Various attempts have been made to ascertain the relationship (if any) between the refractoriness of clays and their chemical composition. If attention is confined strictly to the more refractory clays, some kind of relationship does appear to exist. Thus Richter found that the refractoriness of clay is influenced by certain oxides in the following order: magnesia, lime, ferrous oxide, soda and potash, but this only applies to clays containing less than 3 per cent. of all these oxides. Cramer, in 1895, found that free silica also interfered with the action of these oxides and more recently Ludwig (9) has devised a chart (fig. 7), on the upright sides of which are plotted the equivalents of the lime, magnesia and alkalies, whilst the silica equivalents are plotted on the horizontal base. In each case the 'molecular formula' of the clay is calculated from its percentage composition, and this 'formula' is reduced so as to have one 'molecule' of alumina, thereby fixing the alumina as a constant and reducing the number of variables to two--the metallic oxides and the silica. Unfortunately Ludwig's chart is only applicable to the more refractory clays and cannot be relied upon even for these, though it is extremely useful for comparing clays from identical or similar geological formations. [Illustration: Fig. 7. Ludwig's Chart.] Attempts to express the refractoriness of clays by means of formulae proving abortive, there only remains the direct test of heating a clay under definite conditions in the manner previously described. _Vitrification_ is closely connected with the fusibility and refractoriness of clays, and, as a term, indicates the amount of fusion which has occurred under certain conditions of heating. As already mentioned, all clays, on being subjected to a high temperature, undergo partial fusion, the more powerful bases attacking the finest particles of clay and silica, forming molten silicates, and then slowly attacking the more refractory portion; this slow fusion and solution continues until the whole of the material is melted. If the heating is stopped before the fusion has begun, the clay will be porous and comparatively soft, but as more and more material fuses, the mass (on cooling) becomes harder and less porous, as the fused material occupies the pores and sets to a dense, firm glassy mass. The amount of vitrification, or partial fusion, which occurs is, therefore, of great importance in some industries, as by stopping it at an appropriate stage articles of any desired degree of porosity, translucency or strength may be obtained. Thus for common bricks, only sufficient vitrification is permitted to bind the particles firmly together, but in engineering bricks--where much greater strength is required--the vitrification is more complete. Porcelain and earthenware may be similarly distinguished.