CHAP. II. PRINCIPLES OF PROPORTION. SECT. I. GENERAL REMARKS. 2825. In undertaking to point out some of the mechanical methods of obtaining proportions of length, breadth, and height, in plans and elevations, as traceable upon geometric representations of the design, we would recall the reader's attention to the admirable remarks on the true nature of proportion made by the author of this Encyclopædia in Sect. I of the first chapter in this book. 2826. But, however just those remarks may be, they do not, any more than any of the mechanical means, result in success in the building as executed and seen in perspective. The ever varying relation between the sides of a mass, such as a Greek temple, can hardly be supposed to be at every moment equally beautiful in proportion, and the finest mediaval structure equally owes the satisfactory effect which it produces to the spectator's judicious choice of his point of view. Some very judicious observations on the rectification of proportions according to the position of the spectator are given by James Pennethorne, in his Elements and Mathematical Principles of the Greek Architects, 8vo., London, 1844. 2827. Before the probable effect in execution of an intended design can be ascertained, the designer must have well mastered the routine of drawing, as explained in the several sections on DRAWING, PERSPECTIVE, and SHADOWS, given in this work. He should likewise have familiarised himself with the varying effects of the changes resulting from points of view and alteration of light upon some building of which he may have opportunities to make studies in the usual GEOMETRIC DRAWINGS (explained 2490a. et seq.), so as to become imbued with that sense of general fitness of parts to the whole, which is meant by having the compasses in one's eye.' 66 2828-2837. The simpler such a building may be, the easier it will be at first to begin to acquire the power of anticipating correctly the effect in a design if it be executed: that power can then be applied to designs of more complicated character resulting from the various methods, which we are about to point out, of obtaining proportions. SECT. II. HORIZONTAL AND VERTICAL COMBINATIONS OF BUILDINGS. 2838. The different elements of a building are ranged by the side of or above each other, and in designing an edifice both these combinations must be kept in mind, though in the study of the subject, in order to lighten the labour, they may be separately considered. The two species of disposition are horizontal, as in plans, and vertical, as in sections and elevations. 2839. As respects horizontal disposition of the elements of a fabric, beginning with columns, their distance in the same edifice should be equal, but that distance may be varied as circumstances require. In buildings of small importance, the number is reduced as much as possible, on the score of economy, by increasing the distance between them; but in public buildings they should be introduced in greater number, as contributing to the greater solidity of the edifice by affording a larger number of points of support. They ought not, however, to be at all introduced except for the formation of porticoes, galleries, and the like subdivisions. The least distance at which they can be properly placed from a wall is that which they are apart from one another. This distance, indeed, suits well enough when the columns are moderately wide apart; but when the intercolumniations are small compared with their height and the diameter of the columns, their distance from the walls in porticoes must be increased, otherwise these would be much too narrow for their height, affording shelter neither from the sun's rays nor from the rain. On this account, under such circumstances, they may be set from the walls two or three times the distance between the axes of the columns. From this arrangement will result an agreeable and suitable proportion between the parts. 2840 The ceiling of a portico may be level with the under side of the architrave, or it may be sunk the depth of the architrave, which may return in a direction towards the walls, thus forming sunk panels in the ceiling, or the sinking of the panels may be as much as the whole height of the entablature, whose mouldings should then be carried round them. When several ranks of columns occur in a portico the central part is sometimes vaulted, the two central columns of the width being omitted. The method of disposing pilasters in respect of their diminution has been treated of in a former part of this work. (2671, et seq.) 2841. The exterior walls which enclose the building should run as much as possible in straight continued lines from one angle to another; a straight line being the shortest that can be drawn. The internal walls, which serve for subdividing the building into its several apartments, should, as much as may be, extend from one side to the opposite one. Where they are intercepted by openings, they should be connected again above by lintels or other means. 2842. In fig. 1013. is shown the method of forming a plan or horizontal distribution, and combining it with the vertical distribution in the section and elevation. The thing is so simple that it can hardly want explanation. The equidistant parallel axes being drawn and cut at right angles by similarly equidistant ones, the walls, according to the required accommodations, are placed centrally upon the axes; and the columns, pilasters, &c. upon the intersections of the axes. The doors, windows, niches, and the like are then placed centrally in the interaxes, which must be bisected for that purpose. Above and below the horizontal combination the section and plan are to be drawn. These vertical combinations are infinite, and from every plan many sections and elevations may be formed. The figure exhibits a building of one story only, with a central apartment occupying the height of two stories. But on the same plan a building of two or more stories may be designed. These may have two tiers of porticoes, one above the other, or one only on the ground story, forming by its covering a terrace on the first floor; or a portico might receive on its columns the walls of the next story, and thus become recessed from the main front. So, again, the stories may be equal in height, or of different heights, as circumstances may require. The most usual practice is, above a basement to make the succeeding story higher; but above a principal floor the height of succeeding ones is diminished. The method of placing orders above orders does not require that any addition should be made to what has been said on that subject in Chap. I. Sect. 11. of this Book, and by the same methods arcades over arcades may be conducted. 2843. Not the least important of the advantages resulting from the method of designing just submitted to the reader is the certain symmetry it produces, and the prevention, by the use of these interaxal lines on each floor, of the architect falling into the error of false bearings, than which a greater or more dangerous fault cannot be committed, more especially in public buildings. The subterfuge for avoiding the consequence of false bearings is now a resort to cast iron, a material beneficially enough employed in buildings of inferior rank; but in those of the first class, wherein every part should have a proper point of support, it is a practice not to be tolerated. Neither should the student ever lose sight, in respect of the ties he employs in a building, of the admirable observation of Vignola on the ties and chains proposed by Tibaldi, in his design for the baptistery at Milan: " Che le fabbriche non si hanno da sostenere colle stringhe; "- Buildings must not depend on ties for their stability. The foregoing figure is from Durand's Precis d'Architecture. We now submit, in fig. 1018., an illustration of the principles of interaxal division from the celebrated and exquisite Villa Capra, near Vicenza, by Palladio, wherein it will be seen, on comparing the result with what has actually been executed, how little the design varies from it. It will from this also be seen how entirely and inseparably connected with Fig. 1013. the horizontal are the vertical combinations in the section and elevation, the voids falling over voids, and the solids over solids. Whatever the extent of the building, if it is to be regular and symmetrical in its composition, the principles are applicable, and that even in buildings where no columns are used; for, supposing them to exist, and setting out the design as though they did exist, the design will prove to be well proportioned when they are removed. The full application of the principles in question will be seen in the works of Durand, the Précis and Cours d'Architecture, which we have used freely; and where we have had the misfortune to differ from that author, we have not adopted him. 2844. The student can scarcely conceive the infinite number of combinations whereof every design is susceptible by the employment of the interaxal system here brought under his notice; neither, until he has tested it in many cases, will he believe the great mastery in design which he will acquire by its use. In the temples and other public buildings of the an. cients, it requires no argument to prove that it was the vital principle of their operations, and in the courts, cavædia, &c. of their private buildings it is sufficiently obvious that it must have been extensively used. That its use in the buildings of those who are called the Gothic architects of the middle ages was universal, a glance at them will be sufficient to prove. The system of triangles which appears to have had an influence on the proportions of the early cathedrals may be traced to the same source (see the early translation of Vitruvius by Cæsar Cesarianus), and indeed, followed up to that source, would end in the principle contended for. 2845. It is impossible for us to prove that the interaxal system was that upon which the revivers of our art produced the astonishing examples many whereof are exhibited in our First Book; neither can we venture to assert that it was that upon which our great master Palladio designed the example above given, unquestionably one of his most elegant works; but, to say the least of the coincidence which has been proved between the actual design and the theory upon which it appears to have been founded, it is a very curious, and, if not true, a most extraordinary circumstance. Our belief, however, is, that not only Palladio but the masters preceding him used the system in question, and that is strengthened by the mode (not strictly, we allow, analogous) in which Scamozzi, in the tenth chapter of his third book, directs the student to adopt in buildings seated on plots of ground whose sides are irregular. 2846. To Durand, nevertheless, the public is greatly indebted for the instruction he has imparted to the student in his Précis d'Architecture more especially, and we regret that in our own country the art is treated by its professors too much in the manner of a trade, and that the scramble after commissions has prevented their occupation upon works similar to those which have engaged the attention of professors on the continent. The fault, however, is perhaps not, after all, so much attributable to them as to a government, whatever the party in power, till within the last five years (nay perchance even now) totally indifferent to the success of the fine arts, whose palmy days here were under the reign of the unfortunate Charles. Our feelings on this subject, and love for our art, betray us perchance too much into expressions unsuitable to the subject under consideration, and thereon we entreat, therefore, the patience of our readers, knowing we have a good conscience." 66 Fig. 1014. 2847. Our limits preclude the further enlargement on this part of the subject, which in detail would occupy the pages of a separate work, and which, indeed, from its nature, could not be exhausted. We trust, however, enough has been given to conduct the student on the way to a right understanding of this part of the laws of composition. SECT. III. SUBDIVISIONS AND APARTMENTS OF BUILDINGS AND THEIR POINTS OF SUPPORT. 2848. The subdivisions, apartments, or portions whereof a building consists are almost as many as the elements that separately compose them: they may be ranked as porticoes, porches, vestibules, staircases, halls, galleries, salons, chambers, courts, &c. &c. All these are but spaces enclosed with walls, open or covered, but mostly the latter, as the case may require. When covered, the object is accomplished by vaults, floors, terraces, or roofs, In some of them, columns are employed to relieve the bearing of the parts above, or to diminish the thrust of the vaulting. The horizontal forms of these apartments- - a general name by which we shall designate them, be their application what it may are usually squares, parallelograms, polygons, circles, semicircles, &c.; their size, of course, varying with the service whereto they are applied. Some will require only one, two, or three interaxal divisions; others, five, seven, or more. It is only these last in which columns become useful; and to such only, therefore, the system is usefully applied. The parts whereof we speak may belong to either public or private buildings: the former are generally confined to a single story, and are covered by vaults of equal or different spans; the latter have usually several stories, and are almost invariably covered with roofs or flats. 2849. When columns are introduced into any edifice to diminish the action of the vaults and increase the resistance to their thrust, the choice of the species of vault must be well considered. If, for example, the vault of a square apartment (fig. 1015.) of five interaxal divisions be covered with a quadrangular dome, or, in other words, a quadrantal cove, mitred at each angle, twelve columns would be required for its support. If the vault were cylindrical (fig. 1016.) eight columns only would be necessary; but if the form of the covering be changed to the groined arch (fig. 1017.), four columns only will be required. Supposing a room of similar form on the plan contained seven interaxal divisions each way, twenty columns must be employed for the coved vault, twelve columns for that whose covering was semi-cylindrical, and still but four for the groined vault. It is obvious, therefore, keeping economy in mind, that the consideration and well weighing of this matter is most important, inasmuch as under ordinary circumstances we find it possible to make four columns perform the office of twelve and even twenty. Here, again, we have proof of the value of the interaxal system, whose combinations, as we have in the previous section observed, are infinite. But the importance of the subject becomes still more interesting when we find that economy is inseparable from that arrangement whose adoption insures stability and symmetry of the parts. These are considerations whereof it is the duty of the architect who values his reputation and character never to lose sight. If honour guide him not, the commission wherewith he is intrusted had better have been handed over to the mere builder, — we mean the respectable builder, who will honestly do his best for his employer. 2850. What occurs in square apartments occurs equally in those that are oblong, for the first or square is but the element of the last. If it happen that from the interaxal divisions contained in the length of an oblong or parallelogram, the subdivisions will not allow of three bays of groins, it does not follow that the arrangement must be defective, for one may be obtained in the middle bay. In subdivisions of width, allowing five interaxes, at least four columns would be saved, and in those of seven interaxes eight columns might be dispensed with. (See fig. 1018.) 2851. When the subdivisions on the plan, supposing it not square, take in five interaxes which in the longitudinal extent of the apartment include several bays of groins, whose number must always be odd, one column is sufficient to receive each springing of the arch, but in those of seven interaxal divisions two columns will be necessary. (See fig. 1019, A.) 2852. If the vaulting be on a large scale, its weight and thrust are necessarily increased, and the columns may be changed into pilasters connected with the main walls, as in fig. 1020., or as II in the preceding figure. 2853. The height of the apartment from the floor to the springing of the arches will be found three interaxes in apartments whose horizontal combination is of five interaxes, and four and a half for the height to springing of such as are of seven interaxal divisions on the plan. Where the combinations are different in the adjoining apartments the heights just mentioned afford the facility of lighting the larger one above the crown of the lower one, as at B in fig. 1019. 2854. Sometimes the springing is from the walls themselves, as at C, fig. 1019., instead of from the columns as at L. The first of these arrangements should be permitted only when en suite with the apartment there is another, D, wherein the springings are from columns. When the apartment is the last of the suite, the springings must be from piers or columns, one interaxis at least from the wall. If all these matters are well understood, as also the sections upon the orders, and upon the different elementary parts of a building, a graphic combination has been established by which we shall be much aided in the composition or design of all sorts of buildings, and enabled, with little trouble, and in a much shorter period of time than by any other process, to design easily and intelligently. To do more distinguishes the man of genius from the man who can be taught only up to a certain point. SECT. IV. COMBINATION OF THE PARTS IN LEADING FORMS. 2855. Having shown the mode whereby the parts of a building are horizontally and vertically combined in the several apartments, which may be considered the grammar of composition, we shall now show its application in the leading forms or great divisions of the plan. Keeping in mind the advantage, upon which we have before touched, of arranging the walls of buildings as much as possible in straight lines, we should also equally endeavour to dispose the principal apartments on the same axes in each direction. Upon first thoughts the student may think that a want of variety will result from such arrangement, but upon proper reflection he will in this respect be soon undeceived. The combinations that may be made of the different principal axes are, as above stated, numberless, that is, of those axes whereon the parts may be advantageously placed so as to suit the various purposes to which the building is destined, paying also due regard to the nature of the ground whereon the fabric is to be erected |