TABLE 21.—ROUND
Diameter
of round		 Surface per
pound of steel
XY
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
Diameter
of flat		 Surface per
pound of steel
XY
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 abscissæ, 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 flatsXY = 7.062
For roundsXY = 14.124
For spheresXY = 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 axial bodies, with two of their axes equal, have the same surface for the unit weight.

For example:

SizeLengthSurfaceWeightSurface for 1 lb.
2 in. Sq.12 in.96.0 sq. in.13.60 lb.7.06 sq. in.
2 in. Round12 in.75.4 sq. in.10.68 lb.7.06 sq. in.