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 (DecoraHx^cArt 
 
 STEALING 
 AND FRAN ONE 
 
 CLA1UC 
 ART INSTITUTE 
 LIBRARY* 
 
Digitized by the Internet Archive 
 
 in 2012 with funding from 
 
 Sterling and Francine Clark Art Institute Library 
 
 http://archive.org/details/powerofformappliOObill 
 
THE 
 
 POWER OF FORM 
 
 APPLIED TO 
 
 (Stomeirit Cramg. 
 

POWER OF FORM 
 
 APPLIED TO 
 
 GEOMETRIC TRACERY. 
 
 §u funked gtsips ttitb t|jeir Jfoitithfiniis 
 
 RESULTING FBOlf 
 
 By ROBERT WILLIAM BALLINGS, Architect, 
 
 ASSOCIATE OF THE INSTITUTE OF BRITISH ARCHITECTS, 
 
 AND 
 
 HONOBAEY MEMBER OF TEE SOC1ETT OF ANTIQUARIES OF SCOTLAN-D. 
 
 "Keep toitfifinnc romjiaBBS, bd stall d« H i 
 
 PUBLISHED FOR THE AUTHOR 
 
 BY 
 
 WILLIAM BLACKWOOD AND SONS, 
 
 46, GEORGE STREET, EOINEURGH; 
 
 AND 37, PATERNOSTER ROW, LONDON. 
 
5JP 
 
PREFACE. 
 
 The Author of this treatise was first in the field to prove, 
 that not only was the whole detail of Gothic Architecture 
 founded upon geometric law, but that the power of design 
 still remained with us, waiting only for its application. In 
 addressing himself to the learner, for whose especial use his 
 labours here are intended, he does not wish for one moment 
 to question the previous knowledge upon this subject possessed 
 by many practised Architects, who must have travelled over 
 the same ground as himself in searching for the primary 
 elements of their profession. 
 
 But whatever the knowledge of others may have been 
 upon our present subject, it has not been given to the world, 
 and the Author s claim holds good as the originator of the 
 conjurations embodied here and in other works, and which, 
 like all sleight-of-hand tricks, are very easy. In short 
 everybody can do them — that is, when they know how. 
 
 The general circulation of works on art has been limited 
 by the high price demanded in return for costly production, 
 and thus their general good has been all but lost, because 
 their purchase has been beyond the means of those for whom 
 they were intended. In extenuation of this unfortunate 
 position, it must be admitted that, unlike the works of writers, 
 
 a 2 
 
VI PREFACE. 
 
 their expense is not limited by merely transferring the labours 
 of the brain to the types of the printer, for there is drawing, 
 expensive engraving, and the great cost of printing from 
 copper or steel plates. 
 
 For the first time, during a career of some experience in 
 the publication of architectural works, the producer has 
 changed his tactics, to meet, if possible, the case he has 
 stated. His drawings have been engraved on wood, by his 
 friend Robert E. Branston, whose known ability, both as an 
 artist and a man of business, needs no eulogium here. 
 
 The cost of wood block engravings is upon a par with 
 that of plates ; but here all comparison ends ; and the mere 
 question of paper and print has enabled the Author to place 
 the results of his labour within the means of all who may be 
 interested in the principles he has endeavoured to embody. 
 
 And thus his volume, possessing possibly as much novelty 
 as many romances of the day, is produced with all the cost of 
 illustration, at a less cost to the public than is usually made 
 for a single volume of that class. 
 
 St. Mary's Road, 
 
 Canonbury, London. 
 January, 1851. 
 
To the Student, in his just desire to cultivate the Art of 
 Design, and to those whose hands fashion the creations 
 of the Artist, a new series of leaves upon one of its 
 branches cannot fail to be of immediate interest ; and, were 
 the motive power of Art unanimous upon its advance, our 
 preliminary Essay upon the illustrations comprising the 
 present book, would be necessarily short— our road would 
 indeed be pleasant travel, for we should be sure of a 
 reception as the possible contributor of new stores to its 
 ever varying wants. But we have, unfortunately, to regret 
 that there is a class, and that a very numerous one, who 
 act in all matters concerning Architecture, and the Arts sub- 
 servient to it, as though every thing had been accomplished, 
 that nothing remained for the present or future ages of 
 Architects and Artists generally, but to be continually 
 jumbling together the productions of their forefathers, and 
 then to dignify them with the title of Designs. We can 
 thus fancy the dismay of our mere "antiquity-lovers" at 
 the announcement of an extension of the field of design, 
 entered by means of that which is known as the Gothic style. 
 Opposed to the negative state of art we have described, 
 and protesting most emphatically against the fettering, nay, 
 
8 
 
 of absolutely staying progress in any branch of knowledge 
 by slavish adhesion to mere precedent, we venture to place 
 before the world a production, claiming (although by merely 
 playing with compasses), that much to be desired qualification, 
 originality. Fancied inventors of a theme are generally 
 enthusiasts upon their subject, and doubtless the Author of 
 the present attempt will be pronounced one, when he 
 ventures to describe it as the re -opening of a shaft to the 
 mine of ornamentation, which at the very surface has pierced 
 a vein it will be indeed difficult to exhaust in the working. 
 Nay, in the experience gained by practice, he goes further, 
 and asserts the impossibility of accomplishing such a task ; 
 for to the skilled artist there is no more difficulty in exhibiting 
 new combinations of form than is experienced by the musical 
 composer in producing changes of sound, or by the arith- 
 metician in varying the power of numbers. 
 
 It may be repeated, that there is no real difficulty ; and 
 further, that an advance as palpable as its hitherto admitted 
 retrogression, would have been made in Architecture, as time 
 has produced in other Arts, had the forward movement not 
 been stopped by that extreme veneration for antiquity, which 
 has reached such an absurd point, as to declare all progress 
 at an end — that the modern race of Architects are only 
 to retail the wealth already created, and not to gather for 
 themselves fresh stores from the ever increasing fields of 
 knowledge. It is fortunate, however, for Art, that there 
 are other classes, deeply interested in its progress, and 
 it is to them we would address the few words elucidatory of 
 the object of our work, and by way of introduction to 
 
the Designs, which can be read without the aid of any very 
 voluminous essay. Indeed, it may be fairly asked whether 
 they require an essay, for their true reading is arrived at by 
 the mere use of a pair of compasses. 
 
 The more we examine the powers of Design developed by 
 the aid of fixed diagrams, or foundations, the more absurd does 
 it appear, that ever since the revival of Gothic Architecture 
 we should have gone on for ever copying — taking it for 
 granted as a preliminary that all possible combinations were 
 exhibited in the works of our predecessors ; considering, in 
 short, that the mine was exhausted, that the works completed 
 some hundreds of years since were a " finality, " when in 
 fact, and notwithstanding all that the ancient Architects 
 accomplished in the field of decorative design, they scarcely 
 explored its boundary, while the vast and unlimited space 
 lying beyond is still untrodden. So great, indeed, is the 
 power of this mechanical field of Art, and so simple its 
 cultivation, that it is absolutely easier to produce new 
 combinations than to copy old ones. Of this fact there can 
 be no doubt, and any Artist may prove it by the most 
 cursory study of the subject ; but beyond the mere saving 
 of absolute labour in production, and far above the mere 
 credit due to the most exquisite copy, there is the satisfaction 
 and the pride all men should feel when they have produced 
 an original instead of a repetition, and this, by simply 
 adhering to the same unerring laws of truth which guided the 
 medieval artists in their productions. 
 
 Every eye admires the wonderfully elaborated screen- 
 work, the gorgeous windows of " airy tracery," (whose fragile 
 
10 
 
 appearance would almost seem to contradict an existence of 
 centuries), the intricate network enveloping many of the 
 magnificent towers of the Continental Cathedrals, and in 
 some cases those of our own land ; and why should we not 
 inherit the spirit which animated their Architects ? There is 
 no mystery about the matter, for all are designed upon the 
 most simple of geometric laws, as palpable now as they 
 were of old. Shall we not therefore be permitted to make use 
 of these laws, when it is known that combinations innume- 
 rable may be produced ? Shall our original designs not be 
 allowed to stand on their own merits side by side with the 
 emanations of our forefathers % 
 
 We advocate the extension of knowledge by their 
 experience ; we urge the attainment of their spirit — but 
 while admiring beyond measure their beauties, we protest 
 against mere copyism of their works, as fatal to progression 
 in Art, and as rendering the would-be Artist essentially 
 a mechanic, whether he be a Painter, a Sculptor, or an 
 Architect. Painters do not permit the admirers of pictures to 
 reduce their art to this degraded state, neither do Sculptors 
 rise as mere adaptors of former works, or, speaking plainly, 
 as mechanics — why then should the professor of the noble 
 art of Architecture (without whose protection not one of the 
 sister arts would be able to preserve their productions), be 
 chained to slavish imitation of the buildings of his ancestors, 
 or be prevented from soaring to a higher pitch by the dogmas 
 of amateurs, who can at the best obtain but a smattering 
 of that art whose alphabet is, unfortunately, too easily 
 comprehended, whose general form of words is too easily 
 
11 
 
 recognised, but the profundity of whose language is proved 
 daily by the lack of originality and signal success, in the 
 productions of its most deeply learned Students. It is time, 
 indeed, that a change came over the spirit of the dream, and 
 surely nothing in this age of progression will raise the 
 Architect but the production of original works. He must 
 in short, prove to the world, that if in some cases there is 
 
 truth in the olden rhyme — 
 
 " 9ftg line anti rule foorfcg tnang a fool." 
 
 the opposite and more recent adage is applicable to him, 
 which states in answer that in the composition of such fools 
 the wise man predominates. 
 
 Independent, however, of the baneful effects of influence 
 from without, there has been a division in the camp, perhaps 
 more fatal to Architectural progression than the cause 
 stated ; and although the non-progressive feeling is greatly 
 changed by the spread of mechanical knowledge, it is deeply 
 to be regretted that many of our Architects, while admiring 
 the multifarious designs of medieval art, have declared that 
 they were the result of mere chance, little dreaming of the 
 mischief they were inflicting on their art. Chance, indeed ! 
 It had no more to do with design than it has now, and the 
 sooner the notion is utterly discarded the better, for it is only 
 by admitting at once, and without reservation, the fact of 
 mechanical foundations, that we can ever rise to the creative 
 power, — to that point where the mechanic ends and the 
 artist begins. 
 
 Briefly then, but forcibly, we may ask, what is among the 
 chief merits apparent on the face of all the great compositions 
 
12 
 
 of the old Masters in painting and sculpture? — that quality 
 requiring to be attended to before they dared to attempt the 
 finish of their works ! Is it the existence of a particular 
 geometric figure, or leading line, or is it otherwise ? Has 
 the existence and repetition of the triangle, the circle, — the 
 ogee, or line of beauty, — the radiation of lines and curves, — or 
 the wonderful adaptation of mere vertical or horizontal lines 
 in their pictures, and their sculptured groups, nothing to 
 do with the merits for which the world unconsciously admires 
 them ? There is no possibility of giving more than one 
 answer to the question, and that is, their undoubted founda- 
 tion upon principle. 
 
 If it cannot be denied that geometric laws are evident upon 
 the works of the painter and sculptor, we may fairly ask the 
 objectors to their existence in architectural design, if the 
 common trefoil or quatrefoil of Gothic Architecture is or is 
 not Geometric \ Let any man who fancies the contrary, try 
 to form them without the aid of compasses, and he will be 
 speedily undeceived. Do the adversaries of order for one 
 moment doubt that the pointed arch of architecture is formed 
 of the axes of circles ? They may just as well repudiate the 
 existence of the equilateral triangle, from the points of whose 
 base the first pointed arch was struck. As well might they 
 question the circular form of arches, general previous to the 
 introduction of the pointed form ; we say introduction, for 
 its origin is coeval with the first existence of geometry, and 
 founded upon that figure whose perfect form has been for 
 countless ages used as typifying the unity of the Trinity. 
 Let the unbeliever in this matter go to any freemason and 
 
13 
 
 ask, if the equilateral triangle has anything to do with his 
 secret knowledge ? Talk of working the forms appertaining 
 to Architecture, by rule of thumb, that is, by hand, and 
 without the aid of geometry, forsooth ! It would be just as 
 absurd, just as unreasonable, to ask the artificer to produce 
 good masonry without the use of the square, or the plummet 
 and level. The mechanic would have too much common sense 
 to attempt such a gross breach of practical knowledge ; and 
 surely if this be the case, those who claim to be his superior 
 as artists, should at once and for ever discard the error. 
 
 The diagram chosen as the foundation of our work 
 contains perhaps more than any other geometric figure 
 the power of variation, and we have by no means exhausted 
 its fertility of change. Nay, 
 we can hardly be said to have 
 fairly opened out its vast, its 
 endless, powers of combination. 
 In its primary form it will at 
 
 once be universally recognised 
 
 as the kite star of the schoolboy, 
 
 the very first geometric figure 
 
 the child produces when playing 
 
 with a pair of compasses, by simply striking the radius of a 
 
 circle round its circumference. 
 
14 
 
 In its second form, by the 
 lines cutting through these 
 points on the circumference of 
 the circle, and passing through 
 its centre, we have the skeleton 
 of our diagram, thus : — 
 
 The third form is the perfected 
 figure upon which our designs 
 are produced. It is simply the 
 introduction into the previous 
 figure of three equal circles in 
 contact. 
 
 We have a most remarkable coincidence, and matter for 
 the consideration of the learned, when we reflect that the 
 very first geometric figure, formed intuitively by the child in 
 playing with a pair of compasses, marks in its progress 
 a diagram, known to the initiated as embodying the 
 
15 
 
 profundities of masonic mysteries. The perfections of this 
 figure need no description, for they are evident to the most 
 uneducated eye — but we may remind the reader that whether 
 we regard it as formed by lines or by curves, and whether 
 these are represented as convex or concave, the crafty symbol 
 patent over the whole world, and during all time, still remains 
 
 the same. Our illustrations here are sufficient ; but the reader 
 who wishes to investigate this matter further will find it fully 
 treated of in the 7th chapter of the fifth book of Vitruvius. 
 
 To those who have the knowledge of architectural detail, 
 our diagrams and their results need no particular explanations, 
 but to the uninitiated it may be necessary to state, that the 
 actual diagram, or skeleton pattern, exhibited upon the 
 succeeding pages, does not appear in the completed pattern, 
 being a primary central line (a), used merely as a key 
 
 for placing the expression of mouldings upon it. So 
 
10 
 
 soon then as the result appears this foundation line is 
 removed. We give the sections of mouldings applicable 
 to our designs, for all the varieties will apply correctly 
 as outlines, although the light and shade, from the 
 variety of contour, would be very different. There may be, 
 however, forms of mouldings in which the central or pro- 
 jecting line of the diagram appears — that is where the upper 
 member comes to a point, thus. In particular situations this 
 
 form is effective, but generally 
 speaking the fillet on the top, 
 or nose, as it is commonly called, 
 is by far the most pleasing in its 
 results. 
 
 After forming the lines of the diagram we proceed to 
 those indicated by the section, above the line &. These 
 generally run unbroken, through a composition as a frame- 
 work, while the portion below (b, c), is continually separated 
 into minor detail. It is indeed to this beautiful arrange- 
 ment, to this exquisitely simple combination of primary and 
 secondary forms that medieval architecture owes the peculiar 
 charm — that projecting and recessing of parts which dis- 
 tinguishes it from more recent examples, as essentially 
 containing the elements of the picturesque. And it is the 
 absence of this quality which marks so decidedly the failure of 
 nearly all modern attempts at imitation. 
 
 In a former work* upon another branch of our present 
 
 * "The Infinity of Geometric Design, by Robert William Billings." 
 William Blackwood and Sons. 1849. 
 
17 
 
 subject it was stated that the object was "to carry one 
 diagram to what would appear the possible limits of its 
 varying power." This diagram 
 is here exhibited, and it may be 
 briefly stated, that the power 
 of variation exists principally 
 in the enclosed spaces lying 
 within the large circle, and 
 between the four smaller ones 
 contained within it. Now, if 
 
 we enlarge the enclosed circles these spaces become con- 
 tracted, and so does the power of variation. As we carry 
 out this principle of enlargement, the field becomes smaller* 
 until at last when the circles nearly touch each other, the 
 power of production has fairly ceased, for it is only a few 
 peculiar combinations which are then producible. At least, 
 this conclusion is the author's result. 
 
 But carrying the experiment further, a result is given 
 totally differing from the conclusion just formed, for no 
 sooner are the enclosed circles made to come in contact than 
 a new and even greater power appears than that of our first 
 
 essay, where, as we have just stated, the circles were discon- 
 nected, and to this circumstance may be traced the origin 
 of the present series. As in the first series, the secondary 
 foundation of design in combination with four circles, was 
 necessarily the square, or the octagon, (two figures agreeing 
 in numbers with the primary diagram), so in the present effort 
 the secondary form, in connection with the three inclosed 
 
 circles, is the equilateral triangle or the hexagon. Now, 
 
 o 
 
18 
 
 every geometrical figure numbering upward will be found, 
 upon the most cursory trial, to contribute its quota to this 
 most easily accessible field of design, of this inexhaustible 
 mine of linear development. 
 
 The truth of this general statement cannot be doubted, but 
 of all geometric forms, the triangle as a foundation for 
 design possesses greater power of variation than any other 
 figure. Speaking of the circles here placed in connection 
 with this primary form, we simply state, that the power 
 of the combined diagram is materially contracted by them, 
 and by the larger circle enclosing the whole. Thus there is 
 frequently great difficulty in varying the small central tri- 
 angle formed by the junction of the enclosed circles, and a 
 still greater difficulty in conquering the monotony of the 
 spandrils on their outer boundaries ; for it must b£ remem- 
 bered that the task we have proposed, is, in every design, to 
 retain distinctly all the enclosing circle, and all or the greater 
 part of those enclosed, in order that the same framework 
 may be distinguished amidst the various expressions of form 
 arising from a common foundation. 
 
 Most extraordinary it is to watch the changes produced by 
 mere expression, for although the same skeleton appears in 
 our whole collection, nothing can be more different than the 
 results. It is, in short, with Tracery as with the human face, 
 and even lower in the scale of animal life. Every human 
 face has the same features in common, but what a field of 
 contemplation— what wonderful variety does the mere 
 difference of individual expression present to us, even if we 
 confine our observations to members of the same family. 
 
19 
 
 They are, in fact, so many different designs, and woe to the 
 race of portrait painters were this state of affairs to be 
 changed. Let the disbeliever ask any shepherd if he does 
 not know every one of his flock by their facial differences ? 
 We claim then for the patterns in our work, that the 
 variation of design upon the same diagram may be regarded. 
 
 -Sri { 
 
 as so many modes of expression, or in fact "as so many 
 varied faces having the same bones. 
 
 One glance at the collection of designs here presented will 
 convince the observer that none of the ordinary figures apper- 
 taining to Gothic Architecture have been used, excepting 
 indeed as perfectly subsidiary to the general form. Thus, 
 under the head of what has been usually termed design, 
 the three circles of our diagram might each have been 
 filled with a trefoil, a quatrefoil, a cinquefoil, and so 
 upward in number. Then, again, each of these figures 
 might have enclosed a foliated or other ornamental boss 
 in their centre, and the spandrils might have been varied 
 to an interminable extent by objects from the animal and 
 vegetable kingdom. But all these have been purposely 
 avoided, in order to prove the amount to be accomplished 
 with mere tracery, (a subject once supposed to be perfectly 
 exhausted), if we would but believe in the capability of 
 producing new combinations. 
 
 Foliage is here spoken of, as subservient to Tracery, but 
 foliated design upon geometric foundation was in extensive 
 use centuries before the invention of Gothic windows ; and 
 that luxuriant display of form which has given such 
 
 imperishable interest to the buildings of the fourteenth and 
 
 c 2 
 
20 
 
 fifteenth centuries, was merely an offshoot from mechanical 
 foliation, being literally branches without leaves. But in 
 our present effort, (intended only to facilitate the student 
 in the use of mechanical principles) it was determined at 
 starting to adhere strictly to mere framework, leaving all 
 attempts at leafwork utterly out of the question ; for as yet the 
 world is hardly prepared to admit even the geometric origin 
 of Tracery, much less of the ornamental leaf work of Archi- 
 tecture, although their originals, — the very flowers of the 
 field, have been impressed with this perfection of form by the 
 hand of the Great Creator. Let the sceptic examine the 
 simple daisy, and if he be not convinced, then let him turn 
 to the perfect geometric radiation of the cells of the sunflower. 
 They are only equalled in geometric perfection by the hex- 
 agonal cell of that most industrious insect architect the bee. 
 
 The leafy origin of Tracery is undoubted, and is proved by 
 the terms of its own detail, for what are its projecting orna- 
 ments or points called? They are trefoil, quatrefoil, or 
 cinquefoil, that is three-leaved, four-leaved, or five-leaved, 
 according to the number of circles used in their formation, as 
 the accompanying figures testify. 
 
21 
 
 In some examples these points or foils are (by the close 
 proximity of the circles) very thin. But, numberless ancient 
 specimens prove, that when the circles are smaller, and, conse- 
 quently, more apart within the 
 space occupied by the whole 
 figure, the points become broader. 
 When this occurs they are fre- 
 quently cut into the form of 
 leaves, thus becoming what their 
 name actually implies. 
 
 The mechanical practice of form is always important to 
 the artist, because it makes him familiar with the correct 
 manipulation of detail. And if his knowledge on this head 
 becomes ultimately secondary to effect, it should precede it, 
 for all works of art should bear examination in respect of 
 absolute correctness. If this merit be wanting, they are 
 indeed valueless, excepting for mere show. Were there no 
 other advantage gained by the practice of mechanical design 
 than the habit of calculation, or the methodical spirit which it 
 engenders, it is maintained that these would well repay both 
 the artist and the workman. 
 
 But there are other considerations, and among these, 
 especially to the Architect, the study of the geometric 
 ramifications of Tracery is the key to the restoration of 
 ancient examples, of which time or wanton destruction has 
 but too frequently left us hardly so much of the skeleton 
 as would enable an architectural Cuvier to decipher and 
 declare the order. We may instance the numberless ruins 
 of ancient Churches, of whose once gorgeously . traceried 
 
22 
 
 windows nothing now remains, save the stumps of their 
 severed branches. Yes ! to the initiated in the knowledge of 
 geometrical design these shattered fragments are bones suf- 
 ficient to declare the skeleton, — they are the leaves through 
 which the whole book may be read. By its means the 
 studies of the Architect may benefit art, and create a new 
 fame for his predecessors, by rescuing their works from 
 oblivion. 
 
 The collection of Designs following this introductory Essay 
 may be regarded as experiments merely elementary, upon 
 Tracery, whose framework, by the aid of mechanical diagrams, 
 can be reproduced by any one capable of handling a pair of 
 compasses. Nevertheless, they are not without interest to 
 those more advanced in art, as solving much of the apparent 
 mystery which until recently enshrouded the ramifications of 
 a principal ornament in Gothic Architecture. 
 
 In a large number of Designs, where each bears distinctly 
 
 a common foundation in the result, it must not be expected 
 that all the combinations can be equally successful. It 
 is frankly admitted, that some are peculiar, and others may 
 be called even by a harsher name — but if the case be so 
 with the present series, it is equally so with many examples 
 having only antiquity to recommend them. It is not to be 
 expected that every human face shall be regular in feature, 
 or what is termed pretty, but there may be a quality very 
 far superior — there may be the beauty of expression, 
 marking without doubt the lasting triumph of mind over 
 matter. 
 
 Our present attempt is presumed to be so many varia- 
 
23 
 
 tions upon the same amount of material within the same 
 space, that is to say, it will generally be found that each 
 design has nearly the same number of spaces within an 
 unvarying framework. It is necessary to state this, as a 
 reason for the absence of still greater changes than we 
 have shewn, for by multiplying the number of openings 
 within a given space, or by reducing them, we should in 
 either case be walking into another field of design. 
 
 No difficulty can occur to the student in delineating our 
 productions, because each design has its geometric diagram 
 placed upon the opposite page, with the curves and lines 
 of which they are composed, numbered in the order of 
 formation, and the pons asinorum of Euclid thus needs 
 hardly to be passed in order to comprehend their formation. 
 Following these diagrams successively, the student will find 
 that the mere delineation of one subject gives the clue to 
 other designs ; and so rapidly do the suggestions of varied 
 combinations press one upon another, and apparently, almost 
 without mental efiort, that the subjects may almost be said 
 to come to hand ready designed. 
 
 The application of a principle is surely no part of an 
 author's business. It is fit occupation for those directly 
 interested in the various productions or manufactures to 
 which his raw material may be made subservient, but as 
 it is possible that the author of these productions may 
 again be asked the question, ' c Cui bono?" he deems it 
 right to say a few words by way of anticipation. He might, 
 indeed, shelter himself under the plea of the value of any 
 original contribution be it ever so humble, to our stores 
 
of knowledge ; but there is not the slightest occasion for 
 this unanswerable argument. 
 
 Briefly, then, his wish is to aid in destroying that endless 
 repetition which disgraces our modern buildings, expressed 
 sarcastically as the 'artificial infinite/ by proving that we 
 have the power of producing the reality of infinity. 
 Supposing, (contrary to all modern practice) that a great 
 building had to be erected, in which every window, and 
 every ceiling, the doors, wall decorations, screens and 
 furniture, required not fifty, but fifty thousand different 
 designs, they could be produced by the aid of fixed diagrams. 
 Thus we have only to travel from the question of tracery, to 
 take its framework as branches, and then fit upon them the 
 leaves and blossoms of the vegetable kingdom. There will 
 be found the number at once, each and all merely depending 
 upon the ability displayed, as to whether they are or are not 
 to be classed as works of art. 
 
 Suppose, again, he recommends the application of his 
 designs, to ornamental castings of all kinds, or even the 
 adaptation of their principles to the framework of all kinds 
 of machinery, for the flowing forms of medieval art can 
 be far more easily adapted to any change required for 
 strength, than the set laws of classic architecture ; and 
 besides this reason there is the desirableness of cultivating 
 our own nationality in art. Or turning to matters of 
 ordinary life, let us ask. Why should not a good circular 
 geometric pattern be as applicable for the decoration of a 
 common plate as that most extraordinary and far-famed 
 willow, or Chinese pattern, whose chief merit is, that it 
 
25 
 
 contains more errors of Drawing than those intentionally- 
 displayed in Hogarth's equally celebrated delineation of 
 Perspective Improved ? 
 
 Objectors to works upon Architectural principles start up 
 at every point ; every step taken to elucidate them is at 
 once considered an innovation, rather than an advantage, 
 and strangely enough, the enunciators are received with 
 marked suspicion, as though they had some hidden 
 motive, some undeflnable and selfish object in view, rather 
 than the desire of bringing forward a simple truth. 
 Amongst other defects attributed to the present examples it 
 has been asserted that the designs were made first, and the 
 diagrams then fitted to them — equivalent to the absurdity 
 of saying, that the manufactured article could be produced 
 before the raw material was provided. But, to be serious, we 
 may at once affirm, that the results of Nature's operations 
 are displayed in the most beautiful patterns, and these cannot 
 be delineated with certainty without fitting them to a geometric 
 diagram, whether we instance the rainbow, the honey- comb, 
 the flowers of the field, or the star-fish of the deep. 
 
 Further, let it be asked, where has our still increasing 
 store of knowledge regarding the principles of architecture 
 sprang from, if it be not from the mere fixing of diagrams, 
 which the result of investigation has proved to belong to 
 ancient exemplars — which the patient searcher has proved 
 to be the title-deeds of those vast estates of art we now 
 possess, but whose descent to us is a mystery ; for 
 the secret working of the ancient freemasons, once patent 
 all over Europe, (as the universality of their productions 
 
26 
 
 declare), was utterly lost during the period of the Reforma- 
 tion, when the glare of new light, emanating from the lamp 
 of religious freedom, effectually dimmed, if it did not utterly 
 extinguish, the glimmering taper of architectural knowledge. 
 
 Perhaps enough has been said to answer the objection 
 alluded to ; but there is another not yet stated, which 
 affirms that the designs belong to the kaleidescope, — a term 
 utterly inapplicable, unless indeed the power of reproduction 
 may be said to equal that machine. Kaleidescope designs 
 or patterns are purely mechanical — they are either so 
 many sectors of a circle, or else so many radiations from 
 a common centre ; and a glance will convince any person 
 with the slightest knowledge of Geometry, that the present 
 Designs are not at all of that class. 
 
 Supposing, for the sake of argument, it be admitted that 
 they were first designed, and then reduced to a geometric 
 principle or calculation, it is after all only the minor parts 
 to which the observation can possibly apply, for all are 
 based upon one unvarying foundation ; and this compels an 
 adhesion to geometric law, from which there is no escaping 
 in the general result. 
 
 Order, in short, is the foundation whence they 
 originate, and the pediment in which they terminate. 
 
IIuKfratlans. 
 
I. 
 
 II. 
 
III. 
 
 IV. 
 
VI. 
 
VII. 
 
 VIII. 
 
D 2 
 
IX. 
 
XI. 
 
 211. 
 
XIII. 
 
 XIV. 
 
XV. 
 
 The small unnumbered circles are repetitions of 7. 
 
 XVI. 
 
 The curves Nos. 1 and 4 are of similar radius. 
 
XVII. 
 
 The curves Nos. 4 to 8 are all of one radius, that of the primary circles. 
 
 XVIII. 
 
XL 
 
 XX. 
 
xx r. 
 
 XXII. 
 
XXIII. 
 
 XXIV. 
 
XXV. 
 
 XXIV. 
 
 The arcs 1. 2. 3. are of the same radius. 
 
XXVII. 
 
 This tracery is formed entirely of one secondary curve and the three inclosed 
 circles. Nos. 1. to 8. are therefore so many repetitions. 
 
 xxvni. 
 
XXIX. 
 
 XXX. 
 
XXXI. 
 
 XXXII. 
 
xxx in. 
 
 XXXIV. 
 
 The curves 1. to 4. are repetitions. 
 
XXXV. 
 
 xxxvi. 
 
 It is not the number of different curves that always produces the best patterns ; 
 thus the principal frame of this pattern is the repetitiou of circles 1. 
 
XXXVII. 
 
 XXXVIII. 
 
F 
 
XXXIX. 
 
 XL. 
 
F V 
 
XM. 
 
 XLII. 
 
xlui. 
 
 XLIT. 
 
XLV. 
 
 X LVI. 
 
XLVII. 
 
 XLVIII. 
 
 *•• 
 
 This example is almost wholly the repetition of one curve. Thus, Nos. 1. to 5. 
 
 are all of equal radius. 
 
XLIX. 
 
 L. 
 
LI. 
 
 LII. 
 
Mir. 
 
 Here the circles 3 and 4 are of equal size. 
 
 LIV. 
 
LV. 
 
 Here the circles 1 and 3 are repetitions. 
 
 LVI. 
 
 In this example No. 2 is a repetition of 1, and 3 and 4 are equal circles. In the 
 minor tracery all the foil heads are repetitions of one circle. 
 
a 2 
 
LVII. 
 
 Numbers 1, 2 and 3 are repetitions of one curve. 
 
 LVIII. 
 
LIX. 
 
 Numbers 1, 2 and 3 are repetitions. 
 
 LX. 
 
LXI. 
 
 LX1I. 
 
LXIII. 
 
 The curves 4, 5, 6, 7, are repetitions of one radius. 
 
 LXIV. 
 
LXV. 
 
 LXVI. 
 
lxvii. 
 
 LXVIII. 
 
 The curves 2, 3, 4, are repetitions. 
 
LXIX. 
 
 LXX. 
 
 Here numbers 1 and 2 are of the same radius. 
 
LXXI. 
 
 LXXII. 
 
 Number 1 and 2 are similar, and so are numbers 3 and 4. 
 
LXXIII. 
 
 LXXVI. 
 
LXXTI. 
 
LXXVII. 
 
 LXXVIII. 
 
 The circles Nos. 5 and 7 are equal. 
 
LXXIX. 
 
 LXXX. 
 
 The curves 2 and 3 are repetitions. 
 
LXXXI. 
 
 LXXXII. 
 
LXXXIIL 
 
 LXXXIV. 
 
 Number 6 ; 7, 8, are similar curves. 
 
LXXXV. 
 
 LXXXVI. 
 
LXXXVII. 
 
 LXXXVIII. 
 
 Curves 1, 2, 3, 4, are the same curves, and 5, 6, are also equal. 
 
LXXXIX. 
 
 The radius of curve 1 is the diameter of the outer circle. 
 
 xc. 
 
 The arcs 1, 2, are of the same radius ; and Nos. 4, 5, and 6, are also similar. 
 
ICL 
 
 XCII. 
 
XCIII. 
 
 The radius of this curve is the diameter of the outer circle. 
 
 XCIV. 
 
xcv. 
 
 The radius of Nos. 1, 2, 3, is the diameter of the enclosing circle. 
 
 XCVI. 
 
 The radius of 3, 3, is the diameter of the outer circle. 
 
 of the same radius. 
 
 Nos. 4, 5, are curves 
 
XCVII. 
 
 XCVIII. 
 
 Nos. 4, 5, 6, and 7, are circles of the same size. 
 
XCIX. 
 
 c. 
 
 The repetition of one curve may almost be said to form this, our concluding example, 
 for the curves numbered 3, 4, 5, <5, 7, 8, are all of one radius. 
 

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