The Millerian symbol of a face is always placed within ordinary curved brackets ( ), but if the symbol is to stand for the whole set of faces composing the form, the brackets are of the type { }. Thus the Millerian symbol of the fourth face (that in the top-right front octant), determinative of the unit axial lengths, is (111), as shown in Fig. 46, the face in question being marked with this symbol; while the symbol {111} indicates the set of faces of the whole or such part of the double pyramid as composes the unit form. In the triclinic system this form only consists of the face (111) and the parallel one (̄1̄1̄1), but in the case of the regular octahedron of the cubic system it embraces all the eight faces. The triclinic octahedron, Fig. 46, is thus made up of four forms of two faces each. A negative sign over an index indicates interception on the axis _a_ behind the centre, on the axis _b_ to the left of the centre, or on the vertical axis _c_ below the centre. To take an actual example, suppose a face other than the primary one to make the intercepts on the axes 4, 2, 1; in this case _h_ = _a_/4, _k_ = _b_/2, and _l_ = _c_/1, that is, when referred to the fundamental primary form for which _a_, _b_, _c_ are each unity, _h_ = ¼, _k_ = ½, _l_ = 1, or, bringing them to whole numbers by multiplying by 4, _h_ = 1, _k_ = 2, _c_ = 4, and the symbol in Millerian notation is (124). Again, suppose we wish to find the intercepts on the three cubic axes made by the face (321) of the hexakis octahedron shown in Fig. 21. To get each intercept we multiply together the two other Millerian indices, and if necessary afterwards reduce the three figures obtained to their simplest relative values. For the face (321) we obtain 2, 3, 6. This means that the face (321) in the top-right-front octant of the hexakis octahedron cuts off two unit lengths of axis _a_, three unit lengths of axis _b_, and six unit lengths of axis _c_. No fractional parts thus ever enter into the relations of the axial lengths intercepted by any face on a crystal, and the whole numbers representing these relations are always small, the number 6 being the usual limit. This important law is known as the “Law of Rational Indices,” and is the corner-stone of crystallography. A forecast of it was given in Chapter III., in describing how it was first discovered by Haüy, and it was shown how impressed Haüy was with its obvious significance as an indication of the brick-like nature of the crystal structure. What the “bricks” were, Haüy was not in a position to ascertain with certainty, as chemistry was in its infancy, and Dalton’s atomic theory had not then been proposed.