this beautiful example is given, for the purpose of exhibiting the principle upon which it is set out: it will be evident that the nucleus of the design is composed of two equilateral triangles, and the sides of each continued, constitute the alternate divisions.

The internal hexagon has its parallel sides prolonged, to mark the position of the four divisions that have their pointed heads attached to the small circle, which forms the eye of the pattern; and the length of these prolonged lines is limited to the extent of the sides of an equilateral triangle, which is again divided regularly, the triangular spaces between being filled in with trefoils. The small mullions are in width 2 inches, the next size 3 inches, and those which mark out the figure and have a bead for their termination are 44 inches: another bead and bold projecting label, or rim, circumscribe the whole rose window, the hollow around which is enriched with a curved leaf. On each side of the internal hexagon an equilateral triangle is constructed, around which a circle is struck, uniting elegantly with the next, and forming the six turns which characterise the filling in of

circles at this period; these were the principal decorations after the Lancet style was abandoned, and were continued until succeeded by more flowing and varied designs.

Rose Window of the South Transept at Beauvais, 34 feet 4 inches in diameter, is composed of six large circles and their intersections.

To set out this window the great circle expressed by the outer bead is divided into twelve parts, each Seing equal to half the radius; twelve equilateral triangles are then inscribed, points of which touch each of the divisions, and where they cross nearest to the outer circle, the twelve pointed arches that surround the figure are struck; the other points of intersection of the triangles are centres, from which the other curves are drawn. It must at once be evident, that in a circle so divided, or by any other equal number of equilateral triangles, the portions contained between the smaller angles must be equal to each other; the six circles around the centre have their curves blended into the outer, and if it be required to fix centres for each of these flowing lines, they can only be obtained by covering the entire rose window with lines in the manner already described. The radius being equal to the side of a hexagon, and that figure being composed of two equilateral triangles, was probably the chief reason of its first preference over all others; it certainly affords the extraordinary

and there is carcely a moulding or form in the architecture of this period but is set out from it. The mullions that bound the divisions are all portions of this figure, as are the mouldings, which sweep round the arches of the buildings themselves. Nothing can surpass the brilliant effect of these marigold windows when glazed with rich colours, and exposed to either a rising or setting sun; in the example now described, this effect is still further heightened by making nearly the whole end of the southern transept a continuation of the same design, the glass descending almost to the tops of the doors which afford access to the cathedral. The construction of such works must excite our highest admiration, for it appears scarcely possible to excel the perfect manner in which the parts are put together and worked off, the execution being in every particular worthy the design.

The Rose Window in the South Transept at Amiens, 29 feet 6 inches in diameter is set out upon two squares, which cross each other diagonally.

Sixteen divisions are employed in this figure, and by crossing as many squares, we arrive at the method by which it is set out; each side of the square is equal to the radius by which the master line on the outer bead or circle is struck: where the squares cross each other are the divisions of the pattern, and their several points are the centres upon which the pointed arches are struck, which surround the outer portion of the rose.

Where the lines of the squares cross, in the interior of the figure, the smaller divisions are established, and their points of intersection serve for centres to strike the lesser curves; to show this clearly the whole must be set out, and drawn to a large scale.

The architecture of France underwent a material change after the thirteenth century; the heads of the windows were no longer filled with tracery composed of six foils, generally three in each window, but branched out into a more running pattern, as practised in several parts of England. The fourteenth century not only exhibits windows of more difficult design, but an apparent absence of the principles by which the several parts were proportioned to each other. Before the Perpendicular style appeared, great progress had been made in the groining of the spacious vaults of the naves, as well as those of the side aisles. After the fan tracery was substituted in England, the windows had straight mullions ascending till they intersected the arch; and we have no further display of the varied figures that everywhere prevailed before: geometry was now exercised upon the intricacies which their surprising vaults exhibited. It is somewhat singular that we never find the beauties of a previous era retained, and blended with that which succeeded.

For the 300 years during which the Pointed style continued to flourish, each half century gave to it a new character; hence we have seldom any difficulty in establishing its date. all these changes resulted from an improved knowledge in the art of construction. The lodges of freemasons were gradually approaching the principles which directed the efforts of the architects of the Byzantine school, and which were found too refined and delicate to be practised out of Italy after the eleventh century.

The Rose Window in the Northern Transept of the Church of St. Ouen at Rouen, 28 feet 6 inches in diameter, is an example of the pentagonal setting out.

When the sides of a pentagon are prolonged, they unite and form five isosceles triangles, each having for its base a side of the original pentagon. The equilateral triangle, the square, and the pentagon may have been adopted by different confraternities of freemasons; the first can be formed into hexagons, duodecagons and their multiples; the squares, by crossing diagonally, into octagons; they may be also tripled and quadrupled: the mitre of the equilateral triangle is in the direction of its centre of gravity, as is that of the square and the isosceles triangles; consequently to unite the mouldings around either, the plummet would indicate the direction of the line, when dropped from the angles and suffered to cross, the point of intersection being the centre of gravity common to the several lines.

In the chapel of St. Cecile is the monument of Alexander Berneval, the master mason of the works at St. Ouen, at the time the rose window was executed by his pupil, whom it is reported he murdered from jealousy: such an application of triangles was then called the pentalpha.

The foundations of this church were laid by Marcdargent, about 1318, by whom it was built as far as the transept; but probably the rose window of the northern transept was not inserted till many years after, for the memorial of Berneval bears the date of 1440: this monumental stone is 8 feet 6 inches in length, and 4 feet in width, and in it is represented the architect and his pupil, each employed tracing with his compasses his respective design; these beautiful brasses with their rich tabernacle work were in the highest state of perfection when the writer was last at Rouen, and around the master figure was inscribed in German letters :

Cy gist Maistre Alexandre de Berneval, Maistre des oeuvres de Maconnerie du Roy, notre Sire, du Baillage de Rouen, et de ceste Eglise, qui trespassa, l'an de grace inil. ccccpl. le v jour de Januier.

Prie's Dieu pour l'ame de luy.

The date of the pupil's death is not commemorated, which has led some to imagine the tale of his murder untrue, and that he erected the monument to his master with the intention of being buried by his side.

The North Rose Window at Amiens, 37 feet 8 inches in diameter, is a magnificent example of the application of the pentagon, with 5 isosceles triangles around it.

This window, probably

executed in the fourteenth

century, has a great resemblance to the last described; the fan tracery, of which we have early specimens in the cloisters at Gloucester, required the same know. ledge of geometry to perfect their design. In 1482 Euclid was first printed at Venice from the Greek text; but geometry had been studied in England from the time that A dhelard, in 1130, had introduced a translation of that author from the Arabic versions which he met with during his travels in Spain. In 1256 Campanus of Navarre translated Euclid, who seems to have been commented upon by several eminent writers, and no doubt it was the text-book of the freemasons, who diligently applied the problems it contained to every purpose of their art. In 1486 the Editio Princeps of Vitruvius appeared, and the commentaries of Cæsare Cæsariano followed in 1521; the latter author published three plates of the Cathedral at Milan, covered with equilateral triangles, which have not been described so as to be useful or understood. The compartments which

have the flat sides of the original pentagon for their base, and parallel sides throughout till they terminate in the pointed arch, have their mullions proportioned to their opening, the larger being double the size of the smaller, whilst the latter are equal to half the open space between them: the mullions in these examples, which divide two spaces, 6 inches in width, are usually 3 inches in thickness, and the others are in the same proportion. The next sized mullion is 4 inches, with a bead of 11 inch diameter, which runs round the whole pattern of the figure, the centre of which may be called the master line, by which all the rest are set out; the several mullions are all twice as much in depth as in width.

Baptistery of Pisa. - The internal diameter of this circular building is 100 feet, and the thickness of its outer walls and columns 10 feet 6 inches; its external diameter is 121 feet, the area of which is 11,499 superficial feet, that of the interior being 7854; if we deduct from it what is occupied by the four piers and eight columns, or 188 feet, we have 7666 feet for the void, exactly two-thirds of the entire area. To find these proportions in an edifice commenced about the middle of the twelfth century in Italy, is a curious corroboration of the opinions already advanced, the same rules as those described for the Chapter House at Wells being apparently followed: the conical brick dome was the work of an after period, and may have been the prototype for that of St. Paul's at London; the pointed architecture belonging to the exterior of this edifice, of the same character as that which adorns the crosses of Queen Eleanor in England, was added in the fourteenth century.

The section shows how the equilateral triangle governs the proportions of this celebrated building; the extreme diameter is the base, and its apex the level on which the