west, and the clear width between the plinths about two-thirds of that dimension, and this is the case with many examples.

The Section through the Nave of Winchester Cathedral is highly deserving of our attention: the clear width of the side aisles is 13 feet 1 inch, and that of the nave 32 feet 5 inches; the clear width of the building between the outer walls is 80 feet, the thickness of the walls 16 feet 10 inches, the projection of the buttress 6 feet, and the thickness of the piers 10 feet 8 inches, making for the entire width from north to south 102 feet 8 inches.

The width between the walls forms the base of an equilateral triangle, the apex of which determines the height of the vaulting of the nave; a semicircle struck upon this base, with a radius of 52 feet, determines the intrados of the arches of the flying buttresses on each side, which are admirably placed to resist the thrust opposed to them.

On this section we have endeavoured to apply the principles of Cesare Cesariano, before referred to, to the measurement of mass and void by a method far more simple than that usually adopted.

By covering the design with equilateral triangles we see the number occupied by the solids, and can draw a comparison with those that cover the voids: to prevent confusion in the diagram a portion only of three of the triangles has been subdivided, to show with what facility the quantities of the entire figure might be measured, if the several large equilaterals were subdivided throughout in a similar manner. The band which extends

from the face of the outer buttress to the centre of the section contains 36 small equilateral triangles, six of which cover the pier; consequently it occupies on the section one-sixth of that quantity; no further calculation is requisite to find the proportion it bears to the whole: in like manner the other parts of the section may be compared. Such was the use of equilateral triangles in the middle ages for ascertaining quantity.

The two equilateral triangles which occupy the nave and a portion of the piers are comprised within the figure called a Vesica Piscis; if the horizontal line drawn at half the height, uniting the base of the upper and lower triangles, be taken as a radius, and its extremities as centres, it will be evident that parts of circles may be struck, comprising the two triangles within them. Euclid has shown that a perpendicular may be raised or let fall from a given line by a similar method, the space between the segments being called afterwards a nimbus; and there can be no doubt that from time immemorial all builders have used it: the bee adopts for its honied cell a figure composed of six equilateral triangles, and this is proved to be the most economical method of construction; the sides of each hexagon are all common to two cells, and no space is lost by their junction. The nearer the boundary line of a figure approaches the circle, the more it will contain in proportion to it,

but circles could not be placed above and under each other, or side by side, without interstices occurring, and the equilateral triangle, or a figure compounded of it, is the only form that will admit of it being so arranged.

The interior and exterior division of the choir at Winchester exhibits two styles; the latter is a fine example of the decorated elegance to which architecture had arrived at the coinmencement of the sixteenth century.

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King's College Chapel, Cambridge, has no side aisles, but in lieu of them are small chapels between the buttresses, which are not interrupted in their depth, their whole strength being requisite to maintain in equilibrio the highly wrought stone vault; this they have hitherto perfectly done, to the admiration of all who have studied its principles of construction. The chapel is divided in its length into twelve equal divisions or severies, each of which is formed of four quadrants of a concave parabolic conoid standing on their apex, and is bounded by a main rib or arch of masonry which has its abutments secured by the weighty buttresses added to the outer walls. The width of each severy from centre to centre is 24 feet, the thickness of the buttresses being 3 feet 7 inches, and the length of the chapel between them 20 feet 6 inches; their depth is 13 feet 6 inches in the clear.

The transverse section shows more particularly the proportion of mass and void, which are here equal: the total extent or width from the face of one buttress to that of the other is 84 feet, and the clear width 42 feet; the height from the pavement to the top of the stone vault is 80 feet 1 inch, though this varies from the pavement being out of the level; the thickness of the walls at top is 5 feet 7 inches; in it is a gallery 2 feet 11 inch wide, and 7 feet high, communicating entirely around the building.

The height of the cluster column, whose capital receives the points of the inverted cones, is 59 feet 3 inches, so that the arch, which is struck from four centres, does not rise more than 18 feet 6 inches, and the intersections take place at one quarter of the span when the height is 15 feet 6 inches: this arch or stone rib is 2 feet in depth and 18 inches in breadth, formed of twelve voussoirs on each side, the joints radiating to the centres respectively; it abuts at its extremities against the ponderous buttresses, and remains steadfast and immovable, dividing, as before stated, > the vault into several severies.

The plan of the main piers shows that there has been no after-thought grafted upon the original design, which, in all probability, was commenced soon after the year 1446, as we find that a stone quarry at Haselwode, and another at Huddlestone, in Yorkshire, were granted, for the works to be carried on here. The stone roof does not appear to have been commenced till about 1512, the indenture concerning it bearing date the fourth Fig. 1307. KING'S COLLEGE CHAPEL. year of King Henry VIII.; in this document Thomas Larke is called the " surveyor," John Wastell the "master mason," and Henry Semerk one of the "wardens," the two latter agreeing to set up a sufficient vawte, according to a plat signed; the stone to be from the Weldon quarries: the contracting parties were also to provide "lyme, scaffoldyng, cinctores. moles, ordinaunces," and "every other thyng required for the same vawting: the timbers

of two severies of the "great scaffolding" were given them for the removal of the whole; and they were to havo the uses of all "gynnes, whels, cables, hobynatts, saws, &c.;" they were to pay for the stone, and to have 100l. for each severy, or 1200l. for the whole, money being advanced for wages as the works proceeded: the "chare roff," as the vault is called, was to be sufficiently buttressed, and the whole performed in a perfect manner.

The extreme width, measured from the face of one buttress to that of the other, is 64 feet, and from north to south, from the centre of one pier to that of the other, 24 feet; thus the area comprised in a severy, or space between two lines drawn through the centres of the buttresses on the plan, is 2016 feet, exactly double the area of one of the severies of St. George's Chapel, Windsor: the extreme width is the same, but the difference arises from the divisions in the one being double that of the other, as ineasured from east to

Hence we have for the areas of the space or void on the plan 1680 feet, and for the walls and pier 336 feet, or one-sixth of the whole 2016 feet, similar proportions to those which we

shall afterwards find in St. George's Chapel, Windsor. In King's College the nave comprises half the entire area of a severy, and the remaining half is divided into three, one of which is given to each of the chapels, and the other divided between the points of support: in this beautiful building, with its majestically contrived roof of stone, the lightest construction is adopted. The catenarian curve exhibits the direction of the thrust of the vault, which falls within the base.

The stone roof we are now examining differs somewhat from that of Henry VII.'s chapel at Westminster; the area of the points of support is only one-half of those in the latter elegant example; in no instance have we so much effect produced by the mason's art. with so small a quantity of material: it is evident that the gradual changes made in the architecture of the mediæval period led at last to the greatest perfection, beyond which it seems impossible for us to advance.

In selecting a style of any one period, it may be fairly asked whether the principles found in the latter, or the economy adopted in the constructions of the 15th century, might not be applied to it, and the same effect produced, -the section of the chapter-house at Wells, for instance, lightened of half its material: undoubtedly it might, for the lofty pointed arch, not having the thrust which the latter, struck from four centres, had, would exert less thrust, and be in favour of such a change.

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But at the present day, when copies are rigidly made of the finest examples of each style, it would seem a bold innovation to suggest such an adoption; still it might be introduced, and probably would have been, had the freemasons continued an operative fraternity, and been required to build in the Lancet or other style, which superseded it. The same decoraFig. 1309. VAULTING OF KING'S COLLEGE CHAPEL. tions and form of arch may be used in the later styles as in the earlier, as far as construction is concerned, and we have evidence of sufficient strength in the example before us; the principles are the same in each, though they may differ in form; there would be no more difficulty in transforming one style to that of another, than was experienced by William of Wykeham, when he changed the Saxon nave of Winchester to the Perpendicular.

On the section shown at fig. 1308. a line is drawn exhibiting the catenarian curve, for the purpose of showing that the abutment piers are set out in correspondence with its principles; it is not contended that a knowledge of this curve guided the freemasons in proportioning their piers, or that their flying buttresses were always placed within it; but it is singular that in those structures where their true position seems to have been decided, the catenarian passes through them.

Bath Abbey section (fig. 1319.) is an example which exhibits this most perfectly; and by a comparison of its section with that at Wells (fig. 1272.), it will be perceived that the struts are differently placed, and that the earlier example is defective: fig. 1298. represents Roslyr