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 axial bodies, with two of their axes equal, have the same surface for the unit weight. For example: Size Length Surface Weight Surface for 1 lb. 2 in. Sq. 12 in. 96.0 sq. in. 13.60 lb. 7.06 sq. in. 2 in. Round 12 in. 75.4 sq. in. 10.68 lb. 7.06 sq. in. Although this discussion is at present based upon mathematical analysis, it is hoped that it will open up a new field of investigation in which but little work has been done, and may assist in settling the as yet unsolved question of the effect of size and shape in the heat treatment of steel. HEAT-TREATING EQUIPMENT AND METHODS FOR MASS PRODUCTION The heat-treating department of the Brown-Lipe-Chapin Company, Syracuse, N. Y., runs day and night, and besides handling all the hardening of tools, parts of jigs, fixtures, special machines and appliances, carburizes and heat-treats every month between 150,000 and 200,000 gears, pinions, crosses and other components entering into the construction of differentials for automobiles. The treatment of the steel really begins in the mill, where the steel is made to conform to a specific formula. On the arrival of the rough forgings at the Brown-Lipe-Chapin factory, the first of a long series of inspections begins.