§ XV. The second group of traceries, the intersectional or German group, may be considered as including the entire range of the absurd forms which were invented in order to display dexterity in stone-cutting and ingenuity in construction. They express the peculiar character of the German mind, which cuts the frame of every truth joint from joint, in order to prove the edge of its instruments; and, in all cases, prefers a new or a strange thought to a good one, and a subtle thought to a useful one. The point and value of the German tracery consists principally in turning the features of good traceries upside down, and cutting them in two where they are properly continuous. To destroy at once foundation and membership, and suspend everything in the air, keeping out of sight, as far as possible, the evidences of a beginning and the probabilities of an end, are the main objects of German architecture, as of modern German divinity. § XVI. This school has, however, at least the merit of ingenuity. Not so the English Perpendicular, though a very curious school also in _its_ way. In the course of the reasoning which led us to the determination of the perfect Gothic tracery, we were induced successively to reject certain methods of arrangement as weak, dangerous, or disagreeable. Collect all these together, and practise them at once, and you have the English Perpendicular. [Illustration: Fig. XLVI.] As thus. You find, in the first place (§ V.), that your tracery bars are to be subordinated, less to greater; so you take a group of, suppose, eight, which you make all exactly equal, giving you nine equal spaces in the window, as at A, Fig. XLVI. You found, in the second place (§ VII.), that there was no occasion for more than two cross bars; so you take at least four or five (also represented at A, Fig. XLVI.), also carefully equalised, and set at equal spaces. You found, in the third place (§ VIII.), that these bars were to be strengthened, in order to support the main piers; you will therefore cut the ends off the uppermost, and the fourth into three pieces (as also at A). In the fourth place, you found (§ IX.) that you were never to run a vertical bar into the arch head; so you run them all into it (as at B, Fig. XLVI.); and this last arrangement will be useful in two ways, for it will not only expose both the bars and the archivolt to an apparent probability of every species of dislocation at any moment, but it will provide you with two pleasing interstices at the flanks, in the shape of carving-knives, _a_, _b_, which, by throwing across the curves _c_, _d_, you may easily multiply into four; and these, as you can put nothing into their sharp tops, will afford you a more than usually rational excuse for a little bit of Germanism, in filling them with arches upside down, _e_, _f_. You will now have left at your disposal two and forty similar interstices, which, for the sake of variety, you will proceed to fill with two and forty