378 Proceedings of the Royal Society of Edinburgh. [Sess. 
Other experiments with thin, flat steel bars, 3 inches wide and J inch 
thick, gave £=l7‘6and c = 2T9 tons per square inch. These correspond 
with 
tjc = 0‘804r 
fi = 0-109 
0 = 6° 13' 
a — 48°, and /? = 42°, approximately. 
In this case it was necessary to give lateral support to the bars tested in 
compression in order to prevent buckling. 
3. Cohesion. 
For a bar under a crushing load which gives rise to an axial stress, c , — 
The normal stress on a surface of sliding is c . sin 2 (45° — <p/2) 
= c/2 . (1 — sin 0). 
The frictional resistance along this surface due to the normal stress is 
/x. c/2. (1 — sin 0). 
The tangential stress along the surface is c . sin (45° — 0/2) . cos (45° — 0/2) 
= c/2 . cos 0. 
It is easy to show that, whatever the value of 0, cos 0 cannot be less 
than /x (1 — sin 0), and therefore the tangential stress can never be less than 
the frictional resistance due to the normal stress. 
Since 0 is a small angle, c/2 . cos 0 is considerably greater than 
/x . c/2 . (1 — sin 0). But, on the previous hypothesis, at the moment when 
sliding commences the tangential stress only just overcomes the frictional 
resistance, and there must, therefore, be some resistance to sliding in addi- 
tion to that already considered. If cohesion be regarded as a force acting 
in a direction perpendicular to the surface of each particle of the metal, 
a cohesive force acting normally to the surface of sliding will have the 
effect of increasing the normal stress on this surface due to the compressive 
load, without altering the tangential stress. 
Whether it is legitimate to consider the frictional effect of cohesion, an 
internal molecular force, as comparable with that of an externally applied 
load, is open to serious question, but that some form of internal frictional 
resistance exists can be scarcely doubted. An arbitrary assumption has 
been made as to the nature of this resistance ; and by substituting figures 
found from experiments, a numerical value of the assumed cohesive force 
has been found. This value is compared finally with a number of results 
obtained from tests of steel bars, with which it accords fairly well. Thus 
the original assumptions are in a sense justified, though it is unlikely that 
