§ X. Very often, in the farther treatment of the profiles _e_ or _f_, another limb is added to their curve in order to join it to the upper or lower members of the cornice or capital. I do not consider this addition as forming another family of cornices, because the leading and effective part of the curve is in these, as in the others, the single ogee; and the added bend is merely a less abrupt termination of it above or below: still this group is of so great importance in the richer kinds of ornamentation that we must have it sufficiently represented. We shall obtain a type of it by merely continuing the line of the Matterhorn side, of which before we took only a fragment. The entire line _e_ to _g_ on Plate VII., is evidently composed of three curves of unequal lengths, which if we call the shortest 1, the intermediate one 2, and the longest 3, are there arranged in the order 1, 3, 2, counting upwards. But evidently we might also have had the arrangements 1, 2, 3, and 2, 1, 3, giving us three distinct lines, altogether independent of position, which being applied to one general dotted slope will each give four cornices, or twelve altogether. Of these the six most important are those which have the shortest curve convex: they are given in light relief from _k_ to _p_, Plate XV., and, by turning the page upside down, the other six will be seen in dark relief, only the little upright bits of shadow at the bottom are not to be considered as parts of them, being only admitted in order to give the complete profile of the more important cornices in light. § XI. In these types, as in _e_ and _f_, the only general condition is, that their line shall be composed of three curves of different lengths and different arrangements (the depth of arcs and radius of curvatures being unconsidered). They are arranged in three couples, each couple being two positions of the same entire line; so that numbering the component curves in order of magnitude and counting upwards, they will read-- _k_ 1, 2, 3, _l_ 3, 2, 1, _m_ 1, 3, 2, _n_ 2, 3, 1, _o_ 2, 1, 3, _p_ 3, 1, 2. _m_ and _n_, which are the _Matterhorn line_, are the most beautiful and important of all the twelve; _k_ and _l_ the next; _o_ and _p_ are used only for certain conditions of flower carving on the surface. The reverses (dark) of _k_ and _l_ are also of considerable service; the other four hardly ever used in good work.