FD and FG; FG and FE, having the corresponding angles of each equal; whereas in other triangles (as fig. 1254.) this is not the case.

We give one of his illustrations of the theory as applied to Steyning Church, Sussex, a Norman building. The plan (fig. 1255.) is set out by equal squares, and also the exterior

(fig. 1256.) to some extent. The interior (fig. 1257.) is set out by squares and triangles. The diagrams will explain themselves. The diameter of the columns is determined similar to e eƒ in Rule II. The lower window is set out by II. and the upper one by VI.

Fig. 1258. is the ground-plan, and fig. 1259. the elevation of the east end; and fig. 1260. the elevation of part of the side, of the church of St. John, Wappenbury, Warwickshire. The relation of the lines one with another is well exhibited in the diagrams. At Itchenor Church,

Sussex, the width is divided externally. In the west window of the north aisle of the church of St. Andrew's at Ewerby, the centres of the mullions obtained on the plan by squares diagonally divided. exactly coincide with the same points on the elevation as developed according to Rule VI. This system is shown in figs. 1287. and 1305. Figs. 1262, and 1263. explain the method of setting out the proportions for third pointed work; the height of the bay (R) being first determined by the diagonal of a square. The windo vs S are a square wide

to the outer edge of the moulding, and are fixed by a square on the base of the bays. The windows T have their points fixed much in the same way, bit their width is determined by the diagonal of a square. The height of the arches in the interior are also determined by the diagonal of a square (fig. 1261.).

No one," writes Mr. White, "seems to have carried out upon the equilateral triangle any definite theory of design, or to have reduced the application of it to any tangible shape-The theory is that the several parts of a perfect building must be in certain relative proportions to each other, so that all parts may be brought into an entire and unmistakable harmony with cach other, hence it is not a definite application of these principles that is insisted on, but only a systematic observance of them in some way or other. In secular and domestic buildings, we do not look for the same amount or kind

of beauty, nor is the same exactness of proportion of equal importance as in an ecclesiastical building, where every line ought to be in its proper place, and every form distinctly marked to convey an idea of perfection. In common dwelling-houses, where it is directly evident that the external form is entirely dictated by certain requirements of internal arrangement, a sort of natural beauty always results, and so there is not the same need to have recourse to exactness of proportion to produce some degree of good effect.

"The advantage of a mechanical process for defining proportions and forms would be immense in the mere practical carrying out of the work; for by its means we could, by taking one leading dimension, transcribe, reduce, or enlarge drawings with the greatest accuracy, and with less than half the labour of using scales and compasses. A large body of men, working apart from each other, but under certain and very rigid restrictions, must produce diversity as well as similarity. Their works must all possess the same general character, though the details and form in the application of them must vary in every instance with the circumstances of the case and the workings of the different minds." This system is developed by Mr. White, on numerous plans, details, towers, &c. taken from his own dimensions.

SECT. V.

PROPORTIONS OF MOULDINGS.

To enable us to decide that mouldings may have been also designed according to a measure, there is a very interesting notice recorded by Llaguno, Noticia de los Arquitectos y Arquitectura de España, edited by Cean-Bermudez, 1829, wherein, under the life of Pascual Iturriza, he states that that architect designed, 9th of May, 1541, the capilla mayor to the parish church at Plasencia in Guipuzcoa. While the work was in hand, complaints arose from the townspeople, voters, that he was decorating it with work that was too minute and could not be seen from the floor. To this assertion he replied, according to an entry in the archives of the town, that they might bring some persons, peritos en la gimetria, who could give a judgment in the matter. Such skilled persons were brought to the building and approved the work in debate. Whereon the town council requested the vicar, as being a person who was always in the building, to oversee the remainder of the work. The church is in the Gothic style, with a nave and chancel only, and is executed in cut stone. Iturriza was further employed at Santa Marina de Oxirondo in 1559.

We have given in the section MASONRY an illustration (fig. 662h.) of a mode of setting out the ribs for vaulting, found on an incised block of stone. Such specimens of niediæval work are very rare. Prof. Willis, in his paper on Vaulting, gives another example, and perhaps only two more could be quoted. But these do not show how the mouldings were proportioned.

We insert from the appendix to Roriczer's work, quoted on page 1008, the method of making the template or mould for working the mouldings for a canopy. The directions are:In a given square A B C D (fig. 1264.) inscribe a circle and draw the diagonal and centre lines. With the centre Z. and a radius equal to the given line A B, describe a circle, and therein inscribe a square E F G H parallel to

the diagonals of the first square. This gives the size of the horizontal measurement of the four leaves of the great flower or finial of the canopy. In the same circle inscribe a square I KLM of equal size to the last mentioned square, but parallel to the sides of the square ABCD, and let the line I K intersect the line F G in N, and the line F G intersect K L in O, and the line K L intersect the line G H in P, and the line G H intersect the line L M in Q. Bisect the line B K in R, and with the centre B and the radius B R describe a circle; and with the same radius describe a similar eircle about the centre C. With the centre G, and the same radius, cut off from the line G Z a portion G T, and through the point T draw

Fig. 1264.

a line SS of indefinite length; and from the points O and P draw lines perpendicular te the line SS and joining it. This gives the outline of the template for the arched mould. ings; for MQ will be the internal face of the wall, Q P the external splay, with one hollow moulding C therein; the rectangular parallelogram under PO will contain the jamb mouldings from which the template of the mullion is found, &c.

The jamb and hood mouldings are not described by Roriczer, but probably the back o the hood is obtained by the radius X Y cutting Z E at a, and from a and X the san radius will give the point b. from whence the curve X a is obtained. The curved line Ya is obtained from X. Divide X Y into 5 equal parts, and at 1 draw a line parallel to Za The length af will be equal to the diameter e Y. With a radius equal to de, and the centres f and Y, describe ares of circles intersecting in the point g, and with the centra 9 and the same radius describe the arc ƒ Y. The roll moulding appears to be formed by the length e Y on the line E Y, cutting the line Y X at 1.

The jamb moulding is probably obtained by dividing the line SS into 8 equal parts, a radius equal to one of the parts struck from 2 and 6 will give the curves, and the line V W. Tr will be equal to half T 4, and the jamb is completed. For the remainder of the construction of the canopy we must refer the reader to the publication in question.

"It is in vain," states Cresy, Stone Church, Kent, 1840, "that we attempt to imitate the tracery or mouldings belonging to this (the 13th century) style correctly, unless we consider them to emanate from some simple figure. However numerous the mouldings, they never appear confused, which entirely arises from the order observed in their arrangement." This he illustrates by the mouldings forming the trefoil arches round the

chancel. "The points of inter-
section of the two equilateral
triangles are the centres for the
hollows, and the more promi-
nent parts of the moulding are
set out with the same radius at
the points of the triangles; or, in
other words, four circles are en-
circled within a circle, and by
omitting each alternate one the
figure is formed."

Fig. 1265. is from Mr. White's essay, and represents his system applied to a cap and base of the porch doorway at the church of St. Andrew, at Heckington, in Lincolnshire. The mouldings are reduced from full size drawings whereon the diagrams coincide very accurately with the several members, the whole being set out by subdivisions of the equilateral triangle, or angles of 30° and 60° &c. (as fig. 1253.). Fig. 1265a. illustrates another cap and base from Steyning church, previously selected as an example. The cap of the columns is formed on the principle of Rules II. and III., and the base upon that of VI.

Fig. 1265a. CAP AND BASE AT

STEYNING.

Fig. 1265.

HECKINGTON.

A remarkable circumstance connected with this subject is, that although the German archeologists appear to have reduced the proportioning of mouldings and details to a system, as illustrated and explained by Hoffstadt, Gothisches A B C Buch, Frankfort, 1840, which has been translated into French by T. Aufschlager, Principes du Style Gothique, Paris and Frankfort, 1847, no one has translated it into English, or prepared a corresponding publication on English work (certainly not since the well conceived but lamentably produced system by Batty Langley in 1742), not even the author of the Analysis of Gothic Architecture, from whom it might have been expected. In fact, a true system of mediæval architecture being still unknown in England, designs are made at random, and the school, in disregard of its professed principles, continues disunited. For the satisfaction of those who may desire to subject the mouldings given in Chap. III. to a system, we add that the plans of Fountains, Tintern, and Henry VII.'s Chapel, appear to be designed on the system of the square; that of Howden on the triangle.

SECT. VI.

PRINCIPLES OF PROPORTION.

The following portion of the elucidation of this subject was originally published in 1847 by E. Cresy in his Encyclopædia, as referred to at page 900 of this work, who noticed, while introducing it, that "our attention must not be directed to the decorative portions of the style, but to the construction, from the study of which some valuable lessons may be deduced."

The Saxon manner of Building.—A division of the transept of the cathedral at Winchester has been selected as the best authenticated example of the style in use previous to the Norman Conquest. In a paper read before the British Archæological Association a' their second annual congress, held at Winchester in August, 1845, the author gave his reasons for supposing it to be the work of St. Athelwold, for which the reader is referred to its "Transactions."

Arches upon arches enabled the Saxons to continue their walls to a considerable height, the openings between the piers being proportioned as those of the Roman buildings in the time of the emperors. The plans of the piers differ from those previous to the introduction of Christianity : in Britain both the Greek cross and the circle are applied to them.

At Winchester Cathedral the columns of the triforium recede within the pier, and are set round a circle, (fig. 1267.); the passage in the walls of the clerestory is shown at the side; in another portion of the same building is a similar arrangement in less massive piers. (fig. 1268.)

The Saxon churches were generally divided into three tiers or stories, viz. a lower arcade, a triforium, and clere-story above; and such was the solidity and thickness of the walls, that buttresses were altogether omitted, the outer face of their buildings in this particular bearing a closer resemblance to the Roman than the Norman, although the workmanship was rude, and the decoration scanty.

The proportions found in Saxon buildings are the same as in the Roman, which, without doubt, they took for their models.

The circular temple of the Pantheon at Rome, 142 feet 6 inches diameter internally, and 183 feet 8 inches externally, contains the proportions of two-fifths wall and threefifths void; the area of the latter being 15,948 superficial feet, and of the former 26,493 superficial feet; the difference of these areas giving 10,545 feet for the area of the walls.

We have already seen that in the Coliseum at Rome the points of support are about one-sixth of the entire area of the plan; and the proportions of both these buildings have been admired for nearly 2000 years, the one vaulted, the other uncovered.

Generally the walls and piers of our Saxon cathedrals occupy from one-third to two-fifths of the entire area; in their sections one-third is devoted to walls and piers, and the remainder divided between the nave and side aisles.

The division of the cathedral at Winchester exhibits very perfectly the Saxon manner of building; the piers that support the lower arches are 10 feet wide, and the clear openings between them 12 feet 1 inch. The nave and transepts retain their original construction; in the former under the casing executed by William of Wykeham, and in the latter it is seen in its full purity. The choir stands over the crypts built by St. Athelwold, and though

somewhat changed by the Normans, it yet retains the dimensions given to it by its celebrated Saxon constructor.

The small piers, one of which, in the south transept, is nearly perfect, are set out with great regularity, and measure 9 feet 8 inches from west to east, and 8 feet 2 inches from north to south; their form is that of the Greek cross, composed of five cubes, each 2 feet 7 inches in width, with large and small columns placed around them to receive the mouldings that decorate the arches: six of these columns have their centres on the same circle: it is evident that the hexagon, or the duplication of the equilateral triangle, was applied, and that the whole was set out by one conversant in geometry, and acquainted with the proportions of the cube. The Greek cross, which defines the solid mass, is continued through the triforium and clerestory up to the timber roof.

Fig. 1268. PIER AT TRANSEPT AT WINCHESTER CATHEDRAL.

The columns of the triforium, set round the inner circle, are partly cut into the lateral arms of the Greek cross, but the face of the shafts of the columns are in a line