mences an action in the superior courts, he should prove that he has already applied to one of the courts of conciliation. These courts, which are attended with very small expense to the suitors, were, soon after their establishment, multiplied rapidly in Denmark and Norway, and are said to have produced an astonishing decrease in the amount of contentious litigation. (See 'Tableau des Etats Danois,' par Catteau, tome i., p. 296.)

ARBLAST, or ARBALEST, was the name more particularly given to the cross-bow. Robert of Gloucester, in his 'Chronicle,' published by Hearne, p. 378, makes an especial difference between the bowmen and the arblastes, or arblasters, the cross-bowmen. In the Latin of the middle ages it is called 'arcubalista,' from arcus, a bow, and the Greek word Báλλw, to cast or shoot.

The precise date and origin of the arbalest is unknown; but it seems easily derivable from the larger species of ballista. Vegetius is inclined to consider the scorpio to be the same as the cross-bow: he speaks of scorpions, which he says they now name manuballista; and in later writers the modern weapon is sometimes termed scorpio manualis. Pitiscus, in his 'Lexicon,' has assigned the introduction of the arbalest into the Roman armies to the time of Constantine, or a little earlier.

Strutt thought that the cross-bow was introduced into England about the 13th century; but Daines Barrington comes probably nearer to the truth (Archæologia,' vol. vii. p. 46), when he inclines to the opinion that it was the arbalest, and not the long bow, which was used with such destructive effect at the battle of Hastings by the Normans. There can be little doubt but that the arbalest was introduced by the Normans at their first arrival. We have no mention whatever of it in any writer or document of the Saxon times; but in the 'Domesday Survey,' compiled in 1086, we have several arcubalistarii, captains of cross-bow men, among the tenants in chief. No such appellation is given in that record to any person who held lands in the time of King Edward the Confessor. Brompton, in Twysd n's 'Scriptores,' col. 1278, says, that the use of the arbalest having been laid aside, was revived by King Richard I., who was afterwards killed by an arrow shot from one at the siege of Chalus.

The arrows for the cross-bow were called quarrels, from the French carreaux. [ARCHERY.] ARBORETUM. This name has been lately extended beyond its strict botanical meaning, and made to apply to public parks opened near large manufacturing towns. In 1837 a resolution was passed by the House of Commons to the effect that, in all new Enclosure Acts, some portions of the waste land about to be appropriated should be set apart for the healthful recreation of the neighbouring towns and villages. This resolution has led to the establishment of many places for open-air recreation.

Mr. Joseph Strutt, of Derby, made a munificent gift to the inhabitants of that town, in 1840, of an Arboretum or public park. He expended twelve thousand pounds in the purchase of eleven acres of ground at the south end of the town, and in laying out this ground with walks, lawns, plantations, and other accessaries. The late Mr. Loudon was employed to conduct the operations; and, in a pamphlet on the subject, he has given the reasons which induced him to determine on an Arboretum, instead of a botanic garden or a mere pleasureground. Near each tree and shrub is a small tablet, on which is written the catalogue number of the specimen, the Latin or scientific name, the English name, the habitat, the full-grown height, the date of the introduction, &c. By a deed of settlement the Arboretum is placed in the hands of the corporation of Derby, for the benefit of the inhabitants.

When the modern town of Birkenhead was laid out on so magnificent a scale, a public park was planned on a basis of unusual liberality. An open spot of 190 acres was so arranged, that 120 acres were laid out in shrubberies, lakes, walks, and drives for the free use of the inhabitants; while the remaining 70 acres were appropriated for handsome residences intended to border the park. Mr. (now Sir Joseph) Paxton was employed to form the park. The cost of the land and the laying out of the park was about 130,000l; and it was computed that the 70 acres would resell for building-ground at about the same sum; so that this excellent public-spirited arrangement would in effect cost nothing to the townsmen collectively.

In 1846-7 no fewer than three public parks were established in the neighbourhood of Manchester; namely, Peel Park, opposite Salfordcrescent; Queen's Park, in the Rochdale-road; and Phillip's Park, in Ancoats. The purchasing of the estates and the formation of the parks were effected by a committee, to whose hands munificent donations were entrusted.

In 1852 an Arboretum was opened at Nottingham. It comprised an area of 18 acres, at the northern limits of the town; and it comprised, greenswards, paths, and drives, plantations of trees and shrubs, and a lake containing aquatic birds. This was not the gift of a private individual; it resulted from the provisions of an Enclosure Act passed in 1846.

About the same period an Arboretum was formed at Ipswich. Bradford and Liverpool soon afterwards recognised the importance of places of open-air recreation, whether called by the name of Arboretum or by any other name.

The metropolis has, within a comparatively small number of years obtained an addition of two to its former number of public parks. These are Victoria Park and Battersea Park, situated respectively at the north-east and south-west extremities of the Metropolis. Each contains the beginning of what may one day be an Arboretum. The unsightly Kennington-common has been converted into a park of humble pretensions. A park and arboretum for Finsbury have long been under consideration, but though an Act has been obtained for its construction, no steps have been taken for carrying it into effect. Hampstead-heath, so for as it contains the elements for an Arboretum, has been with difficulty preserved from the builders, who have covered so many other open spots near London with bricks and mortar. Without attempting to notice all the parks for the people, constructed and thrown open within the last few years, we must at any rate devote a few words of description to that at Halifax, munificently presented to the inhabitants by Mr. Crossley, a carpet manufacturer, and member for the borough. This park, which was opened in 1857, covers an area of about 13 acres; and cost, with the laying out of the grounds by Sir J. Paxton, no less a sum than 30,000l. Besides terraces, statues, vases, basins, fountains, a small piece of water, with a bridge, &c., the park contains a collection of trees, shrubs, and flowers, which so far entitle it to the name of an Arboretum. In the autumn of the same year (1857), Blackburn obtained a fine "people's park" of 50 acres, provided by corporate funds, and containing a goodly collection of trees and shrubs.

One of the most interesting examples is that of Aston Hall and park at Birmingham-interesting for the circumstances under which the work was effected. About three miles from the centre of Birmingham is a fine old Elizabethan mansion, Aston Hall (the 'Bracebridge Hall' of Washington Irving). This mansion passed out of the hands of the family whose members had possessed it during many generations; and in 1856, there was a probability that the fine park would soon become covered with houses. This the men of Birmingham-chiefly the working men prevented. A sum of 42,000l. was raised by subscriptions, to purchase Aston Hall and Park" for the people." This was done; and in June 1858, Queen Victoria, amid great splendour, was present at the inauguration of a work so worthily undertaken. A fine collection of trees and shrubs, or Arboretum, forms part of the adornments of the park.

ARBUTIN (CH22020?). A crystalline body obtained from the leaves of the Arctostaphylos uvæ-ursi. In contact with the ferment Synaptase, it is said to be transformed into grape sugar and a crystalline substance to which the name Arcturin has been given :

For the arc of a circle, see ANGLE, where the method of finding the are from its angle, and the converse, is given. For the properties of the arcs of various curves, see their several names.

It is found necessary to assume the following axiom previously to any general investigation of the properties of an arc. Every arc is greater than its chord, but, when concave to the chord throughout, is less than the sum of the sides of any rectilinear figure which contains it. Thus ACB is greater than A B, but less than the sum of A D, DE, and E B. If x and y be the co-ordinates of any point in the general method of finding the arc is by the integration of the formula √dx2 + dy2,

or, in the language of the fluxional calculus,

fluent of √x2+ y2.

curve,

the

The practical method of finding the length of an arc, which is an approximation to the preceding process, is as follows:-Divide the arc into a number of smaller arcs, making the number large in proportion to the degree of accuracy required, and add together the chords of the smaller arcs. The sum of the chords will differ very little from the arc, even when the number of subdivisions is not very large. For instance, the arc of the quadrant of a circle, whose diameter is ten millions of inches, is 7,853,982 inches, within half an inch. Divide this quadrant into ten equal parts, and the sum of the chords is 7,845,910 inches: divide the quadrant into fifty parts, and the same sum is 7,853,659 inches, which is not wrong by more than one part out of 24,316. For only twenty subdivisions the sum of the chords is

7,851,963 inches, wrong only by one part out of 3890. Therefore, for every practical purpose, an arc of a circle (and the same may be said of every other curve) is the polygon made by the chords of a moderate number of subdivisions of the arc.

The preceding property is (but in what manner our limits will not permit us to show) a consequence of the following proposition. Let there be a number of arcs, such as A OB, cut off the same curve, having their chords parallel to the tangent X OY; then, as A B moves parallel

to its first position towards XY, CD not only decreases without limit but its proportion to A B decreases without limit; that is, let any number, however great, be named, then shall A B, before it reaches x Y, reach a position in which it contains CD more than that number of times. This proposition is startling to the beginner in mathematics, and should be considered by him with great attention. It may be illustrated in the following manner :-Suppose that while A B moves from its first position towards X Y, and has reached ab, a miscroscope moves with and over it, which increases in magnifying power as ab moves, in such a manner that ab always appears in the glass as large as A B to the naked eye. Then a cb will not be magnified into the form A C B, but into A QB, where QD grows less and less without limit, as ab approaches towards x Y. But if two straight lines had been taken, as in the following figure, ab could not have been magnified to A B without changing a cb into A O B.

Formerly, the term are was frequently confounded with angle, which arose from the practice of measuring angles by arcs of the circle. For such terms as ARC OF ELEVATION, &c., we refer to ANGLE OF ELEVATION, &c.

ARCADE signifies a series of arches on insulated piers, forming a screen, and also the space inclosed by such. This is, perhaps, a limitation of the term within that usually given to it; but arcade is properly a correlative of colonnade, and should not therefore have a more extensive signification. What, by a strange perversion of the term, are in this country called piazzas, and most particularly the part so termed of the buildings in Covent Garden, London, are strictly arcades; and the market within the inclosed area of that same place or square, to which the term piazza properly applies, exemplifies, in a great part of its exterior, the correlative term colonnade.

In Gothic architecture the term arcade is applied to a series of arches supported on piers, and used as decorations for the walls of churches, and occasionally of other buildings. The arches are sometimes open, but more commonly closed by the masonry of the wall. Good examples of arcades of the Norman and Early English styles (in which arcades are most employed) occur in Canterbury cathedral; of the decorated style in Lichfield cathedral: but most of our cathedrals possess some examples.

In addition to its proper technical meaning, this term has acquired a different signification among us as the popular name for what the Parisians more properly designate a 'passage' or 'galerie,' namely, an alley lined on each side with shops, and roofed over so as to be in fact a sort of in-door' street, entirely protected from the weather, and of uniform design throughout in its architecture. So far, an arcade answers to the idea of a bazaar, the chief distinction between the two being that the latter has not so much of street character about it, but consists either of a single spacious hall or separate rooms, fitted up with counters and stands, and may therefore be likened to a single large shop occupied by a number of different dealers, whereas in an arcade the shops are quite distinct from each other, and enclosed in front with windows after the usual manner; and they have besides dwelling accommodation, kitchen, &c., beneath, and a chamber over them, with the addition sometimes of an entresol. Another distinction is that an arcade serves as a public thoroughfare for foot-passengers. The Burlington Arcade, which was the first place of the kind in London, has indeed little more than its convenience as a thoroughfare and promenade for foot-passengers to recommend it, inasmuch as it makes no pretensions to elegance of design, nor has it anything in accordance with the title bestowed on it, it being neither arcaded in any way nor arched over. The Lowther Arcade in the Strand (erected 1831) manifests a great improvement upon that first specimen, for it is really a handsome piece of architecture; the side elevations are divided by

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pilasters into compartments, each of which contains a shop-front, with an ornamented triple window over it, and above that a semicircular one in the arched head of the compartment. On the plan, each of these divisions is covered by a pendentive dome with a circular skylight; and these numerous domes and their arches produce a pleasing perspective effect. Three other arcades have been opened in London since the erection of the Lowther Arcade. The first of them, Exeter Arcade, running from Wellington Street to Catherine Street in the Strand, erected in 1844 from the designs of Mr. Sidney Smirke, is very short; is more enclosed than either Burlington Arcade or Lowther Arcade; has a vestibule at each end; is glazed, so that the lights form a continuous skylight, and has polychromic embellishment applied both on the upper part of the walls (in ornaments and panels between the windows over the shops) and on the cove of the ceiling. The whole place has indeed more the appearance of a hall or gallery than of a place of thoroughfare and business. The arcade in New Oxford Street, opened in 1851, is short but of rather pretentious character. Both of these have proved commercially unsuccessful, and neither is, in fact, now employed for the purpose for which it was constructed. The South-Eastern Arcade, at the entrance of the South-Eastern Railway Station, London Bridge, is only remarkable for its unmitigated architectural baldness and poverty. In Paris arcades have obtained much greater popularity than in London. Among the Parisian arcades, the Passage Colbert is one of the most striking, both for its extent and architectural display, towards which last its Rotunda contributes in no small degree.

ARCH. The origin of that species of construction called an arch is unascertained; it cannot be stated with certainty either in what country or at what epoch it was first used. There is good reason to think that, though the arch form was certainly known to the Pelasgic inhabitants of Greece, it was unknown to the Greeks at the time when they produced their most beautiful temples, in the fifth, fourth, and third centuries before the Christian era. No structure answering to the true character of an arch has been found in any part of those works, though many occasions occur in which the application of the arch would have been of great service, and would seem unlikely to have been passed over by an intelligent and ingenious people like the Greeks if they had been acquainted with the principle. The want of the arch would necessarily lead them to contract the intercolumniation, or spaces between the columns, and to the general and frequent adoption of columns as the only mode of supporting a superstructure. But though not appropriated--at least for their sacred buildings-by the Greeks, it is now certain that the arch was known both to the Egyptians and the Assyrians. There are brick arches at Thebes in Egypt, which belong to a very remote epoch, and one long prior to the Greek occupation of that country. Minutoli (Reise zum Tempel des Jupiter Ammon') has given two specimens of Egyptian arches, one of which is a false and the other a true arch. The first specimen is from the remains at Abydos in Egypt (p. 245), where the roof has the appearance of an arch, but is formed by three horizontal stones, of which that which occupies the centre and lies over the other two is the largest ; the three stones are cut under in such a way as to form a semicircle. The true specimens are at Thebes (at least as early as B.C. 1490), on the west side of the river (p. 260), near and behind the building which contains the fragments of the enormous statue. They are circular arches, and formed of four courses of bricks (see pl. 29), and on the walls there are Egyptain paintings and hieroglyphics. (See also Belzoni's' Plates,' No. 44, and his remarks on the brick arches of Thebes; and also Sir Gardner Wilkinson's Egypt and Thebes,' pp. 81 and 126; Manners and Customs of the Egyptians,' vol. iii. ; and Colour, p. 297.) The stone arches in the Nubian pyramids can hardly perhaps be adduced in proof of the early use of the arch, as these edifices are probably not of very high antiquity (see Cailliaud's 'Plates,' No. 43), though Mr. Hoskins (Travels in Ethiopia') attributes to the latest of them a date not more recent than that of Cambyses. A stone arch of a date not later than that of Psammeticus has been discovered at Saccara, and another in a tomb near Gizeh. Mr. Layard and M. Place found both round and pointed arches at Nimroud and at Khorsabad, the construction of which shows that the ancient Assyrians were at a very early period sufficiently acquainted with the constructive value of the arch to apply it to a variety of important purposes. In the roofs of the tombs of Lycia, of about the 5th century B.C., the pointed arch occurs. (Fellowes' Lycia;' and the works of Forbes and Spratt.) Etruria seems, from the best evidence that can be obtained, to have been the first place in Europe where the arch was employed; and to the Etrurians may be assigned the honour of its earliest applications, as far as our positive and undisputed information goes, in works of an important size and character, in a pointed as well as in the circular form. The great sewer of Rome, commonly called the Cloaca Maxima, is an arched construction, which can hardly be referred to any period in the history of the city with so much probability as to that to which it is assigned by uniform tradition, namely, the age of the Tarquins. But though we may readily admit this early date, we cannot say whether the architects were Roman or Etrurian, though the latter would seem the more probable.

The application of the arched structure is one of the most useful mechanical contrivances ever discovered by man. By means of it, small masses of burnt clay, and conveniently sized pieces of soft and friable sandstone, are made more extensively useful for the economic

purposes of building, than the most costly and promising materials were in the hands of the Greeks. By means of it, cellars are vaulted; subways, or sewers, are made to pass under heavy structures and along streets with certainty and safety; and secure and permanent road-ways for every purpose of communication are formed across wide, deep, and rapid rivers. Extensively as they made use of the arch, the Romans did not deviate much from the semicircular form. Arches of smaller segments were certainly used by them, as well as elliptical arches, but in these cases they were fortified with enormous abutments, which proves that the architects, who probably in nearly all cases were Greeks, knew very well the weak points of such a construction. It was reserved for the architects of the middle ages, or rather those of the 12th, 13th, and 14th centuries, to show what could be done by varying the form and construction of the arch.

The pointed arch, upon its invention or first introduction into Europe, seems to have exercised the ingenuity of architects in varying its form and application. This we observe in the numerous ecclesiastical structures in this country, in our beautiful pointed styles, and most particularly in some of the greater churches and cathedrals.

The origin of the pointed arch has been almost as much disputed as the discovery of the principle of the arch itself. It became general in most parts of Europe at nearly the same time, and about the period of the return of the warrior-priests and pilgrim-soldiers of the First Crusade. This, and other circumstances which might be adduced, added to the well-ascertained fact of the pointed arch being used among the Eastern nations before that period,-it was certainly used by the Arabs in their mosques in the 9th century, and it occurs in the church built over the Holy Sepulchre in the reign of Constantine-and that an arch of the pointed form was not known to have been used in the northern and western parts of Europe anterior to the first crusade, gave, in the opinion of some French as well as English authorities, a reasonable degree of certainty to the supposition that the notion was brought from the East by the crusaders. But it is pretty certain that the pointed arch was in use in ecclesiastical architecture in some parts of France prior to the return of the first crusaders; and, as is observed by Mr. Fergusson ('Handbook of Architecture,' ii. 598), we need not feel surprised that a people trading with the Levant from their great port of Marseilles, should have thence borrowed this feature; or perhaps we might rather say, that a people descended from a colony of Pelasgic Greeks should revive an old and time-honoured form when they found it particularly suited to their constructive purposes. So remarkably suitable indeed was it, that we should not wonder even if they had actually invented it de novo." Indeed, after all that has been said and written on the subject, it seems most likely that the pointed arch grew out of the exigencies of early ecclesiastical architecture. As Mr. Rickman long ago pointed out, the Norman style was constantly assuming a lighter charater; intersecting arches were a usual mode of embellishing Norman buildings, and they, or the arches formed in vaulting, would have suggested the pointed form,-if, as has been truly said, the mere ordinary use of a pair of compasses had not been sufficient to suggest it, and once suggested, its superior lightness and applicability would insure its employment. Its diffusion from the centre of ecclesiastical architecture evidently requires no explanation. But, as Sir Gardner Wilkinson very truly observes, the pointed arch was assuredly neither exclusively, nor even originally Christian."

The various forms and decorations of the arch will be found under the several divisions indicated in the article ARCHITECTURE ; see especially GOTHIC ARCHITECTURE.

ARCH, the same word as arc in its etymological derivation, and an older English form (having been always used in the sense of arc until that continental form superseded it), is now applied to any solid work, whether of masonry or otherwise, of which the lower part is formed into an arc of a curve supported at the two extremities. We proceed to give some idea of the question of theoretical mechanics connected with this word, referring, for all matters connected with the support, to ABUTMENT, BUTTRESS, IMPOST, PIER, and for history and general information to BRIDGE.

In practice, we have not only the arch itself to consider, but the loose matter with which the space above it is filled, and the roadway or building thereon constructed. The two extreme effects of this load may be thus stated. If it were fluid, the common law of hydrostatics e d

Fig.1

gh

would direct us to consider every small portion ab (fig. 1) of the arch in sustaining a pressure perpendicular to itself, equivalent to the weight

of a column of fluid having the horizontal base ab, and the mean of a c and bd for its altitude. On the other hand, if the whole superincumbent load could be considered as perfectly solid and wholly unsustained by lateral pressure, the portion pqhg might be considered as a part of the arch-stone underneath. In the absence of all trustworthy experiments to determine how far the real superincumbent pressure, where resulting from loose materials, partakes of one or the other supposition, we shall adopt the latter as probably nearer the truth than the former: which is equivalent to treating of the arch only after its superincumbent weight has been added to each arch stone.

A C and B D are called the piers of the arch; it is said to spring from A and B; AE and BF are the haunches, and a the crown or keystone. The lower line of the arch stones is called the intrados or soft, the upper, the extrados or back; the arch-stones are called voussoirs, and the highest stone, G, the key-stone. AB is the span or chord of the arch, and G H its rise, or versed sine. The voussoirs are cemented together, and if the cement were sufficiently strong, any form might be given to the arch, or at least any form which would stand if cut out of the solid material. If we suppose the stones uncemented, their friction upon one another would tend to prevent the disturbance of equilibrium, and allow considerable variety of form in arches constructed with stones of the same weight. But if we suppose the stones perfectly smooth, so that each of them is kept from slipping only by the pressure of the adjoining two, then each intrados ought to have one particular form of extrados, and one only, so long as the manner in which the stones are cut follows one given law.

Let PQ, RS (fig. 2) be parts of the pier, which we suppose firmly fixed, and let there be no key-stone, or suppose the key-stone divided

in the middle at a B. Let the portion ACDB be taken, composed of several arch-stones, and let its centre of gravity be a. Then the weight of ABCD, collected at G, is sustained by pressures at the surfaces A B and C D, perpendicular to those surfaces. Take EF in the continuation of AB, of any length, and draw F H parallel to CD. It is a known theorem, that any three forces which balance each other are proportional to the three sides of a triangle, the directions of the sides of which are perpendicular to the direction of the forces. In the present case, H E F is such a triangle; for H E, being horizontal, is perpendicular to the direction of all weights; F E is the continuation of AB, and therefore perpendicular to the pressure at AB, while FH, being parallel to CD, is perpendicular to the pressure at CD. Hence HE bears to E F the same proportion as the weight of A C D B to the pressure at A. In the same manner it may be shown that, F M being parallel to KL, the weight of the portion A B K L is to the pressure at A B as ME to E F, from which it follows that the weight of A KLB bears to that of ACDB the proportion of M E to H E. Hence the following theorem: R Q P NME

F

Let EF be vertical, Es horizontal, and FM, FN, &c., parallel to the divisions between the voussoirs of an arch which is divided at its highest point: then, no friction being supposed, there can be no equilibrium unless the weights of the successive voussoirs, reckoned from the highest point, are to one another as E M, M N, NP, &c.

It is also necessary to the equilibrium of the arch that the vertical drawn through the centre of gravity G of the part A CDB should cut the parallelogram 123 4, made by perpendiculars to AB and CD drawn from their extremities: for otherwise there would be no point in the vertical through G (at some part of which the weight must be supposed to act), at which the directions of the perpendicular pressures could meet, and no three forces can maintain equilibrium unless their directions pass through one point.

B

An arch constructed upon the preceding principles would, if the stones were perfectly smooth, be totally overturned by the least

X

A

R

D

addition to, or subtraction from, the weight of any one arch-stone: for each arch-stone is only just kept in equilibrium by the pressures of the two adjoining. Such an arch, therefore, would not serve for a bridge, which must bear a considerable addition to its weight at different times. It is to the friction and cements that the power of sustaining additional weights is due. It is evident that before the arch, kept in equilibrium as above, can be overturned, the additional pressure must be such as to overcome the friction against some one arch-stone exerted by the two adjoining. And the advantage is the greater, since the additional pressure itself increases the friction which opposes it. The effect of friction may be thus represented. First ascertain the extreme angle at which a mass of stone, such as the arch is to be built of, would rest upon an inclined plane of the same material: that is, raise the stone A upon the stone plane B O until the least additional elevation would make it slide down. Measure the angle C B D. Now suppose P Q R S T V to be part of an arch kept in equilibrium without friction. From T on both sides make the angles QTX, QTY equal to CBD above measured: then the effect of friction is this, that instead of the two arch-stones meeting in TQ, their line of junction might have been anywhere in the angle Y TX, without endangering the mere equilibrium. Or if, as in a preceding figure, F M and F N are parallel to the lower sides of two arch-stones, and the angles M F X, M F Y, NF X', NFY', be made equal to the angle BCD above measured, then, instead of its being required that the proportions of the weights resting on those sides should be strictly that of EM to EN, they may be in the proportions of any two lines, which, being set off from E towards s, have the end of the first between X and Y, and that of the second between x' and r'. The great latitude which this gives to F the construction (since B C D is, for some materials, as great as 40°) renders attention to the system of equilibration without friction almost unnecessary, so that any arch which does not very materially differ from the arch kept in equilibrium without friction may be considered as safe from all fracture which arises from the slipping of an arch-stone.

S

T

8

YN X'

YM X

V

E

The difficulty in the way of determining the best figure of an arch, lies in our comparative ignorance of the manner in which pressure is actually communicated. The materials supposed in mechanical problems are usually perfectly rigid; those of nature are compressible: and though it is clear that a very slight alteration of form might throw the pressure of one arch-stone almost entirely upon a very small part of the adjoining stone, we do not know enough of the nature of building materials even to guess at the law of distribution of pressure. Again, if a part of an arch be overloaded, but prevented from falling by the friction or cement, a new force, not contemplated in the preceding theory, is exerted upon the remainder. Dr. Robison, as far as we know, was the first who brought forward this method of considering

the subject. He was led to it by observing an arch which fell, the account of which we give in his own words (Mechanical Philosophy,' vol. i. p. 640): "It had been built of an exceedingly soft and friable stone, and the arch-stones were too short. About a fortnight before it fell, chips were observed to be dropping off from the joints of the archstones, about 10 feet on each side of the middle," that is at H and F, "and also at another place on one side the arch, about 20 feet from its middle," that is at I and G. "The masons in the neighbourhood prognosticated its speedy downfall, and said it would separate in

66

those places where the chips were breaking off. At length it fell: but it first split in the middle, and about 15 feet or 16 feet at each side," that is at D and B, "and also at the very springing of the arch," that is at k and . 'Immediately before the fall, a shivering or crackling noise was heard, and a great many chips dropped down from the middle between the two places from whence they had dropped a fortnight before," that is from a and b. "The joints opened above at these new places more than 2 inches, and in the middle of the arch the joints opened below, and in about five minutes after this the whole came down. Even this movement was plainly distinguishable into two parts. The crown sunk a little, and the haunches rose very sensibly, and in this state it hung for about half a minute. The archstones of the crown were hanging by their upper corners. When these splintered off, the whole fell down."

The preceding method of fracture also took place in several model arches of chalk, loaded for the purpose, and Dr. Robison explains the phenomena as follows. He supposes that the pressure from the crown is communicated in a straight line along as many voussoirs as one straight line will pass through. That is, he considers each of the four parts ED, DA, A B, BC, as one separate stone, not liable to be broken. The preliminary chipping from I, H, F, and G, he supposes to have arisen from the whole superincumbent pressure being there sustained at the corner of the arch-stones. When the arch opened underneath A, the whole pressure was supported at a and b, since the opening at B and D deprived the arch of the support at those points. This occasioned the chipping there observed just before the fall. We must, however, remark, that the loose manner in which the preceding account is given renders it impossible to say whether or no Dr. Robison was justified in supposing the line of communication of the pressure to be straight. His hypothesis might equally apply, if A HD were a convex curve, touching the intrados at H. This experiment should be repeated, with more attention to minute circumstances and actual measurement.

This very ingenious and probable explanation, which, supposing the slipping of individual voussoirs to be impossible, may be considered as almost unobjectionable, led its author to recommend that the arch should always be made so flat as to admit the same straight line being drawn so as to pass through some point of every voussoir on each side of the key-stone. That such an arch cannot be destroyed without either removing the pier, or crushing the material, is evident in the case of a triangular arch, slipping being supposed impossible, since there is no part of the arch which exerts any effort to overturn the rest, but

only to crush it. Blackfriars Bridge has arches of this kind, not indeed triangular, but so flat that a straight line can be drawn through all the voussoirs, in the manner recommended by Dr. Robison.

M. Yvon de Villarceau has lately propounded a new theory of the resistance of arches, which perhaps it would be more satisfactory to discuss under the article BRIDGE. For general information upon the subject of arches the reader is, however, referred to Dr. Robison's work above cited; to Professor Moseley's Engineering and Architecture;' or to Gwilt's and Ware's Tracts on Vaults and Bridges. For the method of building an arch, see CENTERING, to which also we must defer the account of a method of constructing arches lately invented by Mr. Brunel, in which the stones are so joined that each half of the arch supports itself independently of the other.

ARCH, TRIUMPHAL, a structure which the Romans used to erect across their roads, or bridges, or at the entrance of their cities, in honour of victorious generals or emperors. They were of two kinds; temporary arches made of wood, on the occasion of a triumph, when the procession passed under the arch, and the conqueror had the triumphal crown placed on his head. These arches were removed after the ceremony. The others were permanent structures, built first of brick, afterwards of hewn stone, and lastly made of, or at least cased with marble. Their general form is that of a parallelopipedon, which has an opening in the longer side, and sometimes a smaller opening on each side of the large one. These openings are arched over with semicircular arches, and the fronts are decorated with columns and their accessories on lofty pedestals: the whole is surmounted by a heavy attic, on the faces of which inscriptions were generally placed.

Triumphal arches were erected under the republic. An arch of P. Cor. Scipio Africanus (Liv. xxxvii. 3), is mentioned as having been built on the Clivus Capitolinus. (See also Liv. xxxiii. 27, on the arches of L. Stertinius.) The Fabian arch is mentioned by Cicero (Pro Planco ') under the name of Fabianus fornix:' it stood by the Via Sacra, near the spot afterwards occupied by the temple of Antoninus and Faustina. It was raised in honour of Fabius, surnamed Allobrogus, from his victory over the Allobroges. This arch is also mentioned by Seneca, who calls it 'Fabianus arcus.' The term used by Dion Cassius for a triumphal arch is avís тpoñaιópopos. The arches