volume may be taken to represent the unit weight. The surfaces
that are considered in this instance are the top and base of the
section, as these surfaces are the ones exposed to cooling."

The results of the calculations are as follows:

TABLE 20.--SPHERE

Diameter Surface per
of sphere pound of steel
_X_ _Y_
8 in. 2.648 sq. in.
6 in. 3.531 sq. in.
4 in. 5.294 sq. in.
3 in. 7.062 sq. in.
2 in. 10.61 sq. in.
_XY_ = 21.185.

TABLE 21.--ROUND

Diameter Surface per
of round pound of steel
_X_ _Y_
8.0 in. 1.765 sq. in.
6.0 in. 2.354 sq. in.
5.0 in. 2.829 sq. in.
4.0 in. 3.531 sq. in.
3.0 in. 4.708 sq. in.
2.0 in. 7.062 sq. in.
1.0 in. 14.125 sq. in.
0.5 in. 28.25 sq. in.
0.25 in. 56.5 sq. in.
_XY_ = 14.124.

TABLE 22.--FLAT

Thickness Surface per
of flat pound of steel
_X_ _Y_
8.0 in. 0.8828 sq. in.
6.0 in. 1.177 sq. in.
5.0 in. 1.412 sq. in.
4.0 in. 1.765 sq. in.
3.0 in. 2.345 sq. in.
2.0 in. 3.531 sq. in.
1.0 in. 7.062 sq. in.
0.5 in. 14.124 sq. in.
0.25 in. 28.248 sq. in.
_XY_ = 7.062.

Having once determined the physical qualities of a certain specimen,
and found its position on the curve we have the means to predict the
decrease of physical qualities on larger specimens which receive
the same heat treatment.

When the surfaces of the unit weight as outlined in the foregoing
tables are plotted as ordinates and the corresponding diameters as
abscissae, the resulting curve is a hyperbola and follows the law
_XY = C_. In making these calculations the radii or one-half of
the thickness need only to be taken into consideration as the heat
is conducted from the center of the body to the surface, following
the shortest path.

The equations for the different shapes are as follows:

For flats _XY_ = 7.062
For rounds _XY_ = 14.124
For spheres _XY_ = 21.185

It will be noted that the constants increase in a ratio of 1, 2,
and 3, and the three bodies in question will increase in hardness
on being quenched in the same ratio, it being understood that the
diameter of the sphere and round and thickness of the flat are
equal.

Relative to shape, it is interesting to note that rounds, squares,
octagons and other three a