The system of Hauey, however, was highly artificial, and only prepared the way for a simpler and more general expression of the facts. The German crystallographer, Weiss, seems to be the first to have recognized the truth that the decrements of Hauey were merely a mechanical mode of representing the fact that all the secondary faces of a crystal make intercepts on the edges of the primitive form which are simple multiples of each other; and, this general conception once gained, it was soon seen that these ratios could be as simply measured on the axes of symmetry of the crystal as on the edges of the fundamental forms; and, moreover, that, when crystal forms are viewed in their relation to these axes, a more general law becomes evident, and the artificial distinction between primary and secondary forms disappears. Thus became slowly evolved the conception of a crystal as a group of similar planes symmetrically disposed around certain definite and obvious systems of axes, and so placed that the intercepts, or parameters, on these axes bore to each other a simple numerical ratio. Representing by _a_:_b_:_c_ the ratio of the intercepts of a plane on the three axes of a crystal of a given substance, then the intercepts of every other plane of this, or of any other crystal of the same substance, conform to the general proportion _m_._a_:_n_._b_:_p_._c_, in which _m_, _n_, _p_ are three simple whole numbers. This simple notation, devised by Weiss, expressed the fundamental law of crystallography; and the conception of a crystal as a system of planes, symmetrically distributed according to this law, was a great advance beyond the decrements of Hauey, an advance not unlike that of astronomy from the system of vortices to the law of gravitation. Yet, as the mechanism of vortices was a natural prelude to the law of Newton, so the decrements of Hauey prepared the way for the wider views of the German crystallographers.