§ X. Look back to Fig. XXIX. Evidently the abstract or ghost line of the arrangement at A is a plain horizontal line, as here at _a_, Fig. XXX. The abstract line of the arrangement at B, Fig. XXIX., is composed of two straight lines, set against each other, as here at _b_. The abstract line of C, Fig. XXIX., is a curve of some kind, not at present determined, suppose _c_, Fig. XXX. Then, as _b_ is two of the straight lines at _a_, set up against each other, we may conceive an arrangement, _d_, made up of two of the curved lines at _c_, set against each other. This is called a pointed arch, which is a contradiction in terms: it ought to be called a curved gable; but it must keep the name it has got. Now _a_, _b_, _c_, _d_, Fig. XXX., are the ghosts of the lintel, the gable, the arch, and the pointed arch. With the poor lintel ghost we need trouble ourselves no farther; there are no changes in him: but there is much variety in the other three, and the method of their variety will be best discerned by studying _b_ and _d_, as subordinate to and connected with the simple arch at _c_. § XI. Many architects, especially the worst, have been very curious in designing out of the way arches,--elliptical arches, and four-centred arches, so called, and other singularities. The good architects have generally been content, and we for the present will be so, with God's arch, the arch of the rainbow and of the apparent heaven, and which the sun shapes for us as it sets and rises. Let us watch the sun for a moment as it climbs: when it is a quarter up, it will give us the arch _a_, Fig. XXXI.; when it is half up, _b_, and when three quarters up, _c_. There will be an infinite number of arches between these, but we will take these as sufficient representatives of all. Then _a_ is the low arch, _b_ the central or pure arch, _c_ the high arch, and the rays of the sun would have drawn for us their voussoirs. § XII. We will take these several arches successively, and fixing the top of each accurately, draw two right lines thence to its base, _d_, _e_, _f_, Fig. XXXI. Then these lines give us the relative gables of each of the arches; _d_ is the Italian or southern gable, _e_ the central gable, _f_ the Gothic gable. [Illustration: Fig. XXXI.] § XIII. We will again take the three arches with their gables in succession, and on each of the sides of the gable, between it and the arch, we will describe another arch, as at _g_, _h_, _i_. Then the curves so described give the pointed arches belonging to each of the round arches; _g_, the flat pointed arch, _h_, the central pointed arch, and _i_, the lancet pointed arch.