The explanation most generally accepted seems to be, that, of the three allotropic forms of iron the gamma and beta varieties are very much harder than alpha iron, which is the one which we have in annealed steel at ordinary temperatures, and, of the two, the beta is harder than the gamma variety. It is thought also, that carbon, perhaps as carbide of iron, is held in solution in gamma or beta iron after the quenching, and increases the hardness proportionately with increase of the carbon content of the steel. While this carbon or iron-carbide solid solution may and probably does itself confer additional hardness to the steel, its main function is to retard or slow down the change from gamma into beta and alpha iron, which change in carbonless iron and low carbon steels is so insistent and extremely rapid that not even the most severe quenching, as in ice-water or liquid air, can prevent or stop it. Not only do we fail to get austenite, which is gamma iron, until we get 1% or more of carbon present and quench from very high to very low temperatures, but we cannot even stop the transition at beta iron, the next lower allotropic variety until we have at least .30% of carbon, and, for serviceable hardening fully .60% of carbon in the steel. Fortunately for us, this beta form of iron is the one we want, for it is harder and more useful than the gamma form. Our most serviceable constituent, martensite, then, is a solid solution of carbon or iron carbide in beta iron. It is magnetic but this probably results from its containing some alpha iron through incomplete stoppage of the change by the quenching. As has been stated, “tempering,” which means careful reheating to 400° F., 500° F., or 600° F., allows the slight “slipping” of enough of the beta solution, always eager at temperatures below the point of recalescence to return to alpha condition, to relieve the excessive brittleness of the hardened steel. [Illustration: No. 72. THE “SORBITE” GRAIN IS PRODUCED BY COOLING IN A BLAST OF AIR AFTER ANNEALING. IT GIVES GOOD WEARING PROPERTIES (_Magnification 70 Diameters_) ] Annealing is the complete release of beta iron and the “trapped” carbon which allows of their return to the normal condition of pearlite with alpha iron. To accomplish this, the hardened steel has to be heated above its point of recalescence and cooled more or less slowly. Different speeds of cooling give different grain size, structures and physical properties. This explanation of hardening, which is known as the “allotropic” theory, is not universally accepted, conclusive evidence being lacking at more than one point. It must be stated also that some who hold the “allotropic theory” of hardening doubt the existence of beta iron. These contend that the so-called beta iron and martensite are only decomposition or transition forms of gamma iron and austenite.