The immediate origin of the present paper lay in a suggestion of the late Sir G. G. Stokes, made early in 1900, that we should attempt the microscopic examination of a few bronzes as an aid to the interpretation of the singularities of the freezing-point curve. This curve was at the time fairly accurately known, largely through the researches of the late Sir W. Roberts-Austen and Dr. Stansfield, published in 1895 and in 1897, and partly by our own work. Microscopic studies of the alloys had been also published by Dr. Charpy and by Mr. Stead, but, so far as we are aware, no attempt had been made to correlate the two lines of research, and the exact nature of this group of alloys remained very obscure. The ingots of alloy which we studied at first had been allowed to cool somewhat slowly and spontaneously in the furnace, so that there had been no sudden chill or alteration in the rate of cooling. Polished and etched sections of these ingots were found to contain very varied and complicated patterns that sometimes appeared to have no connection with the singularities of the freezing-point curve. For example, a tin-rich crystallisation which appeared to be primary, was found to increase to a maximum amount as we descended a branch of the curve, and in more than one region undeniable primary crystals which stood out in relief on the outside of the ingots were found, when polished half-through, to be full of smaller and quite different crystals. In fact, it became evident that the final patterns we were examining were of the nature of a palimpsest in which several different records were superposed, some of these being due to recrystallisations that had taken place after solidification. Two other considerations pointed to the same conclusion, the first was derived from the very valuable cooling curves, published by Roberts-Austen and Stansfield in 1895, which revealed the fact that far below the temperature of solidification considerable evolutions of heat occurred in the alloys as they cooled. The second was derived from Professor Poozeboom’s paper on the “Solidification of Mixed Crystals of Two Substances,” published in the ‘Zeitschrift für Physikalische Chemie,’ of December, 1899. These two researches have been respectively the experimental and the theoretical basis from which the present work has grown, and the possibilities of interpretation which they promised have induced us to make a much more serious study of the bronzes than we originally intended.