374 
Proceedings of the Royal Society of Edinburgh. [Sess. 
XXIII.— On the Cohesion of Steel, and on the Relation between the 
Yield Points in Tension and in Compression. By G. H. 
Gulliver, B.Sc., A.M.I.Mech.E., Lecturer in Engineering in the 
University of Edinburgh. 
(MS. received March. 5, 1908. Read May 18, 1908.) 
1. Direction of Internal Sliding in a Prismatic or Cylindrical Bar of 
Homogeneous Isotropic Material when subjected to a Single Axial 
Load. 
In works on the Strength of Materials, it is shown that the normal 
stress on an oblique section of a uniform prismatic or cylindrical bar, 
subjected to a simple, longitudinal, compressive or tensile load, is p . sin 2 0, 
where p is the stress on a normal cross section — that is, the total load on the 
bar divided by the area of the normal cross section — and 0 is the inclination 
of the oblique section to the axis of the bar. It is shown also that the 
tangential or shearing stress along the same section is p . sin 0 . cos 6, and 
this shearing stress is therefore a maximum on an oblique section inclined 
at 45° to the axis of the bar ; so that if the metal gave way by shearing, 
and there were no internal friction, fracture would take place along such 
a surface. Since there is a resistance to the movement of the metallic 
particles over each other, the surfaces, not necessarily planes, along which 
slipping actually occurs, do not coincide with those over which the shearing 
stress reaches its maximum value. The resistance to sliding is, at least 
partially, of the nature of a simple frictional resistance. Whether it is 
entirely of this character is open to question ; but, on the supposition that 
it is so, and that the coefficient of friction is independent of the load, the 
following results are obtained. 
Let ju. — tan (p be the coefficient of friction. 
(a) Compression. (Fig. 1.) 
The intensity of tangential stress along a surface inclined at an angle 
/3 to the axis is p . sin /3 . cos 8. 
The intensity of normal stress on the same surface is p . sin 2 /3 . 
The frictional resistance per unit of area along this surface is 
fj..p. sin 2 /3 =p . sin 2 /3 . tan <p . 
The frictional resistance increases with the load applied to the bar, 
because the pressure between the surfaces of sliding is increased. Slipping 
