Special apparatus is now obtainable for determination of critical points, heating and cooling curves. Now if on properly spaced, dotted, vertical lines, which we will let represent these various alloys, we mark points number three, two and one as shown by our “cooling” curves, calling the topmost point three, it is readily seen that the points are related. The lines and the alloys which they represent are, (a) The wrought iron, (b) .15% carbon steel, (c) .30% carbon steel, (d) .45% carbon steel, (e) .60% carbon steel, (f) .75% carbon steel, and (g) the steel with .90% carbon. [Illustration: CRITICAL POINT DIAGRAM OF PURE IRON AND THE STEELS ] Of course many more cooling curves, especially of steels with other percentages of carbon would be desirable, but we have enough that we are safe in sketching the horizontal and oblique lines, Ar_{1}, Ar_{2}, Ar_{3}, Ar_{3·2} and Ar_{3·2·1}, through the points which we have arranged. For convenience, metallurgists everywhere mark these points Ar_{1}, Ar_{2} and Ar_{3}, the first being the lower, and Ar_{3} the upper one. Ar_{cm} represents an upper point found in steels having more than .9% of carbon. The letter “r” is derived from the French word, “refroidissement,” meaning “cooling.” The corresponding points disclosed during heating are marked Ac_{1}, Ac_{2}, Ac_{3·2·1}, etc., from the word, “chauffage” meaning “heating.” The “A” apparently “just happened.” Before the upper critical points were known it had been used by Tschernoff to designate the temperature at which steels harden. But it must not be supposed that the skeleton which we have constructed can be fully accepted as true until it has been checked and rechecked hundreds and hundreds of times by other investigators. A great many have worked upon these critical points and upon the “freezing-point” curves of the various alloys. It was of course impossible for all of them to make their determinations in just the same manner and with exactly the same materials. Examination of their work and consideration of the results which they obtained show some discrepancies as might be expected, largely probably because of difference in purity of the materials tested, every impurity such as manganese, nickel, silicon, sulphur, phosphorus, etc., modifying more or less the results obtained. As we discovered, speed of heating and cooling also modify the results. When we consider the difficulties which attend the making of determinations on metals and alloys at high temperatures, the wonder is that there is such close agreement. From these standpoints the differences which exist in the published results seem quite small.