An instance of a mineral with tetrahedral _molécules intégrantes_ Haüy gives in tourmaline, and the primitive form of tourmaline he considered to be a rhombohedron, conformably to the well-known rhombohedral cleavage of the mineral, made up of six tetrahedra. Again, hexagonal structures formed by three prismatic cleavage planes inclined at 60° are considered by him as being composed of _molécules intégrantes_ of the form of 60° triangular prisms, or _molécules soustractives_ of the shape of 120° rhombic prisms, each of the latter being formed by two _molécules intégrantes_ situated base to base. This will be clear from Figs. 13 and 14, the former representing the structure as made up of equilateral prismatic structural units, and the latter portraying the same structure but composed of 120°-parallelepipeda by elimination of one cleavage direction; each unit in the latter case possesses double the volume of the triangular one, and being of parallelepipedal section is capable of producing secondary faces when arranged step-wise, whereas the triangular structure is not. The points at the intersections in these diagrams should for the present be disregarded; they will shortly be referred to for another purpose. [Illustration: FIG. 14. ] Probably, the most permanent and important of Haüy’s achievements was the discovery of the law of rational indices. At first this only took the form of the observation of the very limited number of rows of _molécules intégrantes_ or _soustractives_ suppressed. In introducing it on page 74 of his 1784 “Essai” he says: “_Quoique je n’aie observé jusqu’ici que des décroissemens qui se sont par des soutractions d’une ou de deux rangées de molécules, et quelquefois de trois rangées, mais très rarement, il est possible qu’il se trouve des crystaux dans lesquels il y ait quatre ou cinq rangées de molécules supprimées à chaque décroissement, et même un plus grand nombre encore. Mais ces cas me semblent devoir être plus rares, à proportion que le nombre des rangées soutraites sera plus considérable. On conçoit donc comment le nombre des formes secondaires est néçessairement limité._” The essential difference between Haüy’s views and our present ones, which will be explained in Chapter IX., is that Haüy takes cleavage absolutely as his guide, and considers the particles, into which the ultimate operation of cleavage divides a crystal, as the solid structural units of the crystal, the unit thus having the shape of at least the _molécule intégrante_. Now every crystalline substance does not develop cleavage, and others only develop it along a single plane, or along a couple of planes parallel to the same direction, that of their intersection and of the axis of the prism which two such cleavages would produce, and which prism would be of unlimited length, being unclosed.