436 Proceedings of the Royal Society of Edinburgh. [Sess. 
If a specimen of cast iron is crushed between cast-iron platens, fi and // 
are equal, or nearly so. In this case 
(3 = (45° -$) = 36° 28' to 35° 55'. 
If the platens are of steel, will be somewhat less than 016, and fi' con- 
sequently slightly greater than the above values. The inclination of the 
sliding surfaces, measured from broken specimens of cast iron, usually lies 
between 35° and 37°, and therefore agrees closely with the calculated value 
of fi'. 
Taking fi' = 36° as an average result, the ratio of c' to c is 
c 
c 
fi 1 + fi 2 - /x 
1 + /x 2 — 2 fi 
T2 (nearly). 
In extending this result to the breaking stress of cast iron, it should be 
noted that bars of this material originally cylindrical or prismatic become 
FIG 3 
more or less barrel-shaped towards the end of the test. On this account 
the direction of compressive stress is no longer constant, but varies slightly 
from point to point within the body. In this case the results are closely 
represented by saying that the inclination of the surface of sliding to the 
direction of the compressive stress at each point is constant, and has the 
same value as already found. The most important effect of the change of 
shape of the bar is the resulting curvature of the surface of sliding (fig. 4). 
It may be pointed out that the mere existence of this deformation is 
evidence that cast iron possesses a yield point lower than its breaking 
stress ; but this yield point, as is well known, cannot be located definitely. 
The minimum length of a cast iron specimen necessary to secure a clean 
shearing fracture is cZcot36° — that is, about T4 d, where d is the diameter 
of the bar. The length should not be less than this at the moment of 
