GENERAL MEETING. vcd | 
moment of rupture will be equal to twice the tangent of a. In 
other words 2 tan «@ represents the limit of tension, and will be con- 
stant for any given substance. 
As the conductivity of a cooling body is not directly proportional 
to the degree of radiation from its surface, the difference between 
the contraction of successive layers of a rapidly cooling mass will be 
greater than between those of one cooling less rapidly, and what 
may be styled the angle of contraction will be greater in the former 
case than in the latter. And if we assume a certain rate of cooling 
to have caused a single rupture in a given extent of mass (repre- 
sented in fig. 1), then a greater rate of cooling, which would pro- 
duce in the same extent of mass a contraction represented by a 
n 6 
?tan a 
If the forces producing contraction are unequally distributed over 
the surface a 6, figure 2, being a maximum at ¢, the maximum 
greater angle, ?, will cause as many ruptures as the ratio 
Fig. é. 
strain at the beginning will be in the direction of the surface, and 
the cracks will start normal to it; but their progress inward will 
no longer be uniform. At the end of a given time the limit of ten- 
sion reached by a greater force, at f, will be farther from the sur- 
face than that reached by a less force, at g, and the line of maxi- 
mum strain in this portion of the mass will be 9’ f’, to which the 
crack of parting will be normal. At the end of another given time 
the direction of the crack will be again changed, and the same 
action taking place in the other parts of the mass will result in a 
system of diverging cracks. 
So far we have considered the shrinkage in one direction in one 
plane only, that is, parallel to the cooling surface in a plane at right 
angles to it. But a homogeneous mass contracts equally in all 
