THE MECHANICAL INTERPRETATION OF JOINTS II 
In the case of those substances in which the tensile strength is 
greater than the crushing strength, the formula would indicate 
that the shearing angle is obtuse. That this is indeed the case, 
for instance in the striking case of wood cut with the grain, may 
be seen from Figure 3, page 17, of Leith’s Structural Geology. 
This leads us to the important generalization that the angle of 
shearing of a material is the more acute the more brittle the sub- 
stance is, and vice versa. In fact, it seems possible, if not probable, 
that in the hands of the physicist the angle of shearing will be 
made the chief criterion of brittleness. 
The formula also brings out clearly the fact that the angle of 
shearing is independent of the hardness of the material. In the 
table given above wrought iron ranks with oak and pine wood. 
Small cubes of a “‘brittle’’ rubber, sold under the trade-name 
‘soap rubber,”’ produce shearing planes in the form of pyramids 
exactly like those seen in cubes of sandstone in ordinary crushing 
tests, with apical angles of 50° or even less. This shows that the 
shearing angle is also independent of the absolute amount of defor- 
mation of which the substance is capable below the elastic limit. 
Strongly ductilet bodies, on the other hand, like soap, shear at 
very obtuse angles. 
t The writer knows that in this paper he is using the word “ductile” in a sense 
which is sure to be severely criticized. He would be delighted to see such criticism 
lead to a fruitful open discussion of the fundamental conceptions involved in the 
deformation of solids. At this place the restricted sense in which the word “‘ ductility” 
is used here may be defined best by giving it as one of several purely empirical charac- 
teristics of solids under deformation. 
Substances differ in 
1. The force required to produce the same absolute amount of deformation, 
(Small: rubber, wet clay; large: steel.) 
2. The absolute amount of deformation required to reach the elastic limit. 
(Small: steel, wet clay; large: rubber.) 
3. The percentage of any given deformation which remains permanent when the 
stress is removed. (o per cent=perfect elasticity; 1oo per cent=perfect plasticity.) 
4. The additional force required to produce an additional amount of permanent 
deformation (negative, zero, positive). 
5. The time required to produce the same absolute amount of permanent 
deformation without rupture. 
6. The position of the point of rupture with reference to the yield point. (Point 
of rupture <or> yield point.) 
In this paper a substance is called “brittle” when its point of rupture lies near 
its yield point. It is called “the more ductile” the farther beyond the yield point its 
point of rupture lies. In a “perfectly ductile” substance it lies an infinite distance 
beyond. Ina “perfectly brittle” substance it is reached before the yield point. 
