reducing the height of the risers without giving a correspondent width of tread to the step is inconvenient and unpleasant. SECT. XXIV. CEILINGS. 2815. Economy has worked so great a change in our dwellings, that their ceilings are, of late years, little more than miserable naked surfaces of plaster. This section, therefore, will possess little interest in the eye of speculating builders of the wretched houses erected about the suburbs of the metropolis, and let to unsuspecting tenants at rents usually about three times their actual value. To the student it is more important, inasmuch as a welldesigned ceiling is one of the most pleasing features of a room. 2816. There is, perhaps, no type in architecture more strictly useful in the internal distri bution of apartments than that derived from timber-framing; and if the reader has understood our section on floors, he will immediately see that the natural compartments which are formed in the carpentry of a floor are such as suggest panels and ornaments of great variety. Even a single-framed floor with its strutting or wind-pieces between the joists, gives us the hint for a ceiling of coffers capable of producing the happiest effect in the most insignificant room. If the type of timber-framing be applied to the dome or hemispherical ceiling, the interties between the main ribs, diminishing as they approach the summit, form the skeletons of the coffers that impart beauty to the Pantheon of Agrippa. We allude thus to the type to inculcate the principle on which ornamented ceilings are designed, being satisfied that a reference to such type will insure propriety, and bring us back to that fitness which, in the early part of this Book, we have considered one of the main ingredients of beauty. If the panels of a ceiling be formed with reference to this principle, namely, how they might or could be securely framed in the timbering, the design will be fit for the purpose, and its effect will satisfy the spectator, however unable to account for the pleasure he receives. Whether the architrave be with plain square panels between it and the wall, as in the temples of the Egyptians, or as at a later period decorated with coffers, for instance in the Greek and Roman temple, the principle seems to be the same, and verifies the theory. The writer of the article "Plafond" in the Encyc. Meth. has not entered into the subject at much length, nor with the ability displayed in many other parts of that work; but he especially directs that where a ceiling is to be decorated on the plane surface with painting, the compartments should have reference to the construction. With these preliminary observations, we shall now proceed to the different forms in use. Ceilings are either flat, coved, that is, rising from the walls with a curve, or vaulted. They are sometimes, however, of contours in which one, more, or all of these forms find employment. When a coved ceiling is used, the height of the cove is rarely less than one fifth, and not more than one third the height of the room. This will be mainly dependent on the real height of the room, for if that be low in proportion to its width, the cove must be kept down; when otherwise, it is advantageous to throw height into the cove, which will make the excess of the height less apparent. If, however, the architect is unrestricted, and the proportions of the room are under his control, the height of the cove should be one quarter of the whole height. In the ceilings of rooms whose figure is that of a parallelogram, the centre part is usually formed into a large flat panel, which is commonly decorated with a flower in the middle. When the cove is used, the division into panels of the ceiling will not bear to be so numerous nor so heavy as when the ceiling appears to rest on the walls at once, but the same sorts of figures may be employed as we shall presently give for other ceilings. If the apartment is to be highly finished, the cove itself may be Fig. 1005. Fig. 1004. Fig. 1006. decorated with enriched panels, as in the figs. 1001, 1002, 1003, 1004, 1005, 1006. In all ceilings it is desirable to raise the centre panel higher than the rest, and the main divisions representing the timbers in flat ceilings should, if possible, fall in the centre of the piers between the windows. 2817. Fig. 1007. shows the ceiling of a square room in two ways as given on each side of the dotted line, or it may be considered as representing the ends of a ceiling to a room whose form is that of a parallelogram. The same observation applies to figs. 1008. and 1009. The sofites of the beams should in all cases approach the width they would be, Fig. 1007. Fig. 1008. Fig. 1009. considered as the sofites of architraves of the columns of the order to which the cornice belongs, and they may be decorated with guiloches, as in fig. 1010., or with frets. (See the word "Fret" in Glossary.) Fig. 1010. 2818. In the two following figures (1011. and 1012.) are given four examples of rooms which are parallelograms on the plan, and above each is a section of the compartments. 2819. As to the proportion of the cornice, it ought in rooms to be perhaps rather less than in halls, salons, and the exterior parts of a building; and if the entablature be taken at a fifth instead of one fourth of the height, and a proportional part of that fifth be taken for the cornice, it cannot be too heavy. Perhaps where columns are introduced it will be better to keep to the usual proportions. Chambers, if followed, would make the proportions still lighter than we have set them down. He says that if the rooms are adorned with an entire order, the entablature should not be more than a sixth of the height nor be less than a seventh in flat-ceiled rooms, and one sixth or one seventh in such as are coved; and that when there are neither columns nor pilasters in the decoration, but an entablature alone, its height should not be above one seventh or eighth of those heights. He further says that in rooms finished with a simple cornice it should not exceed one fifteenth nor be less than one twentieth, and that if the whole entablature be used its height should not be more than one eighth of the upright of the room. In the ceilings of staircases the cornices must be set out on the same principles; indeed in these, and in halls and other large rooms, the whole of the entablature is generally used. In vaulted ceilings and domes the panels are usually decorated with panels similar to those in figs. 1001, 1002, 1003, 1004, 1005, 1006., but in their application to domes they of course diminish as they rise towards the eye of the dome. (See 2837.) SECT. XX.V, 2820. The use to which rooms are appropriated, and their actual dimensions, are the principal points for consideration in adjusting the proportions of apartments. Abstractedly considered, all figures, from a square to the sesquialteral proportion, may be used for the plan. Many great masters have carried the proportion to a double square on the plan; but except the room be subdivided by a break the height is not easily proportioned to it. This objection does not however apply to long galleries which are not restricted in length, on which Chambers remarks, “ that in this case the extraordinary length renders it impossible for the eye to take in the whole extent at once, and therefore the comparison between the height and length can never be made." 2821. The figure of a room, too, necessarily regulates its height. If a room, for example, be coved, it should be higher than one whose ceiling is entirely flat. When the plan is square and the ceiling flat the height should not be less than four fifths of the side nor more than five sixths; but when it leaves the square and becomes parallelogramic, the height may be equal to the width. Coved rooms, however, when square, should be as high as they are broad; and when parallelograms, their height may be equal to their width, increased from one fifth to one third of the difference between the length and width. 2822. The height of galleries should be at least one and one third of their width, and at the most perhaps one and three fifths. "It is not, however," says Chambers, "always possible to observe these proportions. In dwelling-houses, the height of all the rooms on the same floor is generally the same, though their extent be different; which renders it extremely difficult in large buildings, where there are a great number of different-sized rooms, to proportion all of them well. The usual method, in buildings where beauty and magnificence are preferred to economy, is to raise the halls, salons, and galleries higher than the other rooms, by making them occupy two stories; to make the drawing-rooms or other largest rooms with flat ceilings; to cove the middle-sized ones one third, a quarter, or a fifth of their height, according as it is more or less excessive; and in the smallest apartments, where even the highest coves are not sufficient to render the proportion tolerable, it is usual to contrive mezzanines above them, which afford servants' lodging-rooms, baths, powdering-rooms," (now no longer wanted !) "wardrobes, and the like; so much the more convenient as they are near the state apartments, and of private access. The Earl of Leicester's house at Holkham is a masterpiece in this respect, as well as in many others: the distribution of the plan, in particular, deserves much commendation, and does great credit to the memory of Mr. Kent, it being exceedingly well contrived, both for state and convenience." 2823. In this country, the coldness of the climate, with the economy of those who build superadded, have been obstacles to developing the proper proportions of our apartments ; and the consequence is, that in England we rarely see magnificence attained in them. We can point out very few rooms whose height is as great as it should be. In Italy, the rules given by Palladio and other masters, judging from their works, seem to be sevenfold in respect of lengths and breadths of rooms, namely, — 1. circular; 2. square; 3. the length equal to the diagonal of the square; 4. length equal to one third more than the square; 5. to the square and a half; 6. to the square and two thirds; or, 7. two squares full. As to the height of chambers, Palladio says they are made either arched or with a plain ceiling: if the latter, the height from the pavement or floor to the joists above ought to be equal to their breadth; and the chambers of the second story must be a sixth part less than them in height. The arched rooms, being those commonly adopted in the principal story, no less on account of their beauty than for the security afforded against fire, if square, are in height to be a third more than their breadth; but when the length exceeds the breadth, the height proportioned to the length and breadth together may be readily found by joining the two lines of the length and breadth into one line, which being bisected, one half will give exactly the height of the arch. Thus, let the room be 12 feet long Another of Palladio's methods of 12+6 and 6 feet wide, = 9 feet the height of the room. proportioning the height to the length and breadth is, by making the length, height, and breadth in sesquialteral proportion, that is, by finding a number which has the same ratio to the breadth as the length has to it. This is found by multiplying the length and breadth together, and taking the square root of the product for the height. Thus, supposing the length 9 and the breadth 4, the height of the arch will be √9 × 46, the height required; the number 6 being contained as many times in 9 as 4 is in 6. 2824. The same author gives still another method, as follows: - Let the height be assumed as found by the first rule (=9), and the length and breadth, as before, 12 and 6. Multiply the length by the breadth, and divide the product by the height assumed; then 12x6 -8 for the height, which is more than the second rule gives, and less than the first. 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 geometrie 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." 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 |