic breakdown. Later he made a few 
experiments with solid mild, tool, and nickel steels in simple tension and 
torsion. The maximum shear stresses were: for mild steel 21,200 and 
24,400, tool steel 33,900 and 38,400, and for nickel steel 40,600 and 40,800 
Ib. per square inch. He says: ‘It is clear that the shear theory is no 
general Jaw which covers all elastic materials. The tool steel shows the 
ereatest inequality of shear in the two distributions of stress ; yet even for 
it the theory that failure occurs through shear is obviously very much 
closer than the tension hypothesis.’ 
Three-dimensional stress was secured by the use of thick steel cylinders 
under internal pressure and longitudinal tension. The tubes were so thick 
that the radial compressive stress was usually about 11,000, but in one 
case reached 17,200 lb. per square inch. The principal stresses were two 
tensions and one compression. The external diameter of the cylinder 
decreased at yield. For one tube the extreme value of the maximum 
shearing stress were 16,600 in simple tension, and 20,900 under simple 
torque. He deduces from these experiments that the shear theory is not 
very far from true, but that it is sensibly untrue. The tube was used for 
several tests with intermediate annealing. The maximum shear stress for 
one test in simple tension was 18,500 lb. per square inch. 
Smith 4 5% 60, 68 tested solid steel specimens in tension or compression 
with torsion. He supported Theory (c). Experiments with non-ferrous 
metals demonstrated the attendant difficulties and did not lead to satis- 
factory results. 
Mason *® extended the range of conditions by testing steel tubes in 
tension, compression, compression and hoop tension, compression and 
hoop compression. His experimental results show an approximate 
agreement between the maximum shear stress at the yield pomt in com- 
pression, and the yield point stress in pure shear (obtained by equal 
tensile and compressive principal stresses), the mean difference in the 
tests of annealed specimens being about 3 per cent. ‘It appears, then, 
that mild steel in direct compression yields by shearing; and to a first 
approximation that the value of this shear stress is independent of any 
normal compressive stress on the planes of the slide.’ The direct applica- 
tion of two compressive principal stresses to steel was an important 
advance. 
Cook and Robertson determined the strength of thick hollow cylinders 
of cast iron and steel under internal pressure. They concluded that the 
failure of cast-iron cylinders is determined solely by the maximum principal 
stress, and for mild steel cylinders the pressure is about 20 per cent. in 
excess of that required by the shear stress theory, or midway between that 
indicated by Theories (b) and (c).* 
* These results differ from those of other observers. Cast-iron cylinders fractured 
according to the formula based on the principal stress law, but since this formula 
applied also to the steel cylinders, there is no proof here that cast iron fractures 
