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one, and we regret that our limited space will not allow us to do more than merely enter upon it. We would warn the student that should be feel inclined to devote any time to this subject himself, he must not be content with the measurements he may usually find in publications, but must found his theories on those taken by himself to be in any degree curtain of his deductions,

The plan on which the earlier Christian churches were constructed, wrote Mr. Gwilt, was that of a cross : be omitted to notice, however, the Italian basilican plan and the domical Greek plan; but he justly observes that (in western Europe) after the 10th cen. tury it would perhaps be difficult to find a cathedral deviating from a cruciform plan. At

the beginning of the 9th century, in an inauguration (of a church) sermon, the preacher observes, “In dextro cornu altaris quæ in modum cruris constructa est ; " and again, " In medio ecclesiæ quæ est instar crucis constructa." (Aeta SS. Benedict.) Round churches, as at Aix la Chapelle, in Ger. many, Rieux and Merinville, in France, with Little Maplestead, Cambridge, Northampton, and the Temple Church, London, in England, are not enough in number to affect the rule. It was in the 13th century that the termination of the choir was changed from a circular to a polygonal form. The general ordonnance of the plan was, however, not changed, and seems almost to have sprung from the laws and proportions upon which surfaces and solid bodies are dependent. The square and its diagonal, the cube and its sides, appear, at least the latter or the side of the former (fig. 1219.), to

furnish the unit on which the system is based. Hence the Fig. 1219.

numbers 3, 5, and 7, become the governing numbers of the different parts of the building. The unit in the Latin cross, placed at the intersection of the nave, gives the development of a perfect cube, according to the rules of descriptive geometry. Here are found the number 3, in the arms of the cross and the centre square; the number 5, in the whole number of squares, omitting the central one; and the number 7, counting them in each direction. The foot, however, of the cross was, in time, lengthened to repetitions of five and six, and even more times. In monumental churches, formed on such a system, there necessarily arises an unity of a geometrical nature; and the geometrical principles emanating therefrom guided not only their principal, but their secondary, detail. Even before the 13th century there seems to have been some relatioa between the number of bays into which the nave was longitudinally divided, and the exterior and interior divisions whereof the apsis consisted; but after the introduction of the pointed style, this relation became so intimate, that from the number of sides of the apsis the number of bays in the nave may be always predicated, where the work has been carried out as it was originally designed. From the examination of many, indeed most, of the churches in Flanders, this circumstance had been long known to us; but for its first publicity, the antiquary is indebted, we believe, to M. Ramée, in 1843.

The connection of the bays of the nave with the terminating polygon of the choir was such, that the polygon is inscribed in a circle, whose diameter is the measuring unit of the nave, and generally of the transepts, and forms always the side of the square intercepted

by them. It is most frequently octagonal (fig. 1220.), and generally formed by three sides of the octagon. When this is used, the governing number will be found to be 8, or some multiple of it. Thus, in the Abbaye aux Hommes, at Caen (this, however

, is previous to the 13th century), the termination of the choir is by a double octagon, and the number of bays in the nave is eight. The same occurs at St. Stephen's, at Vienna ; in the Church of St. Catherine, at Oppenheim ; at Lichfield Cathedral ; at Tewkes

bury Abbey, and at almost every example that is known. It may be well here to observe, that English cathedrals, partly from their great defi. ciency in symmetry, on account of their not having been finished on their original plans, do not afford that elucidation of the theory that is found in those on the Continent. Jo twenty-four instances of them we have sixteen in which the terminations are square instead of polygonal; when polygonal, the rule seems to have been always followed. It must be noted, however, that in contradistinction to the rest of Europe, England kept steadily, as a rule, to a square east end; and though at Canterbury and Tewkesbury, and a few other noted examples, the circular form appears, yet often, as at Peterborough and Westminster, the curved apse was capped with a rectilinear addition, protesting, as it were, against the foreign element.

An eastern termination of the choir in three bays may be produced from the octagon, by omitting the sides in the direction of the length of the building, as in fig. 1221. In fig. 1299 the three sides will be found to be those of a hexagon; and in this case the number 6

Fig. 1220,

Fig. 1221.

Fig. 1222.

Fig. 1223.

Fig. 1224

governs the other parts. Examples of this arrangement are, the minster at Freiburg-imBreisgau; the cathedral at Cologne, where the apsis is do

decagonal, and there are six bays in
the nave; and the abbey at West-
minstHr, where the eastern end is
hexagonal, and there are found
twelve bays in the nave. In re-

spect of a nonagonal termination, the most extraordinary instance of a coincidence with the above-mentioned rules occurs in the duomo of Milan, commenced at the end of the 14th century. Its apsis is formed by three sides of a nonagon, and the bays in the nare are nine in number. One third of the arc contained under the side of an equilateral triangle seeins to be the governing dimension. The number 3, submultiple of 9, pervades the structure. There are three bays in the choir, and the like number in the transepts The vault of the nave is subtended by an equilateral triangle. The lower principal windows are each designed in three bays The plan of the columns in the nave in each quarter contains three principal subdivisions, and, in a transvere section of the nave, the voids are just one-third of the solids. These are curious points, and much more worthy of investigation than many of the unimportant details which now-a-days so much occupy the attention of archæologists. If the stem of the plant is right, the leaves and fruit will be sure to grow into their proper forms.

Figs. 1223. and 1224. show the decagonal terminations of an apsis. In the first, a side of the polygon faces the east; in the second, the angle of the polygon is on the axis of the

church. The last case is of rare
occurrence. Examples of it are,
however, found in the church at
Morienval, and in the choir of
the dom-kirche of Naumburg.
The first case is illustrated by

a variety of examples—such are the cathedrals at Reims, Rouen, Paris, Magdeburg, and Ulm, with the churches of Ste. Elizabeth at Marburg, that at St. Quentin, &c., and, in this country, the cathedral at Peterborough; all of which have either five or ten bays in the nave. The dodecagon, as a termination, is subject to the same observations as the hexagon : indeed they were anticipated by the mention of the cathedral at Cologne. Under the figure of the heptagon must be ciassed the magnificent cathedral of Amiens, wherein seven chapels radiate round the choir end, and there are as many bays in the nave (fig. 297.). The choir at Beauvais is terminated by a double heptagon; and, had the church been completed, it would doubtless have had seven or fourteen bays in the nave. At Chartres, the choir is also terminated by a double heptagon, and the nave contains seven bays. In the duomo at Florence, the eastern termination is octagonal, and there are four bays in the nave; this is an example of the expiring Gothic style in Italy.

On an examination of the principal churches on the Continent, in and after the 13th century, it would appear that the practice of regulating the details was dependent on the number of sides in the apsis, or of bays in the nave. Thus, if the choir is terminated by three bays, formed on an octagonal plan, we find 3, or a multiple of it, is carried into the subdivision of the windows. So, if the number 5 is the dominant of the apsis, that number will be found transferred to the divisions of the windows; and in like manner the remainder is produced. There are two or three other matters affecting the monuments of art erected in and after the 13th century. The aisles are usually half the width of the nave, though ins:ances occur where the width is equal. Mar.y churches have two apsidessuch are the cathedrals at Nevers, and at St. Cyr; and in Germany, St. Sebald at Nuremberg; the dom-kirche at Mayence; the abbey church at Laach ; the cathedrals of Bam. berg, Worms, and others. So far Mr. Gwilt.

" It remains to observe," writes Professor Cockerell, in the Archeological Journal, 1845 “ upon the mysterious numbers employed by Wykeham in the plans of his chapels at Win. chester and Oxford, which are divided longitudinally by 7, and transversely by 4, equal parts. In the first, the chapel consists of 6 of these parts, and the ante-chapel of li in the second, the chapel consists of 5, and the ante-chapel of 2; the width being equal to 4, corresponding with the entire figure of the vesica piscis.”

The recurrence of the number 7, “ a number of perfection," is constant; accordingly we find it employed in the following remarkable instances, sometimes in the nave, and sometimes in the choir. In the cathedrals of York, Westminster, Exeter, Bristol, Durham, Lichfield, Paris, Amiens, Chartres, and Evreux; in the churches of Romsey, Waltham, Buildwas, St. Alban's (Norman portion), and Castle Acre; and in St. George's Chapel, at Windsor, Roslyn Chapel, and many others. See also the notice on page 1011.

Sect. II.

EARLY USE OF GEOMETRY AND OF A MEASURE. The idea is now generally sanctioned, that the mediæval architects had some settle system of proportioning their designs either by simple geometric forms or by combination of them. It will be our endeavour to indicate the sources whence the facts on this subjec can be drawn, and to notice such of the details as our space will permit.

The knowledge of geometry previous to, and in, the 12th century has been commentet upon in par. 309, et seq. The Album of Wilars de Honecort, an architect living in th middle of the 19th century, exhibits the use of geometry in various ways. This manu script was published in facsimile by M. Lassus in 1858, and an English translation sa edited by Professor Willis in 1859. The sketches also show a certain mastership of bgun drawing, besides many designs of portions of buildings. Some original drawings still exis of Reims Cathedral, known to be before 1270, thus of the same period as those of Wilars and two of them have been published in the Annales Archéologiques

, vol. v. page 92. Tht drawings were traced with a masterly line; they only showed how the design was to bi arranged ; and by means of arial lines only, the whole was set out as regularly as could be done for the most classical building. Scarcely any of the later original drawings stil existing in many continental cities show the use of geometric figures (see fig. 1079.). Yet on the 14th of February, 1321, during the erection of the cathedral at Siena, five person who had been appointed for the purpose reported that “the new work ought not to be pro ceeded with any further, because if completed as it had been begun, it would rot have that measure in length, breadth, and height, which the rules for a church require" The ola structure, it also appears, " was so justly proportioned, and its members so well agreed with each other in breadth, length, and height, that if in any part an addition were made to it under the pretence of bringing it to the right measure of a church, the whole would be destroyed.” Della Valle, Lettere Sanesi, ii. p. 60; noticed in Hawkins, Gothic Archi. tecture, 1813, p. 183. This statement would seem to prove that some system had existed.

In par. 620, we have already mentioned the disputes on the great question of propor. tioning the cathedral at Milan, 1387-1392, by the foreign system of squares, or by the native theory of triangles. The first notice in England of this unique instance of a dispute appears to have been taken by J. W. Papworth, who presented in 1854 to the Institute of British Architects some extracts from the Records of the Board of Works for Milan Cathedral, published by Giulini, Memorie di Milano, 4to. Milan 1776, part 2, pp. 448-60 of the Continuazione. These notes further condensed show, that on the 1st of May 1392, fourteen of the artists employed upon the works made affidavit of their opinion on ter points submitted to them, on the part of the German Enrico di Gamondia, who was one of the number. On the third point, thirteen declared that the said church, not including the intended cupola, should be raised non al quadrato ma fino al triangolo, that is to say on the triangular proportion. The same opinion is given on the fifth point as to the versed sine of the vaulting. Enrico, who on all the points held a contrary opinion to the thirteen, was thereupon dismissed. Another meeting of similar character, held 26th of March, 1401, of thirteen artists employed on the building, and two amateurs, was not so nearly unani. mous upon the question of the alterations proposed by the Frenchman Giovanni Mignotto, and upon tha occasion Guidolo della Croce (one of those employed) declared that the alterations were correct, and that Mignotto was a verus operurius geometra, because his ratios were like those of the dismissed maestro Enrico. The dismissal of this Jean Mignot, 13th of October, 1401, was accompanied by a charge for the expense of pulling down the work that he had erected during two years. Although the chronicle makes the curious mistake that the magister Enricus and the magister Annex (i.e. Johann von Fernach 1391-92 1, also a German, had advocated the triangular system, it rightly adds that the triangular system prevailed over that of the square; and the lines may be supposed to have been truly given by Cesare Cesariano. The conclusion we have arrived at in the matter is that the plan was designed on the principle of the square (exhibited in fig. 1231.), while the elevation was designed on that of the triangle (shown in fig. 1292.).

Cesare Cesariano, the first translator of Vitruvius, Como, 1521, terms the geometric principle of design, “ Germanic symmetry," and "rule of the German architects." Rivius, who translated this work (Nur. 1548), names the order resulting from the triangle as the highest and most distinguished principle of the stonemasons." One principle rested on the arrangement of the square, or of the octagon which proceeds from it, in the same way as that of the equilateral triangle was based upon the hexagon or dodecagon which resulted from it. On this law of the square is founded the work by M. Roriczer, On the Ordination of Pinnacles, 1486, which was printed by Heideloff, in Die Bauhütte des Mittelalters in Deutschland, Nuremberg, 1844; and also by Reichensperger, who translated it into

modern German, Trier, 1845. It was noticed in the Journal of the Archæological Institute of Great Britain, 1847; and translated in a concise manner by J. W. Papworth for the Architectural Publication Society, Detached Essay, 1848, with woodcuts. An appendix follows On the Construction of a Canopy, which was also given in Heideloff's publication.

The square, or octagon system, maintained itself among the German stonemasons until the commencement of the 19th century. Heideloff relates that the chef-d'æuvre of Kieskalt, the last city architect of Nuremberg (1806), was founded on the rules used in Roriczer, and those in the book of instructions written 1506 by Laurenz Locher, architect of the Count Palatine, on the art of the stonemason, nach des Choresmaass und Gerichtigkeit, * according to the measure and ordination of the choir."

“ The system depending on the equilateral triangle for its variety of form," states E. Cresy, Stone Church, 1840, “ continued in use till the beginning of the 15th century in France, when it underwent a great ard important change by the introduction of the isosceles triangle and its compound the pentagon. A pupil of Berneval, the designer of the Church of St. Ouen at Rouen, proved that these figures could furnish novelties in design. We can well imagine how displeasing this innovation must have been to the whole fraternity of masons; their mystery was invaded.” Pommeraye, in his History of the Abbey of St. Ouen, mentious that the master was so incensed at the clergy preferring the rose window of the northern transept ( fig. 1293.) executed by his pupil, where this innovation was first introduced, to that of the south (fig. 1288.), of his own execution, upon the ancient triangular system, that in a fit of jealousy he killed his rival, and was himself condemned to be hanged. (See page 1036.)

In the year 1525, Albert Duerer published in German his Geometrical Elements, showing therein clustered columns, and a few other details of Gothic architecture, In 1532 a Latin edition was published at Paris, entitled Albertus Durerus, Institutionum Geometri. carum; and in 1606 a second edition was printed at Arnheim. It is this author who first brings to our notice the use of a figure called the vesica piscis, which is explained in Sect. III. In 1589 Spenser published his Faëry Queene, and in it allusion is made to the proportion of a building in words which deserve attention (b. 2, canto 9, v. 21). In 1593 Sir Thomas Tresham erected the curious lodge at Rushton Hall, Northamptonshire, entirely constructed on the equilateral triangle; it contains one room of an hexagonal form; the upper windows are mostly triangular openings (Builder, iii. 538. 550.).

Stieglitz, in Altdeutscher Baukunst, 4to. Leipzig, 1820, records the possession of a manuscript Treatise on Architecture, giving the rules and instructions according to which the ancient werkmeisters and steinmetzen worked. Judging from the character of the handwriting, it must belong to the middle of the 17th century, and this is also indicated by the drawings which exhibit the Italian style of that epoch. But the rules for the construction of churches belong to a more remote period, and the author of the manuscript states that these rules were never described, but were transferred in a traditional way to, and kept by, the artists, who called them, like the ancients, Measure of the Choir and Justice. It seems to be the only written directions for a building which has come down to us. The drawings in it, which are only shaded, are finely executed by a steady and practised hand, They show the formation of the several cornices, mouldings, jambs for doors and windows, plinths, and arches, and also the formation and the arches of the vaulting. The building is proved to have strict rules and an established module, according to which all the members are regulated by the ensemble of the structure, and the whole is again regulated by the members. The choir is considered as the key, and after its breadth is regulated, the thickness of the enclosure-wall, and also all the dimensions for the cornices and other members are obtained. Thence the saying, “ Measure of the Choir and Justice."

At first, from a given circle an octagon is to be constructed, and according to it, the ground-plan and the pentagonal projection of the choir are to be devised. Should the choir contain 20 feet in the clear, its wall would be 2 feet thick ; and if 30 feet wide, then 3 feet. The pillars of the choir are commonly 24 feet thick at their base, exclusive of the ground table (schrägesims), and the depth is double of the thickness. The width of the windows is regulated by the space between the columns, which is divided into 5 parts: 3 are given to the window in the clear, together with the inullions. If the choir be very extensive, and therefore the lights of the windows be too wide, in such case intermediate mullions are introduced; but small windows have only one main or two subsidiary mullions.

The nave and aisles are regulated after the manner of the choir, being made equal to it in width, yet in such a manner that the pillars, although equal in thickness to the wall of the choir, do not run in the same line of the opening, but project with three sides of their octagonal form. The breadth of the choir being divided into 3 equal parts, 2 are to be given to each aisle, including the wall of the choir. The same dimension of two such parts is applied to the pillars from one centre to the other, which shows at the same time the space for the buttresses on the enclosure-wall. As, in consequence of the aisles, the nave portion requires a wider vaulting than the choir, the enclosure-wall of the wave ought to

be constructed one-third thicker than that of the choir. The buttresses are the same in thickness and breadth as for the choir. The windows are kept of the same width throughout the whole structure. The transept projects as far as the breadth of the aisles, and its wall has the same thickness as the wall of the choir. The length of the church is for the most part regulated according to the requirements of the population.

The towers, erected on both sides of the façade, are devised from the width of the inner shafts and external pillars, which width formed into a square gives the external enclosureline of the towers. If only a single tower be constructed, it ought to be regulated after the choir, and agree with the same. The thickness of the tower-wall is regulated by the height of the tower itself. Thus for every 100 feet of height, 5 feet in thiekness is required for the wall. Then, to this thickness one half more is to be given for the foundation. But if the ground be firm and good, this thickness need only be kept as far as the base, and thence gradually reduced. The formation of the groining is not so clearly developed by the editor, and we therefore omit it,

The outline and elevation of the choir are also calculated from its width. A choir which is 20 feet broad, ought to be one and a half or twice as high. The latter height was called the real height. An ordinary choir requires only four tables or strings. The ground table (schrägesims) rises from the floor or ground to a height equal to the thickness of the counterforts. The string course (kaffsims) above is placed as high as the distance between the pillars. The supporting string (tragesims) ought not to rise higher than the capital of the pillars in the interior of the choir. The top, or roof-cornice (dachsims ) ought to be placed at least half a foot higher than the vaulting. The pillar-cornice is measured by taking the thickness of the pillars twice down from the top cornice. A choir of greater height requires more cornices and decorations. The height of the nave portion is fixed by taking twice the width of the choir, and this is measured from the ground-table to above the top.cornice. The ground floor of the tower ought to be as high as the whole tower is broad, and the upper floors to be regulated accordingly. We have only to add that the form given to the towers by the author of the MS. shows the Italian style of his epoch, whilst the church itself is constructed in German fashion, that is, with high pointed. arched windows and buttresses, which are drawn without any mouldings.

Sect. III.

THE VESICA PISCIS.

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If on the diameter of a circle (fig. 1225.), with an axis perpendicular to it, an equilateral

triangle be described, whose vertical height shall be equal to the semi-diameter of such circle, and from the angles of the triangle on the diameter, with a radius equal to one side of the triangle, arcs of circles be described cutting each other superiorly and inferiorly, the figure described is that which is called the vesicu piscis, or fish's bladder.

The Greek word ixovs, signifying a fish, seems to have been in early

ages a mystical word, under which Christ was denominated, “ Eò quod Fig. 1225.

in hujus mortalitatis abysso, velut in aquarum profunditate, sine peccato esse potuerit, quemadmodum nihil salsedinis a marinis aquis pisci affricatur ;* that is, Because in the unfathomed deep of this mortal life he could exist without sin, even as a fish in the depths of the sea is not affected by its saltness. The term, too, at a very early period, furnished an anagram, whose parts were expanded into the expression, 'Intous Xplotds Deoù Tids Ewrhp. The initials of these words were, in their turn, erpanded into a long acrostic (to which reference may be had, sub voce Acrostichia, and also under the term Ichthys, in Hoffmann's incomparable Lexicon) on the Day of Judgment, said to have been delivered, divino afflatu, by the Erythrean sybil, but much more resembling the hard-spun verses of a learned and laborious man than the extemporaneous effusions of a mad woman. This acrostic is recognised by Eusebius, and by St. Augustine, Civ. Dei, &c. There is nothing, declared Mr. Gwilt, to afford any proof of the connection of this monogram with the form and plan of the churches erected during the mediæval period of the

Apology, perhaps, would be due for any digression upon it, had it not been for an opinion in favour of its use expressed by the late Professor C. R. Cockerell, whose talents and learning deservedly ranked high in the eyes of the public, in his essay on the Architectural Works of William of Wykeham, read 1845, before the Archæological Institute of Great Britain and Ireland. Ramée, in his Histoire, has also gone more at length into this subject Professor Cockerell likewise noticed that the writers of the 16th century, Cesariano 1521, Caporali 1536, and De Lorme 1576, recommend this figure, chiefly as that geometrical rule by which "two lines may be drawn on the ground at right angles with each other in any scale, according to the conception of Euclid's mind.”

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