The size of the piece influences the physical properties obtained in steel by heat treatment. This has been worked out by E. J. Janitzky, metallurgical engineer of the Illinois Steel Company, as follows: [Illustration: FIG. 55.--Effect of size on heating.] "With an increase in the mass of steel there is a corresponding decrease in both the minimum surface hardness and depth hardness, when quenched from the same temperature, under identical conditions of the quenching medium. In other words, the physical properties obtained are a function of the surface of the metal quenched for a given mass of steel. Keeping this primary assumption in mind, it is possible to predict what physical properties may be developed in heat treating by calculating the surface per unit mass for different shapes and sizes. It may be pointed out that the figures and chart that follow are not results of actual tests, but are derived by calculation. They indicate the mathematical relation, which, based on the fact that the physical properties of steel are determined not alone by the rate which heat is lost per unit of surface, but by the rate which heat is lost per unit of weight in relation to the surface exposed for that unit. The unit of weight has for the different shaped bodies and their sizes a certain surface which determines their physical properties. "For example, the surface corresponding to 1 lb. of steel has been computed for spheres, rounds and flats. For the sphere with a unit weight of 1 lb. the portion is a cone with the apex at the center of the sphere and the base the curved surface of the sphere (surface exposed to quenching). For rounds, a unit weight of 1 lb. may be taken as a disk or cylinder, the base and top surfaces naturally do not enter into calculation. For a flat, a prismatic or cylindrical 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