Such changes seem to indicate what are known as “allotropic” modifications. More familiar examples of allotropic forms of materials may be mentioned. Phosphorus, for example, may exist, either as the “yellow” variety which is poisonous and so inflammable that it must be kept constantly under water, or as the “red” variety which is non-poisonous and non-inflammable. Too, there is carbon, which may exist in any one of several forms such as amorphous carbon (soot), graphite, and the diamond. It is believed that iron, itself, exists in three allotropic states. These have been named “alpha,” “beta” and “gamma” iron. We do not need to go into this part of the great subject except to state that at ordinary temperatures and up to Ar_{2}, we have alpha iron, between Ar_{2} and Ar_{3}, beta iron, and above Ar_{3}, gamma iron. Both beta and gamma iron are non-magnetic, while alpha iron is strongly magnetic. In cooling through Ar_{3}, i.e., from gamma to beta iron, some rearrangement of its molecules produces the dilatation or expansion and the change in conductivity which was noted above. From the fact that by chemical analysis any certain steel must have the same composition in its hardened that it has in its unhardened condition, it will readily be seen how futile it would be to expect chemical analysis to give us complete information regarding it. Too, tensile strength and the other usual physical tests can hardly tell us all that we wish to know. Microscopic analysis or metallography, however, shows us internal structure of properly prepared pieces of either the hardened or unhardened alloy that we may see the actual condition or grouping of the constituents. The view points given by all three of these methods, chemical, physical and metallographical, are, of course, much better than any one or two alone. The Structures of Quenched and Unquenched Steel We saw that the lag or tardiness is greater the more rapid the cooling. Along with this very great lag which is brought about by very rapid cooling comes increasing slowness, i.e., less ability to catch up, as the temperature is lowered. Hence quenching produces such a wide lag and so slows the changes which should take place that they do not take place at all, i.e., the structure which the piece had at the higher temperatures cannot change but is set or fastened by the quickness of the cooling. Though no degree of suddenness is sufficient to set completely the structure existing at very high temperatures, for our present purposes we can say that by quenching in cold water we can freeze or fix any structure. Then after we have quenched a piece of steel, it will have when cold, the structure which corresponded with or resulted from the temperature which it had at the moment before the quenching. If so, the microscope should give us aid. [Illustration: ILLUMINATION OF THE SAMPLE UNDER THE MICROSCOPE ]