(8) There is also the substance D', which is never found in contact with the liquid. The substance D' is pure at the point D', where we believe it to be the compound Cu 4 Sn. This phase will be considered somewhat later.
The relations of the first seven phases can best be stated by con- sidering the solidus (or, as we are inclined to call it, the melting- point curve). The solidus is a broken line consisting of the branches Ab, Icdef, E 2 E 3 , and H'H".
The solidus and the liquidus (or freezing-point curve) are so related that if we draw a horizontal, that is, an isothermal line, cutting the solidus and liquidus, the points of intersection give the percentage compositions of the solid and liquid that can exist in equilibrium at the given temperature. To take an example, the isothermal at 900 C. cuts the lines Ab and ABLC in points which correspond respectively to a uniform solid containing 3 atomic per cents, of tin, and a liquid containing 11 atomic per cents. These two would be in equilibrium, for when the liquid was cooled it would begin to deposit the solid, and when the solid was heated it would begin to melt and form the liquid.
Whenever a branch of the solidus is sloping, as Ab, or curved, as Icdef, the solid phase is one of a series of mixed crystals. On the other hand, when a branch of the solidus is vertical, as we have drawn EoEs and H'H", one can infer that mixed crystals are not formed. It is possible that we are wrong in drawing E^Es and H'H" quite vertical ; the phase E' may here consist of Cu 3 Sn having some H in solid solution, and the phase H may also contain some Cu 3 Sn or tin in solid solution, in which cases the solidus would not be a vertical straight line. But we have several reasons, some of which will be stated later, for thinking that the mutual solubility of these bodies is not great.
The angle C of the liquidus indicates that the composition of the solid phase changes abruptly at this temperature, for while the branch ABC corresponds to the solidus Ab, the branch CD corresponds to the solidus Ic. The angle C was a great stumbling-block to us so long as we only examined alloys that had not been chilled, but Roozeboom's theory explains in the most perfect manner all the phenomena at this angle. It tells us that just above the temperature C the cooling saturated liquid deposits, and is in equilibrium with, the a mixed crystal whose composition is given by the point b, while just below the temperature C the liquid forms (3 mixed crystals, much richer in tin and given in composition by the point /. Thus, as the saturated liquid cools through the temperature C an isothermal transformation a + liquid = ft takes place. The heat evolved by this reaction is well marked in the cooling curves. No uniform mixed crystals of per- centages between b and I can exist. The angle D probably indicates
