429 
1908-9.] Internal Friction in Cases of Compound Stress. 
The experiments of Hancock * were performed upon steel tubes and solid 
round bars, these being submitted to tension and to torsion, both singly and 
combined in various proportions. Similar calculations, taking /u as 0T4, 
gave results appreciably more uniform than the maximum shear, especially 
in the case of the thinnest tube. The divergences in Hancock’s results 
become much greater as the thickness of the tube is increased. The values 
of fj., calculated from the simple tension and simple torsion experiments, are 
given also in the above table. The absurd result shown by the solid bar 
is probably connected with the variation in stress over the cross section, 
caused by torsion. 
Scoble j* subjected solid round steel bars to combined bending and torsion. 
The magnitude of the stress across a section of a bar in such conditions 
varies considerably, so that it is impossible to determine the yield-point with 
any degree of accuracy. Recognising this difficulty, Scoble made use of a 
purely arbitrary point, found by prolonging the plastic curve backwards to 
meet the elastic curve. This point is certainly not identical with the yield- 
point, and since it depends upon the individual judgment in extrapolating 
a curve, which is itself liable to considerable variations in character, the 
results cannot be considered of great value. As they stand, however, they 
would give no definite value for jm, as is pointed out by Scoble himself. 
Goodman’s experiments were confined to the application of combined 
bending and torsion to solid round bars of cast iron — a brittle material — 
instead of the ductile substance, steel. The two cases are very different, 
and the results must be considered in a somewhat different manner. 
There is a distinct dissimilarity between ductile and brittle bodies in their 
behaviour under stress. When broken by simple tension, a ductile substance 
shows a more or less perfect shearing fracture, but a brittle substance 
ruptures along a direction approximately perpendicular to the direction of 
the stress. On the other hand, under a compressive stress brittle bodies 
give shearing fractures, while ductile materials are simply flattened, but 
sometimes crack along planes parallel to the direction of the load. Thus 
the ratio of the tensile strength to the compressive strength for ductile 
materials is a somewhat indefinite quantity, if strength be defined as the 
stress necessary to cause rupture. The same ratio for brittle substances is 
usually small, the compressive strength being much greater than the tensile 
strength; the ratio is 1/4 to 1/7 for cast iron, and as small as 1/50 for some 
stones. 
When subjected to combined stresses, ductile and brittle pieces may be 
* Phil. Mag., xi., 1906, 276 ; xii., 1906, 418. 
+ Ibid., xii., 1906, 533. 
