and counterforts, to support large walls laid deep in the earth; for triumphal arches, gates, windows, &c.; and, above all, for the foundations of bridges and aqueducts they are supported by piers, abutments, imposts, &c.-Arches are of several kinds, circular, elliptical, cycloidal, catenarian, &c., according as their curve is in the form of a circle, ellipse, cycloid, catenary, &c.-Arches are to be found in the Greek theatres, stadia, and gymnasia, some of them erected probably 400 years before Christ. The most ancient arches of which we have correct data are those of the cloaca at Rome. The emperor Hadrian threw a bridge over the Cephisus, between the territories of Attica and Eleusis, on the most frequented road of Greece. Arch (the theory of). This important

subject has exercised the talents and ingenuity of some of the greatest mathematicians in modern times, and many different solutions have been given to the various problems connected with it; but, as the greater part of them are founded on suppositions that have no existence whatever either in nature or practice, they have had a tendency rather to mislead than direct those who are engaged in the operations of bridge-building. Dr. Olinthus Gregory, in the preface to his excellent work on Mechanics, states, that "theoretical and practical men will most effectually promote their mutual interests, not by affecting to despise each other, but by blending their efforts; and further, that an essential service will be done to mechanical science, by endeavouring to make all the scattered rays of light they have separately thrown upon this region of human knowledge converge to one point." Gauthey, speaking of the theory of La Hire, observes that such analytical researches are founded on hypotheses which every day's experience contradicts. The following are

the principal writers on the equilibrium of the arch. In 1691, the celebrated mathematicians, Leibnitz, Huygens, James and John Bernouilli, solved the problem of the catenary curve: it was soon perceived that this was precisely the curve of that should be given to an arch which the materials were infinitely small and of equal weight, in order that all its parts may be in equilibrium. In the Philosophical Transactions' for the year 1697, it is stated that David Gregory first noticed this identity; but his mode of argument, though sufficiently rigorous, appears not to be so perspicuous as could be desired. In one of the posthumous works of James Bernouilli, two direct solutions of this problem are given, founded on the different modes of viewing the action of the voussoirs : the first is clear, simple, and precise, and easily leads to the equation of the curve, which he shows to be the catenary inverted; the second requires a little correction, which Cramer, the editor of his works, has pointed out. In 1695, La Hire, in his Treatise on Mechanics,' laid down, from the theory of the wedge, the proportion according to which the absolute weight of the materials of masonry ought to be increased from the keystone to the springing in a semicircular arch. The historian of the Academy of Sciences relates, in the volume for the year 1704, that Parent determined on the same principle, but only by points, the figure of the extrados of an arch, the intrados being a semicircle, and found the force or thrust of a similar arch against the piers. In the 'Memoirs of the Academy of Sciences' for the year 1712, La Hire gave an investigation of the thrusts in arches under a point of view suggested by his own experiments: he supposed that arches, the piers of which had not solidity enough to resist the thrust, split towards the haunches

at an elevation of about 45 degrees above the springings or impost; he consequently regarded the upper part of the arch as a wedge that tends to separate or overturn the abutments, and determined, on the theory of the wedge and the lever, the dimensions which they ought to have to resist this single effort. Couplet, in a memoir composed of two parts, the first of which was printed in the volume of the Academy for 1729, treats of the thrusts of arches and the thickness of the voussoirs, by considering the materials infinitely small, and capable of sliding over each other without any pressure or friction. But, as this hypothesis is not exactly conformable to experiment, the 2nd part of the memoir, printed in the volume for 1730, resumes the question by supposing that the materials have not the power of sliding over each other, but that they can raise themselves and separate by minute rotatory motions. It cannot, however, be said that Couplet has added materially to the theories of La Hire and Parent, and none of them treated the subject, either in theory and practice, in such a satisfactory manner as was afterwards done by Coulomb. Subsequently a memoir was published by Bouguer on the curve lines that are most proper for the formation of the arches of domes. He considers that there may be an infinite number of curve lines employed for this purpose, and points out the mode of selecting them. He lays it down uniformly that the voussoirs have their surfaces infinitely smooth, and establishes, on this hypothesis, the conditions of equilibrium in each horizontal course of the dome, but has not given any method of investigating the thrusts of arches of this kind, nor of the forces that act upon the masonry when the generating curve is subjected to given conditions. In 1770, Bossut gave investigations of arches of the

different kinds, in two memoirs, which were printed among those of the Academy of Sciences for the years 1774 and 1776: he appears to have been engaged in this in consequence of some disputes concerning the dome of the French Pantheon, begun by the celebrated architect Soufflot, and finished from his designs. In 1772, Dr. Hutton published his principles of bridges, in which he investigated the form of curves for the intrados of an arch, the extrados being given, and vice versa. He set out by developing the properties of the equilibrated polygon, which is extremely useful in the equilibrium of structures. Mr. Attwood has written a dissertation on the construction of arches on the same principles as La Hire.

Arch, in architecture, a concave structure raised or turned upon a mould, called the centering, in form of the arc of a curve, and serving as the inward support of some superstructure. Sir Henry Wotton says, "An arch is nothing but a narrow or contracted vault; and a vault is a dilated arch."

Arch, in geometry, a part of any

curved line, as of a circle or ellipsis Arch, in masonry, a part of a building

suspended over a hollow, and concave towards the area of the hollow: the top of the wall or walls which receives the first arch-stones is technically called the abutment or springing

Arch, in mining, a piece of ground left unworked

Arch-buttress, a piece of insulated masonry usually named a flyingbuttress, extending from the clerestory of a church and over the roof of its aisle, where it rests on the buttress of the outer wall Arch of equilibration, that which is in

equilibrium in all its parts, having no tendency to break in one part more than in another Arch, triumphal, a building of which

an arch is the principal feature,

usually raised to

commemorate

some great achievement Archæology, the study of ancient art, but more particularly that of the middle ages

Arched, in mining: the roads in a mine, when built with stones or bricks, are generally arched level drifts

Archeion, a recess in a Grecian tem

ple, for the reception of the treasures of the deity to whom the temple was dedicated

Archeion, in Athens, the office in which the decrees of the people and other state documents were preserved

Archetus, a saw for cutting stones : Muratori used the term for a crane or pulley for raising stones to the upper part of a building Archimedean screw, a machine invented by Archimedes for raising water; also now applied to propel vessels through water Architect, a person skilled in the art of building; one who forms, plans, and designs for edifices, conducts the work, and directs the secondary artificers employed; and whose emoluments are generally 5 per cent. on the amount of money expended

Architecture, a science applicable to the art of constructing domestic, ecclesiastical, municipal, palatial, or other buildings, and the adornment of the same according to the rules of the several orders, Doric, Ionic, and Corinthian, also the Tuscan, and Composite, from Roman models, or other styles, each for its purpose, such as is usually called Gothic architecture, and modes subservient to climate and fashion, or caprice. "Architecture," says Palladio, "being grounded upon rules taken from the imitation of Nature, admits of nothing that is contrary or foreign to that order which Nature has prescribed to all things. An architect is not restrained from departing sometimes from common methods or usage,

provided such variation be agreeable and natural."

The public at large has a claim over the architecture of a country. It is common property, inasmuch as it involves the national taste and character; and no man has a right to pass off his own barbarous inventions as the national taste, and to hand down to posterity his own ignorance and disgrace to become a satire and a libel on the knowledge and taste of his age. There is perhaps no subject on which persons are more apt to differ in their opinions than on the beauty of a building. In architecture the creative power of Nature herself is the model imitated. It is an art which appeals directly to the understanding, and has not the means of flattering the senses in the same way as the sister arts: hence its productions are not universally appreciated. The beautiful models of Nature, however, are the index and guide of the painter and sculptor a successful imitation of these models, even without an advance on the part of the artist towards those higher intellectual beauties which distinguish the historical painter, is capable of affecting us with very agreeable sensations. The object of an artist's inquiry is not so much to investigate metaphysically the cause of beauty in the productions of his art, as to study the effects that flow from those which by the common consent of ages are esteemed beautiful, and thus shorten his road by an a priori method. It is in this way that he will more readily obtain information on those qualities which act on the understanding and excite our affections by means of the beautiful result they exhibit. These qualities may be classed as follows:

MAGNITUDE AND SOLIDITY, as qualities which affect the eye.

ORDER AND HARMONY, as qualities which affect the understanding.

RICHNESS AND SIMPLICITY, as qualities which excite the affections, in which taste is the principal guide.

These qualities answer to the three divisions which those who have written on architecture have usually adopted, namely—

CONSTRUCTION, in which the chief requisites are solidity and strength.

DESIGN OR DISPOSITION, in which the principal requisites are

order and harmony.

DECORATION, whose requisites are richness or simplicity, according to the nature of the composition.

That there are, however, many other circumstances which tend to the production of an agreeable and beautiful result, is sufficiently obvious: one of them should be more particularly noticed, because there can be no doubt of its influence in the excitement of our admiration of the splendid monuments of Grecian art; it is an association with the times and countries which are most hallowed in our imagination. It is difficult for us to see them, even in their modern copies, without feeling them operate upon our minds, as relics of those polished nations where they first arose, and of that great people by whom they were afterwards borrowed.

The business of an architect requires him rather to be a learned judge than a skilful operator; and when he knows how to direct and instruct others with precision, to examine, judge, and value their performances with masterly accuracy, he may truly be said to have acquired all that most men can acquire there are but few instances of such prodigies as Michael Angelo Buonarotti, who was at once the first architect, painter, geometrician, anatomist, and sculptor of his time.

Vitruvius furthermore observes, that an art enriched with such variety of knowledge is only to be

learned by long and constant application; and advises his contemporaries never to assume the title of architects till they are perfect masters of their own profession, and of the arts and sciences with which it is connected; a caution that even in the present times may perhaps not be unnecessary. Architecture (the application of the orders of). Among the ancients, the use of the orders was very frequent; many parts of their cities were provided with spacious porticoes, their temples were surrounded with colonnades, and their theatres, baths, basilicæ, triumphal arches, mausolea, bridges, and other public buildings were profusely enriched with columns; as were likewise the courts, vestibules, and halls of their private villas and houses.

In pure architecture, says A. W. Pugin,the smallest detail should have a meaning or serve a purpose; and even the construction itself should vary with the material employed, and the designs should be adapted to the material in which they are executed.

Strange as it may appear at first sight, it is in pointed architecture alone that these great principles have been carried out: we may be enabled to illustrate them from the vast cathedral to the simplest erection. Moreover, the architects of the middle ages were the first who turned the natural properties of the various materials to their full account, and made their mechanism a vehicle for their art. The wonderful strength and solidity of their buildings are the result, not of quantity or size of the stones employed, but of the art of their disposition.

On the following page is a synopsis of the proportions of the orders, and of the various examples of each, compiled expressly by Mr. W. H. Leeds for Pugin's edition of Normand's 'Parallel of the Orders.'