§ IX. These then being the two primal groups, we have next to note the combined group, formed by the concave and convex lines joined in various proportions of curvature, so as to form together the reversed or ogee curve, represented in one of its most beautiful states by the glacier line _a_, on Plate VII. I would rather have taken this line than any other to have formed my third group of cornices by, but as it is too large, and almost too delicate, we will take instead that of the Matterhorn side, _e f_, Plate VII. For uniformity's sake I keep the slope of the dotted line the same as in the primal forms; and applying this Matterhorn curve in its four relative positions to that line, I have the types of the four cornices or capitals of the third family, _e_, _f_, _g_, _h_, on Plate XV. These are, however, general types only thus far, that their line is composed of one short and one long curve, and that they represent the four conditions of treatment of every such line; namely, the longest curve concave in _e_ and _f_, and convex in _g_ and _h_; and the point of contrary flexure set high in _e_ and _g_, and low in _f_ and _h_. The relative depth of the arcs, or nature of their curvature, cannot be taken into consideration without a complexity of system which my space does not admit. Of the four types thus constituted, _e_ and _f_ are of great importance; the other two are rarely used, having an appearance of weakness in consequence of the shortest curve being concave: the profiles _e_ and _f_, when used for cornices, have usually a fuller sweep and somewhat greater equality between the branches of the curve; but those here given are better representatives of the structure applicable to capitals and cornices indifferently.