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at Salisbury. The masonry of the arches is admi. rably constructed, and the joints all radiate to a common centre

The total width of this cathedral from face to face of the buttress is 86 feet 5 inches, and that of the nave 31 feet 10 inches, instead of 28 feet 9 inches, as it would have been if a third had been adopted; the side aisles are also diminished in consequence, being only 13 feet 74 inches in the clear ; they are, however, equal to the buttress, outer wall, and main pillar added together, the first pro. jecting 2 feet 8 inches, the second or outer wall being 6 feet in thickness, and the piers 5 feet diameter; whilst the width of the side aisle measures 13 feet 74 inches, an approximation sufficiently near to suppose that the proportions of thirds was still adopted in practice. The nave has been increased at the expense of the side aisles, and its height is 68 feet 9 inches to the top of the vaulting from the pave




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Chapter House at Wells, erected between the years 1293 and 1302, is an octangular building of great beauty. A section through the buttresses shows that two equilateral triangles crossing each other have determined the mass and void, which are in the proportion of one to two, or the thickness of the two walls is equal to one-third the entire diameter : the base line of the triangle, on which the supports of the crypt are placed, clearly indicates this arrangement. Of the twelve equilateral triangles comprised in the parallelogram formed by uniting the bases of the two larger, each outer wall and buttress occupy two, or the two walls and their buttresses four of the twelve divisions, leaving eight for the space between them.

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Where it is determined that the walls shall occupy one-third of the section of a building, no figure is so well calculated for such a distribution as the equilateral triangle; it enables the architect at once to limit and fix the proportions of his design; hence its universal application : and the mysterious qualities attached to it by the freemasons no doubt arose from the extraordinary facility it afforded them in setting out their several works. What can be more simple or more beautiful than the distribution of this edifice? Within a circle a hexagon is set out, the perpendicular sides of which mark the outer faces of the buttresses ; the junctions of the angles, by forming a base to every two sides, produce the two equilateral triangles, which sub-divided not only enable us to arrange the other portions accurately, but also to meas re with the greatest nicety their relative dimensions.

The quantities of material employed in construction can be estimated by such means much more easily than by measuring each portion separately, cubing it, and adding the numerous dimensions so obtained together ; there is decidedly more simplicity in the former than in the latter system : the area of one triangle being found, we at once know that of all the rest.



Fig. 1276. or of any portion. In the subject before us the distance from the middle of one buttress to that of the other is 31 feet 6 inches, and the diameter taken through them at this level is 92 feet; omitting the buttresses, the outer side measures 26 feet, and the inner 21 feet 6 inches, the respective radii of the circles which comprise the octangular outer walls and the void being 38 feet and 31 feet 5 inches. Hence we find that the entire area of the building without the buttress is

3264 feet. The area of the void

2176 feet.

And of the walls or points of support

1088 feet.

At the level of the crypt, above the outer plinth, we have these regular proportions, twothirds void and one-third walls.

The height of the entire building, from the pavement to the top of the parapet, is 72 feet 6 inches, and to the top of the pinnacles 92 feet, the total height being equal to the extreme diameter taken above the plinth moulding on the outside. The interior of this chapter.

house exhibits the most perfect proportions as well as appropriate decorations; the eight windows, divided into four days, have their heads filled in with circles set out upon equilateral triangles ; the vaulted stone roof rests partly upon the octangular central pillars, 3 feet in diameter, surrounded by sixteen small columns, one at each angle and another between ; the height of the pillar is 22 feet 8 inches.

Thoroughly to comprehend the expression, as well as use of the various members found in the architecture of the middle ages, we must trace the progress made in vaulting, and observe the changes it underwent, from the simple cylindrical to the more complex and difficult display of fan tracery or conoidal arches. The ridge ribs, or liernes, as they are termed, in the crypt of the Chapter-house at Wells, pass from the centre of the building to the middle of each buttress ; the diagonals, or croissées, mitre into them as well as into the formerets or ribs against the outer walls.

In the vaulting of the Chapter-room, we have evidence of greater refinement, and an

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Fig. 1977, improvement' in the decoration, by the addition of a number of intermediate ribs terminating against the octangular one in the middle.

At a later period we find transverse ribs made use of, then others between ; but although the design may seem complicated, yet when laid down the plan will assume the greatest simplicity, as shown in the division representing the groining of the crypt.

When this system had been carried out to a considerable extent, the fan tracery was introduced, and although apparently more difficult of execution, it is far more scientific in its application and arrangement, evincing a higher knowledge of mathematical principles and geometry, and is another evidence of the gradual progress of the mind towards perfection in this style of architecture.

Westminster Abbey, commenced in the year 1245, is in that style which for many years prevailed in France : the fine church at St. Denys, near Paris, is exactly similar in all its detail. The windows are wide, divided by mullions, and have their heads filled in with plain circles, the origin of the cusp, or that kind of decoration which every pointed arch afterwards received. This style, which succeeded the Lancet, is found throughout England, and many of the parish churches exhibit fine examples of it. Stone Church, in Kent, of which the writer has published an account, may be eited as one of the best ; its ornament shows the skill and taste that prevailed among the freemasons at that period. Salisbury, Wells, and York Cathedrals abound with rich foliage and sculptures of the highest merit executed at the same time, and it is wonderful to observe to what a state of perfection the artists of this country had arrived. The effects of the chisel of the Pisan school were displayed upon marble, but our sculptors worked upon an inferior material; yet the draperies of their figures, as seen in the front at Wells, and else. where, are quite equal to those wrought by the pupils of Italian masters at the same time. The circle and its intersections at this period were alone employed for the plans of piers, sections of mouldings, and the filling in of windows and doorways: from them we trace the origin of the style which immediately succeeded.

The cathedrals of Cologne, Amiens, Beauvais, the Sainte Chapelle at Paris, and numerous other examples on the continent, exhibit the same proportions and style with that of Westminster; the lofty pointed arches, which rest upon the main cluster, are decorated with numerous small mouldings; the triforium, in some instances glazed, have their pointed arches filled in with trefoils, cinquefoils, or sexfoils, and the clerestory, carried up to the very apex of the vaulting, is similarly adorned. Westminster Abbey is one of the finest examples of building executed in the thirteenth century.

Tracery and Geometric Forms.—To comprehend thoroughly the principles which directed the freemasons of the middle ages in the execution of all their works would require far greater illustration than can be bestowed upon the subject in the present volume: it must be sufficient if we point out a few which influenced the design of some of their best examples, and show that it is a perfectly erroneous opinion to suppose they were executed without a thorough knowledge of certain rules, originating with themselves, and perfected by a constant study of what was not only useful, but productive of the best effect. Those who inquire into this subject must collect the data upon which an opinion can be formed, for it is scarcely possible, without positive measurement, to arrive at any conclusion upon the matter : the admirer of the Greek, or the commentator upon Vitruvius, alone can scarcely hope to be successful : it is true that in one of the early printed Italian editions of the valuable author quoted, there are several diagrams which seem to point to the subject, but the student will find only the nucleus around

Fig. 1978. which the lovers of geometry in the middle ages arranged their varying and beautiful forms; this is the equilateral triangle, and by inclosing the plan, section, or elevation of a building within it, the several proportions can be accurately measured, and if sub-divided into a number, either of the triangles vould show the proportion it bore to the whole area.




In one of the tracery heads of the windows in the cloister at Westminster, the date of which is about 1348, we have two figures that resemble the plans given to clustered pillars, indicating at once that the same principles were applied to the setting out of both windows and points of support. When the circumference of a circle is divided into twelve equal parts, the points which divide them form the termination of four equilateral triangles, and we have at their intersections, not only the centres of the circles that constitute the filling in, but also the several mitres and other portions of the figure.

These rules were evidently applied to windows, and to tracery of every description, executed at the end of the thirteenth and commencement of the fourteenth Fig. 1979. centuries ; also to the plans of the main cluster of pillars in many cathedrals and churches. For nearly a century, circles and their intersections formed the ornamental portions of every kind of panel and window head; they were afterwards blended into other figures, and apparently set out upon different principles; but the hexagon and equilateral triangles were necessary to produce the flow. ing lines which succeeded. The change which took place in design no doubt arose from the facility which had been attained by the practice of this method, and if it were possible to exhibit each variety in England alone, there would be ample evidence of the inventive power of the freemasons, and the progressive improvement in their school for depicting form. The quatrefoil in fig. 1279. is met Fig. 1280. with in the panels of several altar tombs, in the spandrills of the arches of door. ways, and it is worthy of observation that all the mitres, where the figures change their form, are perfect for each : had these considerations been neglected, we should not have had the graceful flowing lines found in these designs: no other triangles crossing are so universally applicable, or require less skill in their adoption. The student of the present day might occupy a life in the collection of these subjects, and they are most excellent models for the application of the rules of theoretical geometry to practice.

Windows of three Days or Divisions are met with, having heads of singular beauty, inclosed within an equilateral triangle, and

are the designs, that it is rare to meet with two exactly similar. In





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