**ABC—XYZ**

MEDI/EVAL WORK.] BUILDING 475 thereto, make CE equal to A1, join IE, bisect the same, and proceed as before. The points FG, as has before been explained, arc the points where the circles will meet each other. The joints to these arches will all radiate to their respective centres. Specimens of various sorts of the tracery which adorn the windows of the mediaeval periods, and are in fact their greatest glory, are shown in Plates XVIII., XIX., and XX. of vol. ii. The designs for tracery are almost in finite, and the various methods of setting them out would fill a volume. But although they display such ingenuity and fancy that one would think the design to be quite arbitrary, it will be found that they are all, or very nearly all, set out on the principle of geometrical intersections. An example will show the principles on which the mediaeval architects proceeded to describe the tracery, and also the method of finding the joints of the various pieces of stone. Let a b (fig. 27) be the opening of the arch ; as there are to be two mullions^ divide the same into three equal parts, as ac,cd,db; then determine the points from which to strike the arch. In this instance, for the sake of simplicity, we make it equilateral (as in fig. 24) ; a and b then are the centres for striking the main a cod FIG. 27. Construction of Window Tracery. arch a eg, bfg, and the height og is that of an equilateral triangle. Produce the springing line, and the same opening of the compasses through c and d will give the principal inner branches of the tracery c e, df. From the centre o, with an opening extend ing to the middle of the lights ac, db, strike a semicircle ; raise perpendiculars from d and c to 1 and 2 ; draw a line through 1 and 2 ; on this and the springing line will be found the centres of the lower ogees ; bisect the part of g o cut off by 1 2 in 7i, which is in fact the same thing as dividing the whole height o cj into three ; divide h g into three parts, at 3 and 4 ; through 3 drav a horizon tal line, and set off from 3 distances one-third of the width od, or draw the perpendicular lines as shown, which is better ; then 5 and 6 will be the centres of the upper quatrc-foil. From the line 1 2, on the same perpendicular as last, set down similar points, as at 7. These will be the centres for the lower subdivision as shown. Next draw c hf and subdivide by similar perpendicu lars, and where the lines intersect, as at 8, will be the centres for the upper subdivisions. The lines thus drawn will form a species of skeleton diagram, as shown on the right side of fig. 27, which is called the clement of tJie tracery, and is in fact the centre line of the roullion, as shown by a, fig. 28. On each side of this, using always the same centres for the same branches, draw lines, showing the face (or what the workmen call the nose) of the mullion, and answering to b c ; and then others answering to the sides of the mullion, as d e. Any other mould ings upon their sides or faces maybe drawn in like manner. Put in the cusping as shown, and the tracery is complete. The practical p IG 23 Mullion stone-mason will take care never to make a joint where there is an angle of any sort, as the point of a cusp. In all eases the joints must tend to the centres of the circles from which they are struck, and where the lines branch off in two direc tions, the joints must not be in one line, but must tend in two, or as many directions as there arc branches, and each to the centre of such respective branch. When the lines are perpendicular, as at c and d, and at the joint below h, the joints are horizontal. A close inspection of fig. 27, where they are carefully drawn, will fully elucidate the matter. The elaborate west window at York Cathedral (see Plate XV 11 1. of vol ii.) is entirely set out on this principle ; and so is the still more remarkable instance, the eastern window at Carlisle, which is composed of 86 pieces of stone, and the design for which is drawn from 263 centres. All the upper construction of windows and doors, and of aisle arches, should be protected from superincumbent pressure by strong relieving arches above the labels, as shown by the dark tints in fig. 27, which should be worked in with the ordinary masonry of the walls, and so set that the weight above should not press on the fair work, in which case the joints of the tracery, &c., will sometimes flush or break out. In mediaeval vaults the crowns a b, c d, are not level, Mediaeval but all have a slight curve or spring, as shown in fig. 29, vaulting, and the filling-in between them also is slightly curved, so as to partake in some degree of the character of the dome as well as of the groined arch ; and for the most part the ribs in early vaulting are not true segments of ellipses, but approximations drawn by the compasses. The FlG - 29. Mediaeval Vaulting. triumph of mediaeval stone-masonry, however, is that species of groin known as fan-vaulting. It is unlike that of any other age or time. The roofs of King s College Chapel at Cambridge and of Henry VII. s Chapel at West minster are eminent and late examples. The earliest are supposed to be in the cloisters of Gloucester Cathedral. It is impossible in our limited space to give demonstrations of them, and we must refer our readers to the admirable treatise on the subject by Professor Willis, published in the first volume of the Transactions of the Eoyal Institute of British Architects. The filling-in between the ribs of mediaeval groins is generally of chinch, or of some soft stone, over which a layer of concrete is sometimes placed in such manner as to bind all together and to resist the thrust. The bold and beautiful termination to mediaeval towers, Spires, which we call a spire, and the French callJJeche, is another proof of the skill of the mediaeval masons. These are generally octagonal, and rise partly from the wall of the tower and partly from arches thrown angle-wise from wall to wall inside, to cut off the corners, as it were, and afford a springing to the spire. The wonder of these construc tions is their extreme lightness and thinness. The top of the spire at Salisbury is 411 feet from the ground, of which the tower takes up 207 feet, leaving, of course, 204 feet for the height of the spire itself; this is only 9 inches thick at the bottom, diminishing to 7 inches, or on an average only about the 300th part of its height. It has been attempted to show mathematically that the joints of a spire would be stronger if formed at right angles to its face ; but they would then slope inwards and hold the wet, which in sudden frosts would do most serious injury ; practically, therefore, it is found best to lay the courses on a level bed. They should, however, be frequently dowel i .1 and cramped together, but not with metal, for the extreme thinness of the stone would soon cause it to rust and break out the stone. The principal publications on masonry are as follows : English. Moxon, Mcchanick Exercises, 4to, 1677-93, 1700 ; Batty Langley, Ancient Masonry, fol., 1736 ; Nicholson, Practical

Builder, 4to, 1823, &c. ; Practical Treatise on Masonry, 8vo, 1828 ;