Front matter (continued 4)

Six hearts should be made trumps and five with two honours unless the hand is very weak; five hearts with one honour or four hearts with three honours should be declared if the hand is nearly strong enough for no trumps, also if the hand is very irregular with one suit missing or five of a black suit. Six diamonds with one honour, five with three honours or four all honours should be declared; weaker diamonds should be declared if the suits are irregular, especially if blank in hearts. Six clubs with three honours or five with four honours should be declared. Spades are practically only declared with a weak hand; with only a king in the hand a suit of five spades should be declared as a defensive measure. With nothing above a ten a suit of two or three spades can be declared, though even with the weakest hands a suit of five clubs or of six red cards will probably prove less expensive.

Declarations by Dummy.—From the fact that the call has been passed, the dealer's partner must credit the dealer with less than average strength as regards the rank of his cards, and probably a slightly increased number of black cards; he must therefore be more backward in making a high declaration whenever he can make a sound declaration of less value. On the other hand, he has not the option of passing the declaration, and may be driven to declare on less strength because the only alternative is a short suit of spades. For example, with the hand: Hearts, ace, kv. 2; diamonds, qn. 9, 7, 6, 3; clubs, kg. 10, 4; spades, 9, 2, the chances are in the dealer's favour with five trumps, but decidedly against with only two, and the diamond declaration is to be preferred to the spade. Still, a hand may be so weak that spades should be declared with two or less, but five clubs or six diamonds would be preferable with the weakest of hands.

Declarations to the Score.—When one's score is over twenty, club declarations should be made more frequently by the dealer. Spades should be declared with six at the score of twenty-six and with five at twenty-eight. When much behind in the score a risky no-trumper such as one with an established suit of seven or eight cards without a card of entry, may be declared.

Declaring to the score is often overdone; an ordinary weak no-trump declaration carries with it small chances of three by tricks unless dummy holds a no-trump hand.

Doubling.—Practically the leader only doubles a no-trump declaration when he holds what is probably an established suit of seven cards or a suit which can be established with the loss of one trick and he has good cards of re-entry. Seven cards of a suit including the ace, king and queen make sound double without any other card of value in the hand, or six cards including king, queen and knave with two aces in other suits.

Doubling by the third hand is universally understood to mean that the player has a very strong suit which he can establish. In response to the double his partner, according to different conventions, leads either a heart or his own shortest suit as the one most likely to be the third player's strongest. Under the short suit convention, if the doubler holds six of a suit headed by the ace, king and queen, it is about an even chance that his suit will be selected; he should not double with less strength. Under the heart convention it is not necessary to have such great strength; with a strong suit of six hearts and good cards of re-entry, enough tricks will be saved to compensate for the doubled value. A player should ascertain the convention followed before beginning to play.

Before doubling a suit declaration a player should feel almost certain that he is as strong as the declarer. The minimum strength to justify the declaration is generally five trumps, but it may have been made on six. If, then, a player holds six trumps with an average hand as regards the rank of his cards, or five trumps with a hand of no-trump strength, it is highly probable that he is as strong as the declarer. It must be further taken into account that the act of doubling gives much valuable information to the dealer, who would otherwise play with the expectation of finding the trumps evenly distributed; this is counterbalanced when the doubler is on the left of the declaring hand by the intimation given to his partner to lead trumps through the strong hand. In this position, then, the player should double with the strength stated above. When on the declarer's right, the player should hold much greater strength unless his hand is free from tenaces. When a spade declaration has been made by dummy, one trump less is necessary and the doubler need not be on the declarer's left. A spade declaration by the dealer can be doubled with even less strength. A declaration can be rather more freely doubled when a single trick undoubled will take the dealer out, but even in this position the player must be cautious of informing the dealer that there is a strong hand against him.

Redoubling.—When a declaration has been doubled, the declarer knows the minimum that he will find against him; he must be prepared to find occasionally strength against him considerably exceeding this minimum. Except in the case of a spade declaration, cases in which redoubling is justifiable are very rare.

The Play of the Hand.—In a no-trump declaration the main object is to bring in a long suit. In selecting the suit to establish, the following are favourable conditions:—One hand should hold at least five cards of the suit. The two hands, unless with a sequence of high cards, should hold between them eight cards of the suit, so as to render it probable that the suit will be established in three rounds. The hand which contains the strong suit should be sufficiently strong in cards of re-entry. The suit should not be so full of possible tenaces as to make it disadvantageous to open it. As regards the play of the cards in a suit, it is not the object to make tricks early, but to make all possible tricks. Deep finesses should be made when there is no other way of stealing a trick. Tricks may be given away, if by so doing a favourable opening can be made for a finesse. When, however, it is doubtful with which hand the finesse should be made, it is better to leave it as late as possible, since the card to be finessed against may fall, or an adversary may fail, thus disclosing the suit. It is in general unsound to finesse against a card that must be unguarded. From a hand short in cards of re-entry, winning cards should not be led out so as to exhaust the suit from the partner's hand. Even a trick should sometimes be given away. For instance, if one hand holds seven cards headed by ace, king, and the other hand hold's only two of the suit, although there is a fair chance of making seven tricks in the suit, it would often be right to give the first trick to the adversaries. When one of the adversaries has shown a long suit, it is frequently possible to prevent its being brought in by a device, such as holding up a winning card, until the suit is exhausted from his partner's hand, or playing in other suits so as to give the player the lead whilst his partner his a card of his suit to return, and to give the latter the lead when he has no card to return. The dealer should give as little information as possible as to what he holds in his own hand, playing frequent false cards. Usually he should play the higher or highest of a sequence; still, there are positions in which playing the higher gives more information than the lower; a strict adherence to a rule in itself assists the adversaries.

With a suit declaration, if there is no chance of letting the weak hand make a trump by ruffing, it will generally be the dealer's aim to discard the losing cards in the declaring hand either to high cards or to the cards of an established suit in the other hand, sometimes after the adverse trumps have been taken out, but often before, there being no time for drawing trumps. With no card of any value in a suit in one hand, the lead should come from that hand, but it is better, if possible, to let the adversaries open the suit. It is generally useless to lead a moderately high card from the weaker hand in order to finesse it, when holding no cards in sequence with it in either hand. Sometimes (especially in no-trumps) it is the better play to make the weak hand third player. For instance, with king, 8, 7, 5, 2 in one hand, knave, 4 in the other, the best way of opening is from the hand that holds five cards.

In a no-trump declaration the opponents of the dealer should endeavour to find the longest suit in the two hands, or the one most easily established. With this object the leader should open his best suit. If his partner next obtains the lead he ought to return the suit, unless he himself has a suit which he considers better, having due regard to the fact that the first suit is already partially established. The opponents should employ the same tactics as the dealer to prevent the latter from bringing in a long suit; they can use them with special effect when the long suit is in the exposed hand.

Against no-trumps the leader should not play his winning cards unless he has a good chance of clearing the suit without help from his partner; in most cases it is advisable to give away the first trick, especially if he has no card of re-entry, in order that his partner on gaining the lead may have a card of the suit to return; but holding ace, king and queen, or ace, king with seven in the suit, or ace, king, knave, ten with six, the player may lead out his best. With three honours any two of which are in sequence (not to the ace) the player should lead the higher of the sequence. He should lead his highest card from queen, knave, ten; from queen, knave, nine; from knave, ten, nine; knave, ten, eight, and ten, nine, eight. In other cases the player should lead a small card; according to the usual convention, the fourth best. His partner, and also the dealer, can credit him with three cards higher than the card led, and can often place the cards of the suit: for instance, the seven is led, dummy holds queen and eight, playing the queen, the third player holds the nine and smaller cards; the unseen cards higher than the seven are ace, king, knave and ten of which the leader must hold three; he cannot hold both knave and ten or he would have led the knave; he must therefore hold the ace, king and either knave or ten. The "eleven" rule is as follows: the number of pips in the card led subtracted from eleven (11-7=4 in the case stated) gives the number of cards higher than the one led not in the leader's hand; the three cards seen (queen, nine and eight) leave one for the dealer to hold. The mental process is no shorter than assigning three out of the unseen cards to the leader, and by not noting the unseen cards much valuable information may be missed, as in the illustrative case given.

With a suit declared the best opening lead is a singleton, failing which a lead from a strong sequence. A lead from a tenace or a guarded king or queen is to be avoided. Two small cards may be led from, though the lead is objected to by some. A suit of three small cards of no great strength should not be opened. In cases of doubt preference should be given to hearts and to a less extent to diamonds.

To lead up to dummy's weak suits is a valuable rule. The converse, to lead through strength, must be used with caution, and does not apply to no-trump declarations. It is not advisable to adopt any of the recent whist methods of giving information. It is clear that, if the adversaries signal, the dealer's hand alone is a secret, and he, in addition to his natural advantage, has the further advantage of better information than either of the adversaries. The following signals are however, used, and are of great trick-making value: playing an unnecessarily high card, whether to one's partner's suit or in discarding in a no-trump declaration, indicates strength in the suit; in a suit declaration a similar method of play indicates two only of the suit and a desire to ruff,—it is best used in the case of a king led by one's partner.

The highest of a sequence led through dummy will frequently tell the third player that he has a good finesse. The lowest of a sequence led through the dealer will sometimes explain the position to the third player, at the same time keeping the dealer in the dark.

When on dummy's left it is futile to finesse against a card not in dummy's hand. But with ace and knave, if dummy has either king or queen, the knave should usually be played, partly because the other high card may be in the leader's hand, partly because, if the finesse fails, the player may still hold a tenace over dummy. When a player is with any chance of success trying to establish his long suit, he should keep every card of it if possible, whether it is a suit already opened or a suit which he wishes his partner to lead; when, however, the main object of the hand is to establish one's partner's suit, it is not necessary for a player to keep his own long suit, and he should pay attention to guarding the other suits. In some circles a discard from a suit is always understood to indicate strength in the suit; this convention, while it makes the game easier for inferior players, frequently causes the player to throw away one of his most valuable cards.

Playing to the Score.—At the beginning of the hand the chances are so great against any particular result, that at the score of love-all the advantage of getting to any particular score has no appreciable effect in determining the choice of suit. In the play of the hand, the advantage of getting to certain points should be borne in mind. The principal points to be aimed at are 6, 18, and, in a less degree, 22. The reason is that the scores 24, 12 and 8, which will just take the dealer out from the respective points, can each be made in a variety of ways, and are the most common for the dealer to make. The 2 points that take the score from 4 to 6 are worth 4, or perhaps 5, average points; and the 2 points that take the score from 6 to 8 are worth 1 point. When approaching game it is an advantage to make a declaration that may just take the player out, and, in a smaller degree, one that will not exactly take the adversaries out. When the score is 24 to 22 against the dealer, hearts and clubs are half a trick better relatively to diamonds than at the score of love-all. In the first and second games of the rubber the value of each point scored for honours is probably about a half of a point scored for tricks—in a close game rather less, in a one-sided game rather more. In the deciding game of the rubber, on account of the importance of winning the game, the value of each point scored for honours sinks to one-third of a point scored for tricks.

Other Forms of Bridge.—The following varieties of the game are also played:—

Three-handed Bridge.—The three players cut; the one that cuts the lowest card deals, and takes dummy for one deal: each takes dummy in turn. Dummy's cards are dealt face downwards, and the dealer declares without seeing them. If the dealer declares trumps, both adversaries may look at their hands; doubling and redoubling proceeds as at ordinary bridge, but dummy's hand is not exposed till the first card has been led. If the dealer passes the declaration to dummy, his right-hand adversary, who must not have looked at his own hand, examines dummy's, and declares trumps, not, however, exposing the hand. The declaration is forced: with three or four aces sans atout (no trumps) must be declared: in other cases the longest suit: if suits are equal in length, the strongest, i.e. the suit containing most pips, ace counting eleven, king, queen and knave counting ten each. If suits are equal in both length and strength, the one in which the trick has the higher value must be trumps. On the dummy's declaration the third player can only double before seeing his own cards. When the first card has been led, dummy's hand is exposed, never before the lead. The game is 30: the player wins the rubber who is the first to win two games. Fifty points are scored for each game won, and fifty more for the rubber. Sometimes three games are played without reference to a rubber, fifty points being scored for a game won. No tricks score towards game except those which a player wins in his own deal; the value of tricks won in other deals is scored above the line with honours, slam and chicane. At the end of the rubber the totals are added up, and the points won or lost are adjusted thus. Suppose A is credited with 212, B with 290, and C with 312, then A owes 78 to B and 100 to C; B owes 22 to C.

Dummy Bridge.—The player who cuts the lowest card takes dummy. Dummy deals the first hand of all. The player who takes dummy always looks at his own hand first, when he deals for himself or for dummy; he can either declare trumps or "leave it" to dummy. Dummy's declaration is compulsory, as in three-handed bridge. When the dealer deals for dummy, the player on the dealer's left must not look at his cards till either the dealer has declared trumps or, the declaration having been left to dummy, his own partner has led a card. The latter can double, but his partner can only double without seeing his hand. The dealer can only redouble on his own hand. When the player of dummy deals for himself, the player on his right hand looks at dummy's hand if the declaration is passed, the positions and restrictions of his partner and himself being reversed. If the player of dummy declares from his own hand, the game proceeds as in ordinary bridge, except that dummy's hand is not looked at till permission to play has been given. When the player on dummy's right deals, dummy's partner may look at dummy's hand to decide if he will double, but he may not look at his own till a card has been led by dummy. In another form of dummy bridge two hands are exposed whenever dummy's adversaries deal, but the game is unsuited for many players, as in every other hand the game is one of double-dummy.

Misery Bridge.—This is a form of bridge adapted for two players. The non-dealer has the dummy, whilst the dealer is allowed to strengthen his hand by discarding four or fewer cards and taking an equal number from the fourth packet dealt; the rest of the cards in that packet are unused and remain unseen. A novel and interesting addition to the game is that the three of clubs (called "Cato") does not rank as a club but can be played to any trick and win it. The dealer, in addition to his other calls, may declare "misery" when he has to make less than two tricks.

Draw- or Two-handed Bridge.—This is the best form of bridge for two players. Each player has a dummy, which is placed opposite to him; but the cards are so arranged that they cannot be seen by his opponent, a special stand being required for the purpose. The dealer makes the declaration or passes it to his dummy to make by the same rules as in three-handed or dummy bridge. The objection to this is that, since the opponent does not see the dealer's dummy, he has no chance of checking an erroneous declaration. This could be avoided by not allowing the dealer the option of passing.

Auction Bridge.—This variety of the game for four players, which adds an element characteristic of poker, appears to have been suggested about 1904, but was really introduced at the Bath Club, London, in 1907, and then was gradually taken up by a wider circle. The laws were settled in August 1908 by a joint committee of the Bath and Portland clubs. The scoring (except as below), value of suits, and play are as at ordinary bridge, but the variety consists in the method of declaration, the declaration not being confined in auction bridge to the dealer or his partner, and the deal being a disadvantage rather than otherwise. The dealer, having examined his hand, must declare to win at least one "odd" trick, and then each player in turn, beginning with the one on the dealer's left, has the right to pass the previous declaration, or double, or redouble, or overcall by making a declaration of higher value any number of times till all are satisfied, the actual play of the combined hands (or what in ordinary bridge would be dealer and dummy) resting eventually with the partners making the final declaration; the partner who made the first call (however small) in the suit finally constituting the trump (or no-trump) plays the hands, the other being dummy. A declaration of a greater number of tricks in a suit of lower value, which equals a previous call in value of points (e.g. two in spades as against one in clubs) is "of higher value"; but doubling and redoubling only affect the score and not the declaration, so that a call of two diamonds overcalls one no-trump even though this has been doubled. The scoring in auction bridge has the additional element that when the eventual player of the two hands wins what was ultimately declared or more, his side score the full value below the line (as tricks), but if he fails the opponents score 50 points above the line (as honours) for each under-trick (i.e. trick short of the declaration), or 100 or 200 if doubled or redoubled, nothing being scored by either side below the line; the loss on a declaration of one spade is limited, however, to a maximum of 100 points. A player whose declaration has been doubled and who fulfils his contract, scores a bonus of 50 points above the line and a further 50 points for each additional trick beyond his declaration; if there was a redouble and he wins, he scores double the bonus. The penalty for a revoke (unaffected by a double) is (1) in the case of the declarer, that his adversaries add 150 above the line; (2) in the case of one of his adversaries, that the declarer may either add 150 points above the line or may take three tricks from his opponents and add them to his own; in the latter case such tricks may assist him to fulfil his contract, but shall not entitle him to any bonus for a double or redouble. A revoking side may score nothing either above or below the line except for honours or chicane. As regards the essential feature of auction bridge, the competitive declaration, it is impossible here to discuss the intricacies involved. It entails, clearly, much reliance on a good partner, since the various rounds of bidding enable good players to draw inferences as to where the cards lie. The game opens the door to much larger scores than ordinary bridge, and since the end only comes from scores made below the line, there are obvious ways of prolonging it at the cost of scores above the line which involve much more of the gambling element. It by no means follows that the winner of the rubber is the winner by points, and many players prefer to go for points (i.e. above the line) extorted from their opponents rather than for fulfilling a declaration made by themselves.

Authorities.—"Hellespont," Laws and Principles of Bridge; W. Dalton, Saturday Bridge, containing full bibliography (London, 1906); J. B. Elwell, Advanced Bridge; R. F. Foster, Bridge Tactics; "Badsworth," Laws and Principles of Bridge; E. Bergholt, Double-Dummy Bridge: Biritch, or Russian Whist, pamphlet in Brit. Mus.; W. Dalton, Auction Bridge (1908).

(W. H. W.*)

BRIDGEBUILDING BROTHERHOOD, a confraternity (Fratres Pontifices) that arose in the south of France during the latter part of the 12th century, and maintained hospices at the chief fords of the principal rivers, besides building bridges and looking after ferries. The brotherhood was recognized by Pope Clement III. in 1189.

BRIDGE-HEAD (Fr. tête-du-pont), in fortification, a work designed to cover the passage of a river by means of fortifications on one or both banks. As the process of moving an army over bridges is slow and complicated, it is usually necessary to secure it from hostile interruption, and the works constituting the bridge-head must therefore be sufficiently far advanced to keep the enemy's artillery out of range of the bridges. In addition, room is required for the troops to form up on the farther bank. In former days, with short-range weapons, a bridge-head was often little more than a screen for the bridge itself, but modern conditions have rendered necessary far greater extension of bridge defences.

BRIDGEND, a market town in the southern parliamentary division of Glamorganshire, Wales, on both sides of the river Ogwr (whence its Welsh name Penybont-ar-Ogwr). Pop. of urban district (1901) 6062. It has a station 165 m. from London on the South Wales trunk line of the Great Western railway, and is the junction of the Barry Company's railway to Barry via Llantwit Major. Bridgend has a good market for agricultural produce, and is an important centre owing to its being the natural outlet for the mining valleys of the Llynvi, Garw and the two Ogwr rivers, which converge about 3 m. north of the town and are connected with it by branch lines of the Great Western railway. Though without large manufacturing industries, the town has joinery works, a brass and iron foundry, a tannery and brewery. There are brick-works and stone quarries, and much lime is burnt in the neighbourhood. Just outside the town at Angelton and Parc Gwyllt are the Glamorgan county lunatic asylums.

There was no civil parish of Bridgend previous to 1905, when one was formed out of portions of the parishes of Newcastle and Coity. Of the castle of Newcastle, built on the edge of a cliff above the church of that parish, there remain a courtyard with flanking towers and a fine Norman gateway. At Coity, about 2 m. distant, there are more extensive ruins of its castle, originally the seat of the Turbervilles, lords of Coity, but now belonging to the earls of Dunraven. Coity church, dating from the 14th century, is a fine cruciform building with central embattled tower in Early Decorated style.

BRIDGE OF ALLAN, a police burgh of Stirlingshire, Scotland. Pop. (1901) 3240. It lies on the Allan, a left-hand tributary of the Forth, 3 m. N. of Stirling by the Caledonian railway and by tramway. Built largely on the well-wooded slopes of Westerton and Airthrey Hill, sheltered by the Ochils from the north and east winds, and environed by charming scenery, it has a great reputation as a health resort and watering-place, especially in winter and spring. There is a pump-room. The chief buildings are the hydropathic and the Macfarlane museum of fine art and natural history. The industries include bleaching, dyeing and paper-making. The Strathallan Gathering, usually held in the neighbourhood, is the most popular athletic meeting in mid-Scotland. Airthrey Castle, standing in a fine park with a lake, adjoins the town on the south-east, and just beyond it are the old church and burying-ground of Logie, beautifully situated at the foot of a granite spur of the Ochil range.

BRIDGEPORT, a city, a port of entry, and one of the county-seats of Fairfield county, Connecticut, U.S.A., co-extensive with the town of Bridgeport, in the S.W. part of the state, on Long Island Sound, at the mouth of the Pequonnock river; about 18 m. S.W. of New Haven. Pop. (1880) 27,643; (1890) 48,866; (1900) 70,996, of whom 22,281 were foreign-born, including 5974 from Ireland, 3172 from Hungary, 2854 from Germany, 2755 from England, and 1436 from Italy; (1910) 102,054. Bridgeport is served by the New York, New Haven & Hartford railway, by lines of coast steamers, and by steamers to New York City and to Port Jefferson, directly across Long Island Sound. The harbour, formed by the estuary of the river and Yellow Mill Pond, an inlet, is excellent. Between the estuary and the pond is a peninsula, East Bridgeport, in which are some of the largest manufacturing establishments, and west of the harbour and the river is the main portion of the city, the wholesale section extending along the bank, the retail section farther back, and numerous factories along the line of the railway far to the westward. There are two large parks, Beardsley, in the extreme north part of the city, and Seaside, west of the harbour entrance and along the Sound; in the latter are statues of Elias Howe, who built a large sewing-machine factory here in 1863, and of P.T. Barnum, the showman, who lived in Bridgeport after 1846 and did much for the city, especially for East Bridgeport. In Seaside Park there is also a soldiers' and sailors' monument, and in the vicinity are many fine residences. The principal buildings are the St Vincent's and Bridgeport hospitals, the Protestant orphan asylum, the Barnum Institute, occupied by the Bridgeport Scientific and Historical Society and the Bridgeport Medical Society; and the United States government building, which contains the post-office and the customs house.

In 1905 Bridgeport was the principal manufacturing centre in Connecticut, the capital invested in manufacturing being $49,381,348, and the products being valued at $44,586,519. The largest industries were the manufacture of corsets—the product of Bridgeport was 19.9% of the total for the United States in 1905, Bridgeport being the leading city in this industry—sewing machines (one of the factories of the Singer Manufacturing Co. is here), steam-fitting and heating apparatus, cartridges (the factory of the Union Metallic Cartridge Co. is here), automobiles, brass goods, phonographs and gramophones, and typewriters. There are also large foundry and machine shops. Here, too, are the winter headquarters of "Barnum and Bailey's circus" and of "Buffalo Bill's Wild West Show." Bridgeport is a port of entry; its imports in 1908 were valued at $656,271. Bridgeport was originally a part of the township of Stratford. The first settlement here was made in 1659. It was called Pequonnock until 1695, when its name was changed to Stratfield. During the War of Independence it was a centre of privateering. In 1800 the borough of Bridgeport was chartered, and in 1821 the township was incorporated. The city was not chartered until 1836.

See S. Orcutt's History of the Township of Stratford and the City of Bridgeport (New Haven, 1886).

BRIDGES, ROBERT (1844- ), English poet, born on the 23rd of October 1844, was educated at Eton and at Corpus Christi College, Oxford, and studied medicine in London at St Bartholomew's hospital. He was afterwards assistant physician at the Children's hospital, Great Ormond Street, and physician at the Great Northern hospital, retiring in 1882. Two years later he married Mary, daughter of Alfred Waterhouse, R.A. As a poet Robert Bridges stands rather apart from the current of modern English verse, but his work has had great influence in a select circle, by its restraint, purity, precision, and delicacy yet strength of expression; and it embodies a distinct theory of prosody. His chief critical works are Milton's Prosody (1893), a volume made up of two earlier essays (1887 and 1889), and John Keats, a Critical Essay (1895). He maintained that English prosody depended on the number of "stresses" in a line, not on the number of syllables, and that poetry should follow the rules of natural speech. His poetry was privately printed in the first instance, and was slow in making its way beyond a comparatively small circle of his admirers. His best work is to be found in his Shorter Poems (1890), and a complete edition of his Poetical Works (6 vols.) was published in 1898-1905. His chief volumes are Prometheus (Oxford, 1883, privately printed), a "mask in the Greek Manner"; Eros and Psyche (1885), a version of Apuleius; The Growth of Love, a series of sixty-nine sonnets printed for private circulation in 1876 and 1889; Shorter Poems (1890); Nero (1885), a historical tragedy, the second part of which appeared in 1894; Achilles in Scyros (1890), a drama; Palicio (1890), a romantic drama in the Elizabethan manner; The Return of Ulysses (1890), a drama in five acts; The Christian Captives (1890), a tragedy on the same subject as Calderon's El Principe Constante; The Humours of the Court (1893), a comedy founded on the same dramatist's El secreto á voces and on Lope de Vega's El Perro del hortelano; The Feast of Bacchus (1889), partly translated from the Heauton-Timoroumenos of Terence; Hymns from the Yattendon Hymnal (Oxford, 1899); and Demeter, a Mask (Oxford, 1905).

BRIDGES. 1. Definitions and General Considerations.—Bridges (old forms, brig, brygge, brudge; Dutch, brug; German, Brücke; a common Teutonic word) are structures carrying roadways, waterways or railways across streams, valleys or other roads or railways, leaving a passage way below. Long bridges of several spans are often termed "viaducts," and bridges carrying canals are termed "aqueducts," though this term is sometimes used for waterways which have no bridge structure. A "culvert" is a bridge of small span giving passage to drainage. In railway work an "overbridge" is a bridge over the railway, and an "underbridge" is a bridge carrying the railway. In all countries there are legal regulations fixing the minimum span and height of such bridges and the width of roadway to be provided. Ordinarily bridges are fixed bridges, but there are also movable bridges with machinery for opening a clear and unobstructed passage way for navigation. Most commonly these are "swing" or "turning" bridges. "Floating" bridges are roadways carried on pontoons moored in a stream.

In classical and medieval times bridges were constructed of timber or masonry, and later of brick or concrete. Then late in the 18th century wrought iron began to be used, at first in combination with timber or cast iron. Cast iron was about the same time used for arches, and some of the early railway bridges were built with cast iron girders. Cast iron is now only used for arched bridges of moderate span. Wrought iron was used on a large scale in the suspension road bridges of the early part of the 19th century. The great girder bridges over the Menai Strait and at Saltash near Plymouth, erected in the middle of the 19th century, were entirely of wrought iron, and subsequently wrought iron girder bridges were extensively used on railways. Since the introduction of mild steel of greater tenacity and toughness than wrought iron (i.e. from 1880 onwards) it has wholly superseded the latter except for girders of less than 100 ft. span. The latest change in the material of bridges has been the introduction of ferro-concrete, armoured concrete, or concrete strengthened with steel bars for arched bridges. The present article relates chiefly to metallic bridges. It is only since metal has been used that the great spans of 500 to 1800 ft. now accomplished have been made possible.

2. In a bridge there may be distinguished the superstructure and the substructure. In the former the main supporting member or members may be an arch ring or arched ribs, suspension chains or ropes, or a pair of girders, beams or trusses. The bridge flooring rests on the supporting members, and is of very various types according to the purpose of the bridge. There is also in large bridges wind-bracing to stiffen the structure against horizontal forces. The substructure consists of (a) the piers and end piers or abutments, the former sustaining a vertical load, and the latter having to resist, in addition, the oblique thrust of an arch, the pull of a suspension chain, or the thrust of an embankment; and (b) the foundations below the ground level, which are often difficult and costly parts of the structure, because the position of a bridge may be fixed by considerations which preclude the selection of a site naturally adapted for carrying a heavy structure.

3. Types of Bridges.—Bridges may be classed as arched bridges, in which the principal members are in compression; suspension bridges, in which the principal members are in tension; and girder bridges, in which half the components of the principal members are in compression and half in tension. But there are cases of bridges of mixed type. The choice of the type to be adopted depends on many and complex considerations:—(1) The cost, having regard to the materials available. For moderate spans brick, masonry or concrete can be used without excessive cost, but for longer spans steel is more economical, and for very long spans its use is imperative. (2) The importance of securing permanence and small cost of maintenance and repairs has to be considered. Masonry and concrete are more durable than metal, and metal than timber. (3) Aesthetic considerations sometimes have great weight, especially in towns. Masonry bridges are preferable in appearance to any others, and metal arch bridges are less objectionable than most forms of girder.

Most commonly the engineer has to attach great importance to the question of cost, and to design his structure to secure the greatest economy consistent with the provision of adequate strength. So long as bridge building was an empirical art, great waste of material was unavoidable. The development of the theory of structures has been largely directed to determining the arrangements of material which are most economical, especially in the superstructure. In the case of bridges of large span the cost and difficulty of erection are serious, and in such cases facility of erection becomes a governing consideration in the choice of the type to be adopted. In many cases the span is fixed by local conditions, such as the convenient sites for piers, or the requirements of waterway or navigation. But here also the question of economy must be taken into the reckoning. The cost of the superstructure increases very much as the span increases, but the greater the cost of the substructure, the larger the span which is economical. Broadly, the least costly arrangement is that in which the cost of the superstructure of a span is equal to that of a pier and foundation.

For masonry, brick or concrete the arch subjected throughout to compression is the most natural form. The arch ring can be treated as a blockwork structure composed of rigid voussoirs. The stability of such structures depends on the position of the line of pressure in relation to the extrados and intrados of the arch ring. Generally the line of pressure lies within the middle half of the depth of the arch ring. In finding the line of pressure some principle such as the principle of least action must be used in determining the reactions at the crown and springings, and some assumptions must be made of not certain validity. Hence to give a margin of safety to cover contingencies not calculable, an excess of material must be provided. By the introduction of hinges the position of the line of resistance can be fixed and the stress in the arch ring determined with less uncertainty. In some recent masonry arched bridges of spans up to 150 ft. built with hinges considerable economy has been obtained.

For an elastic arch of metal there is a more complete theory, but it is difficult of application, and there remains some uncertainty unless (as is now commonly done) hinges are introduced at the crown and springings.

In suspension bridges the principal members are in tension, and the introduction of iron link chains about the end of the 18th century, and later of wire ropes of still greater tenacity, permitted the construction of road bridges of this type with spans at that time impossible with any other system of construction. The suspension bridge dispenses with the compression member required in girders and with a good deal of the stiffening required in metal arches. On the other hand, suspension bridges require lofty towers and massive anchorages. The defect of the suspension bridge is its flexibility. It can be stiffened by girders and bracing and is then of mixed type, when it loses much of its advantage in economy. Nevertheless, the stiffened suspension bridge will probably be the type adopted in future for very great spans. A bridge on this system has been projected at New York of 3200 ft. span.

The immense extension of railways since 1830 has involved the construction of an enormous number of bridges, and most of these are girder bridges, in which about half the superstructure is in tension and half in compression. The use of wrought iron and later of mild steel has made the construction of such bridges very convenient and economical. So far as superstructure is concerned, more material must be used than for an arch or chain, for the girder is in a sense a combination of arch and chain. On the other hand, a girder imposes only a vertical load on its piers and abutments, and not a horizontal thrust, as in the case of an arch or suspension chain. It is also easier to erect.

A fundamental difference in girder bridges arises from the mode of support. In the simplest case the main girders are supported at the ends only, and if there are several spans they are discontinuous or independent. But a main girder may be supported at two or more points so as to be continuous over two or more spans. The continuity permits economy of weight. In a three-span bridge the theoretical advantage of continuity is about 49% for a dead load and 16% for a live load. The objection to continuity is that very small alterations of level of the supports due to settlement of the piers may very greatly alter the distribution of stress, and render the bridge unsafe. Hence many multiple-span bridges such as the Hawkesbury, Benares and Chittravatti bridges have been built with independent spans.

Lastly, some bridges are composed of cantilevers and suspended girders. The main girder is then virtually a continuous girder hinged at the points of contrary flexure, so that no ambiguity can arise as to the stresses.

Fig. 1.—Trajan's Bridge.

Whatever type of bridge is adopted, the engineer has to ascertain the loads to be carried, and to proportion the parts so that the stresses due to the loads do not exceed limits found by experience to be safe. In many countries the limits of working stress in public and railway bridges are prescribed by law. The development of theory has advanced pari passu with the demand for bridges of greater strength and span and of more complex design, and there is now little uncertainty in calculating the stresses in any of the types of structure now adopted. In the modern metal bridge every member has a definite function and is subjected to a calculated straining action. Theory has been the guide in the development of bridge design, and its trustworthiness is completely recognized. The margin of uncertainty which must be met by empirical allowances on the side of safety has been steadily diminished.

The larger the bridge, the more important is economy of material, not only because the total expenditure is more serious, but because as the span increases the dead weight of the structure becomes a greater fraction of the whole load to be supported. In fact, as the span increases a point is reached at which the dead weight of the superstructure becomes so large that a limit is imposed to any further increase of span.

Fig. 2.—Bridge of Alcantara.

History of Bridge Building

Fig. 3.—Ponte Salario.

4. Roman Bridges.—The first bridge known to have been constructed at Rome over the Tiber was the timber Pons Sublicius, the bridge defended by Horatius. The Pons Milvius, now Ponte Molle, was reconstructed in stone by M. Aemilius Scaurus in 109 B.C., and some portions of the old bridge are believed to exist in the present structure. The arches vary from 51 to 79 ft. span. The Pons Fabricius (mod. Ponte dei Quattro Capi), of about 62 B.C., is practically intact; and the Pons Cestius, built probably in 46 B.C., retains much of the original masonry. The Pons Aelius, built by Hadrian A.D. 134 and repaired by Pope Nicholas II. and Clement IX., is now the bridge of St Angelo. It had eight arches, the greatest span being 62 ft.^[1] Dio Cassius mentions a bridge, possibly 3000 to 4000 ft. in length, built by Trajan over the Danube in A.D. 104. Some piers are said still to exist. A bas-relief on the Trajan column shows this bridge with masonry piers and timber arches, but the representation is probably conventional (fig. 1). Trajan also constructed the bridge of Alcantara in Spain (fig. 2), of a total length of 670 ft., at 210 ft. above the stream. This had six arches and was built of stone blocks without cement. The bridge of Narses, built in the 6th century (fig. 3), carried the Via Salaria over the Anio. It was destroyed in 1867, during the approach of Garibaldi to Rome. It had a fortification such as became usual in later bridges for defence or for the enforcement of tolls. The great lines of aqueducts built by Roman engineers, and dating from 300 B.C. onwards, where they are carried above ground, are arched bridge structures of remarkable magnitude (see Aqueducts, § Roman). They are generally of brick and concrete.

Fig. 4.—First Span of Schaffhausen Bridge.

5. Medieval and other Early Bridges.—Bridges with stone piers and timber superstructures were no doubt constructed from Roman times onward, but they have perished. Fig. 4 shows a timber bridge erected by the brothers Grubenmann at Schaffhausen about the middle of the 18th century. It had spans of 172 and 193 ft., and may be taken as a representative type of bridges of this kind. The Wittingen bridge by the same engineers had a span of 390 ft., probably the longest timber span ever constructed. Of stone bridges in Great Britain, the earliest were the cyclopean bridges still existing on Dartmoor, consisting of stone piers bridged by stone slabs. The bridge over the East Dart near Tavistock had three piers, with slabs 15 ft. by 6 ft. (Smiles, Lives of the Engineers, ii. 43). It is reputed to have lasted for 2000 years.

Fig. 5.—Crowland Bridge.

The curious bridge at Crowland near Peterborough (fig. 5) which now spans roadways, the streams which formerly flowed under it having been diverted, is one of the earliest known stone bridges in England. It is referred to in a charter of the year 943. It was probably built by the abbots. The first bridges over the Thames at London were no doubt of timber. William of Malmesbury mentions the existence of a bridge in 994. J. Stow (Survey of the Cities of London and Westminster) describes the building of the first stone bridge commonly called Old London Bridge: "About the year 1176, the stone bridge was begun to be founded by Peter of Colechurch, near unto the bridge of timber, but more towards the west." It carried timber houses (fig. 6) which were frequently burned down, yet the main structure existed till the beginning of the 19th century. The span of the arches ranged from 10 to 33 ft., and the total waterway was only 337 ft. The waterway of the present London Bridge is 690 ft., and the removal of the obstruction caused by the old bridge caused a lowering of the low-water level by 5 ft., and a considerable deepening of the river-bed. (See Smiles, Lives of the Engineers, "Rennie.")

Fig.

6.—Old London Bridge,

A.D.

1600. From a Drawing in the Pepysian Library Magdalene College, Cambridge.

The architects of the Renaissance showed great boldness in their designs. A granite arch built in 1377 over the Adda at Trezzo had a span at low water of 251 ft. This noble bridge was destroyed for military reasons by Carmagnola in 1416. The Rialto bridge at Venice, with a span of 91 ft., was built in 1588 by Antonio da Ponte. Fig. 7 shows the beautiful Ponte dellà Trinità erected at Florence in 1566 from the design of B. Ammanati.

6. Modern Bridges.—(a) Timber.—In England timber bridges of considerable span, either braced trusses or laminated arches (i.e. arches of planks bolted together), were built for some of the earlier railways, particularly the Great Western and the Manchester, Sheffield & Lincolnshire. They have mostly been replaced, decay having taken place at the joints. Timber bridges of large span were constructed in America between the end of the 18th and the middle of the 19th century. The Amoskeag bridge over the Merrimac at Manchester, N.H., U.S.A., built in 1792, had 6 spans of 92 ft. The Bellows Falls bridge over the Connecticut (built 1785-1792) had 2 spans of 184 ft. The singular Colossus bridge, built in 1812 over the Schuylkill, a kind of flat arched truss, had a span of 340 ft. Some of these timber bridges are said to have lasted ninety years with ordinary repairs, but they were road bridges not heavily loaded. From 1840, trusses, chiefly of timber but with wrought-iron tension-rods and cast-iron shoes, were adopted in America. The Howe truss of 1830 and the Pratt truss of 1844 are examples. The Howe truss had timber chords and a lattice of timber struts, with vertical iron ties. In the Pratt truss the struts were vertical and the ties inclined. Down to 1850 such bridges were generally limited to 150 ft. span. The timber was white pine. As railway loads increased and greater spans were demanded, the Howe truss was stiffened by timber arches on each side of each girder. Such a composite structure is, however, fundamentally defective, the distribution of loading to the two independent systems being indeterminate. Remarkably high timber piers were built. The Genesee viaduct, 800 ft. in length, built in 1851-1852 in 10 spans, had timber trestle piers 190 ft. in height. (See Mosse, "American Timber Bridges," Proc. Inst. C.E. xxii. p. 305, and for more modern examples, cxlii. p. 409; and clv. p. 382; Cooper, "American Railroad Bridges," Trans. Am. Soc. C.E. vol. xxi pp. 1-28.) These timber framed structures served as models for the earlier metal trusses which began to be used soon after 1850, and which, except in a few localities where iron is costly, have quite superseded them.

Fig. 7.—Ponte della Trinità, Florence.

7. (b) Masonry.—The present London Bridge, begun in 1824 and completed in 1831, is as fine an example of a masonry arch structure as can be found (figs. 8 and 9). The design was made by John Rennie the elder, and the acting engineer was his son, Sir John Rennie. The semi-elliptical shape of the arches the variation of span, the slight curvature of the roadway, and the simple yet bold architectural details, combine to make it a singularly beautiful bridge. The centre arch has a span of 152 ft., and rises 29 ft. 6 in above Trinity high-water mark; the arches on each side of the centre have a span of 140 ft. and the abutment arches 130 ft. The total length of the bridge is 1005 ft., its width from outside to outside 56 ft., and height above low water 60 ft. The two centre piers are 24 ft. thick, the exterior stones are granite, the interior, half Bramley Fall and half from Painshaw, Derbyshire. The voussoirs of the centre arch (all of granite) are 4 ft. 9 in. deep at the crown, and increase to not less than 9 ft. at the springing. The general depth at which the foundations are laid is about 29 ft. 6 in. below low water. The total cost was £1,458,311, but the contractor's tender for the bridge alone was £425,081.

Fig. 8.—London New Bridge.

Since 1867 it had been recognized that London Bridge was inadequate to carry the traffic passing over it, and a scheme for widening it was adopted in 1900. This was carried out in 1902-1904, the footways being carried on granite corbels, on which are mounted cornices and open parapets. The width between parapets is now 65 ft., giving a roadway of 35 ft. and two footways of 15 ft. each. The architect was Andrew Murray and the engineer, G. E. W. Cruttwell. (Cole, Proc. Inst. C.E. clxi. p. 290.)

The largest masonry arch is the Adolphe bridge in Luxemburg, erected in 1900-1903. This has a span of 278 ft., 138 ft. rise above the river, and 102 ft. from foundation to crown. The thickness of the arch is 4 ft. 8 in. at the crown and 7 ft. 2 in. where it joins the spandrel masonry. The roadway is 52 ft. 6 in. wide. The bridge is not continuous in width, there are arch rings on each face, each 16.4 ft. wide with a space between of 19.7 ft. This space is filled with a flooring of reinforced concrete, resting on the two arches, and carrying the central roadway. By the method adopted the total masonry has been reduced one-third. One centering was used for the two arch rings, supported on dwarf walls which formed a slipway, along which it was moved after the first was built.

Fig. 9.—Half Elevation and Half Section of Arch of London Bridge.

Till near the end of the 19th century bridges of masonry or brickwork were so constructed that they had to be treated as rigid blockwork structures. The stability of such structures depends on the position of the line of pressure relatively to the intrados and extrados of the arch ring. Generally, so far as could be ascertained, the line of pressure lies within the middle half of the depth of the voussoirs. In finding the abutment reactions some principle such as the principle of least action must be used, and some assumptions of doubtful validity made. But if hinges are introduced at crown and springings, the calculation of the stresses in the arch ring becomes simple, as the line of pressures must pass through the hinges. Such hinges have been used not only for metal arches, but in a modified form for masonry and concrete arches. Three cases therefore arise: (a) The arch is rigid at crown and springings; (b) the arch is two-hinged (hinges at springings); (c) the arch is three-hinged (hinges at crown and springings). For an elementary account of the theory of arches, hinged or not, reference may be made to a paper by H. M. Martin (Proc. Inst. C. E. vol. xciii. p. 462); and for that of the elastic arch, to a paper by A.E.Young (Proc. Inst. C.E. vol. cxxxi. p. 323).

In Germany and America two- and three-hinged arches of masonry and concrete have been built, up to 150 ft. span, with much economy, and the calculations being simple, an engineer can venture to work closely to the dimensions required by theory. For hinges, Leibbrand, of Stuttgart, uses sheets of lead about 1 in. thick extending over the middle third of the depth of the voussoir joints, the rest of the joints being left open. As the lead is plastic this construction is virtually an articulation. If the pressure on the lead is uniformly varying, the centre of pressure must be within the middle third of the width of the lead; that is, it cannot deviate from the centre of the voussoir joint by more than one-eighteenth of its depth. In any case the position of the line of pressures is confined at the lead articulations within very narrow limits, and ambiguity as to the stresses is greatly diminished. The restricted area on which the pressure acts at the lead joints involves greater intensity of stress than has been usual in arched bridges. In the Württemberg hinged arches a limit of stress of 110 tons per sq. ft. was allowed, while in the unhinged arches at Cologne and Coblentz the limit was 50 to 60 tons per sq. ft. (Annales des Fonts et Chaussées, 1891). At Rechtenstein a bridge of two concrete arches has been constructed, span 75½ ft., with lead articulations: width of arch 11 ft.; depth of arch at crown and springing 2.1 and 2.96 ft. respectively. The stresses were calculated to be 15, 17 and 12 tons per sq. ft. at crown, joint of rupture, and springing respectively. At Cincinnati a concrete arch of 70 ft. span has been built, with a rise of 10 ft. The concrete is reinforced by eleven 9-in. steel-rolled joists, spaced 3 ft. apart and supported by a cross-channel joist at each springing. The arch is 15 in. thick at the crown and 4 ft. at the abutments. The concrete consisted of 1 cement, 2 sand and 3 to 4 broken stone. An important series of experiments on the strength of masonry, brick and concrete structures will be found in the Zeitschr. des österreichen Ing. und Arch. Vereines (1895).

The thermal coefficient of expansion of steel and concrete is nearly the same, otherwise changes of temperature would cause shearing stress at the junction of the two materials. If the two materials are disposed symmetrically, the amount of load carried by each would be in direct proportion to the coefficient of elasticity and inversely as the moment of inertia of the cross section. But it is usual in many cases to provide a sufficient section of steel to carry all the tension. For concrete the coefficient of elasticity E varies with the amount of stress and diminishes as the ratio of sand and stone to cement increases. Its value is generally taken at 1,500,000 to 3,000,000 lb per sq. in. For steel E = 28,000,000 to 30,000,000, or on the average about twelve times its value for concrete. The maximum compressive working stress on the concrete may be 500 lb per sq. in., the tensile working stress 50 lb per sq. in., and the working shearing stress 75 lb per sq. in. The tensile stress on the steel may be 16,000 lb per sq. in. The amount of steel in the structure may vary from 0.75 to 1.5%. The concrete not only affords much of the strength to resist compression, but effectively protects the steel from corrosion.

8. (c) Suspension Bridges.—A suspension bridge consists of two or more chains, constructed of links connected by pins, or of twisted wire strands, or of wires laid parallel. The chains pass over lofty piers on which they usually rest on saddles carried by rollers, and are led down on either side to anchorages in rock chambers. A level platform is hung from the chains by suspension rods. In the suspension bridge iron or steel can be used in its strongest form, namely hard-drawn wire. Iron suspension bridges began to be used at the end of the 18th century for road bridges with spans unattainable at that time in any other system. In 1819 T. Telford began the construction of the Menai bridge (fig. 10), the span being 570 ft. and the dip 43 ft. This bridge suffered some injury in a storm, but it is still in good condition and one of the most graceful of bridges. Other bridges built soon after were the Fribourg bridge of 870 ft. span, the Hammersmith bridge of 422 ft. span, and the Pest bridge of 666 ft. span. The merit of the simple suspension bridge is its cheapness, and its defect is its flexibility. This last becomes less serious as the dead weight of the structure becomes large in proportion to the live or temporary load. It is, therefore, a type specially suited for great spans. Some suspension bridges have broken down in consequence of the oscillations produced by bodies of men marching in step. In 1850 a suspension bridge at Angers gave way when 487 soldiers were marching over it, and 226 were killed.

Fig. 10.—Menai Suspension Bridge.

To obtain greater stiffness various plans have been adopted. In the Ordish system a certain number of intermediate points in the span are supported by oblique chains, on which girders rest. The Ordish bridge built at Prague in 1868 had oblique chains supporting the stiffening girders at intermediate points of the span. A curved chain supported the oblique chains and kept them straight. In 1860 a bridge was erected over the Danube canal at Vienna, of 264 ft. span which had two parallel chains one above the other and 4 ft. apart on each side of the bridge. The chains of each pair were connected by bracing so that they formed a stiff inverted arch resisting deformation under unequal loading. The bridge carried a railway, but it proved weak owing to errors of calculation, and it was taken down in 1884. The principle was sound and has been proposed at various times. About 1850 it was perceived that a bridge stiff enough to carry railway trains could be constructed by combining supporting chains with stiffening girders suspended from them. W. J. M. Rankine proved (Applied Mechanics, p. 370) that the necessary strength of a stiffening girder would be only one-seventh part of that of an independent girder of the same span as the bridge, suited to carry the same moving load (not including the dead weight of the girder which is supported by the chain). (See "Suspension Bridge with Stiffened Roadway," by Sir G. Airy, and the discussion, Proc. Inst, C.E., 1867, xxvi. p. 258; also "Suspension Bridges with Stiffening Girders," by Max am Ende, Proc. Inst. C.E. cxxxvii. p. 306.)

Fig. 11.—Niagara Suspension Bridge.

The most remarkable bridge constructed on this system was the Niagara bridge built by J. A. Roebling in 1852-1855 (fig. 11). The span was 821 ft., much the largest of any railway bridge at that time, and the height above the river 245 ft. There were four suspension cables, each 10 in. in diameter; each was composed of seven strands, containing 520 parallel wires, or 3640 wires in each cable. Each cable was carried on a separate saddle on rollers on each pier. The stiffening girder, constructed chiefly of timber, was a box-shaped braced girder 18 ft. deep and 25 ft. wide, carrying the railway on top and a roadway within. After various repairs and strengthenings, including the replacement of the timber girder by an iron one in 1880, this bridge in 1896-1897 was taken down and a steel arch built in its place. It was not strong enough to deal with the increasing weight of railway traffic. In 1836 I. K. Brunei constructed the towers and abutments for a suspension bridge of 702 ft. span at Clifton over the Avon, but the project was not then carried further; in 1860, however, the link chains of the Hungerford suspension bridge which was being taken down were available at small cost, and these were used to complete the bridge. There are three chains on each side, of one and two links alternately, and these support wrought iron stiffening girders. There are wrought iron saddles and steel rollers on the piers. At 196 ft. on either side from the towers the chains are carried over similar saddles without rollers, and thence at 45° with the horizontal down to the anchorages. Each chain has an anchor plate 5 ft. by 6 ft. The links are 24 ft. long at the centre of the bridge, and longer as they are more inclined, so that their horizontal projection is 24 ft. The chains are so arranged that there is a suspending rod at each 8 ft., attached at the joint of one of the three chains. For erection a suspended platform was constructed on eight wire ropes, on which the chains were laid out and connected. Another wire rope with a travelling carriage took out the links. The sectional area of the chains is 481 sq. in. at the piers and 440 sq. in. at the centre. The two stiffening girders are plate girders 3 ft. deep with flanges of 11 sq. in. area. In addition, the hand railing on each side forms a girder 4 ft. 9 in. deep, with flanges 4½ sq. in. area.

Fig. 12.—Williamsburg Suspension Bridge.

Of later bridges of great span, perhaps the bridges over the East river at New York are the most remarkable. The Brooklyn bridge, begun in 1872, has a centre span of 1595½ and side spans of 930 ft. The Brooklyn approach being 971 ft., and the New York approach 1562½ ft., the total length of the bridge is 5989 ft. There are four cables which carry a promenade, a roadway and an electric railway. The stiffening girders of the main span are 40 ft. deep and 67 ft. apart. The saddles for the chains are 329 ft. above high water. The cables are 15¾ in. in diameter. Each cable has 19 strands of 278 parallel steel wires, 7 B.W.G. Each wire is taken separately across the river and its length adjusted. Roebling preferred parallel wires as 10 % stronger than twisted wires. Each strand when made up and clamped was lowered to its position. The Williamsburg bridge (fig. 12), begun in 1897 and opened for traffic in 1903, has a span of 1600 ft., a versed sine of 176 ft., and a width of 118 ft. It has two decks, and carries two elevated railway tracks, four electric tramcar lines, two carriageways, two footways and two bicycle paths. There are four cables, one on each side of the two main trusses or stiffening girders. These girders are supported by the cables over the centre span but not in the side spans. Intermediate piers support the trusses in the side spans. The cables are 18¾ in. in diameter; each weighs about 1116 tons, and has a nominal breaking strength of 22,320 tons, the actual breaking strength being probably greater. The saddles are 332 ft. above the water. The four cables support a dead load of 7140 tons and a live load of 4017 tons. Each cable is composed of 37 strands of 208 wires, or 7696 parallel steel wires, No. 8 B.W.G., or about 3/16 in. in diameter. The wire was required to have a tensile strength of 89 tons per sq. in., and 2½% elongation in 5 ft. and 5% in 8 in. Cast steel clamps hold the cable together, and to these the suspending rods are attached. The cables are wrapped in cotton duck soaked in oxidized oil and varnish, and are sheathed in sheet iron. A later bridge, the Manhattan, is designed to carry four railway tracks and four tramway lines, with a wide roadway and footpaths, supported by cables 21¼ in. in diameter, each composed of 9472 galvanized steel wires 3/16 in. in diameter.

Fig. 13.—Tower Bridge, London.

The Tower Bridge, London (fig. 13), is a suspension bridge with a secondary bascule bridge in the centre span to permit the passage of ships. Two main towers in the river and two towers on the shore abutments carry the suspension chains. The opening bridge between the river towers consists of two leaves or bascules, pivoted near the faces of the piers and rotating in a vertical plane. When raised, the width of 200 ft. between the main river piers is unobstructed up to the high-level foot-bridge, which is 141 ft. above Trinity H.W. The clear width of the two shore spans is 270 ft. The total length of the bridge is 940 ft., and that of the approaches 1260 ft. on the north and 780 ft. on the south. The width of the bridge between parapets is 60 ft., except across the centre span, where it is 49 ft. The main towers consist of a skeleton of steel, enclosed in a facing of granite and Portland stone, backed with brickwork. There are two high-level footways for use when the bascules are raised, the main girders of which are of the cantilever and suspended girder type. The cantilevers are fixed to the shore side of the towers. The middle girders are 120 ft. in length and attached to the cantilevers by links. The main suspension chains are carried across the centre span in the form of horizontal ties resting on the high-level footway girders. These ties are jointed to the hanging chains by pins 20 in. in diameter with a ring in halves surrounding it 5 in. thick. One half ring is rigidly attached to the tie and one to the hanging chain, so that the wear due to any movement is distributed over the length of the pin. A rocker bearing under these pins transmits the load at the joint to the steel columns of the towers. The abutment towers are similar to the river towers. On the abutment towers the chains are connected by horizontal links, carried on rockers, to anchor ties. The suspension chains are constructed in the form of braced girders, so that they are stiff against unsymmetrical loading. Each chain over a shore span consists of two segments, the longer attached to the tie at the top of the river tower, the shorter to the link at the top of the abutment tower, and the two jointed together at the lowest point. Transverse girders are hung from the chains at distances of 18 ft. There are fifteen main transverse girders to each shore span, with nine longitudinal girders between each pair. The trough flooring, ⅜ in. thick and 6 in. deep, is riveted to the longitudinals. The anchor ties are connected to girders embedded in large concrete blocks in the foundations of the approach viaducts.

The two bascules are each constructed with four main girders. Over the river these are lattice girders, with transverse girders 12 ft. apart, and longitudinal and subsidiary transverse girders dividing the floor into rectangles 3 ft. by 3½ ft. covered with buckled plates. The roadway is of pine blocks dowelled. The bascules rotate through an angle of 82°, and their rear ends in the bascule chambers of the piers carry 365 tons of counterweight, the total weight of each being 1070 tons. They rotate on steel shafts 21 in. in diameter and 48 ft. long, and the bascules can be lifted or lowered in one minute, but usually the time taken is one and a half minutes. They are worked by hydraulic machinery.

9. (d) Iron and Steel Girder Bridges.—The main supporting members are two or more horizontal beams, girders or trusses. The girders carry a floor or platform either on top (deck bridges) or near the bottom (through bridges). The platform is variously constructed. For railway bridges it commonly consists of cross girders, attached to or resting on the main girders, and longitudinal rail girders or stringers carried by the cross girders and directly supporting the sleepers and rails. For spans over 75 ft., expansion due to change of temperature is provided for by carrying one end of each chain girder on rollers placed between the bearing-plate on the girder and the bed-plate on the pier or abutment.

Fig. 14 shows the roller bed of a girder of the Kuilenburg bridge of 490 ft. span. It will be seen that the girder directly rests on a cylindrical pin or rocker so placed as to distribute the load uniformly to all the rollers. The pressure on the rollers is limited to about p = 600 d in lb per in. length of roller, where d is the diameter of the roller in inches.

Fig. 14.—Roller Bed of a Girder.

In the girders of bridges the horizontal girder is almost exclusively subjected to vertical loading forces. Investigation of the internal stresses, which balance the external forces, shows that most of the material should be arranged in a top flange, boom or chord, subjected to compression, and a bottom flange or chord, subjected to tension. (See Strength of Materials.) Connecting the flanges is a vertical web which may be a solid plate or a system of bracing bars. In any case, though the exact form of cross section of girders varies very much, it is virtually an I section (fig. 15). The function of the flanges is to resist a horizontal tension and compression distributed practically uniformly on their cross sections. The web resists forces equivalent to a shear on vertical and horizontal planes. The inclined tensions and compressions in the bars of a braced web are equivalent to this shear. The horizontal stresses in the flanges are greatest at the centre of a span. The stresses in the web are greatest at the ends of the span. In the most numerous cases the flanges or chords are parallel. But girders may have curved chords and then the stresses in the web are diminished.

Fig. 15.—Flanged Girder.

At first girders had solid or plate webs, but for spans over 100 ft. the web always now consists of bracing bars. In some girder bridges the members are connected entirely by riveting, in others the principal members are connected by pin joints. The pin system of connexion used in the Chepstow, Saltash, Newark Dyke and other early English bridges is now rarely used in Europe. But it is so commonly used in America as to be regarded as a distinctive American feature. With pin connexions some weight is saved in the girders, and erection is a little easier. In early pin bridges insufficient bearing area was allowed between the pins and parts connected, and they worked loose. In some cases riveted covers had to be substituted for the pins. The proportions are now better understood. Nevertheless the tendency is to use riveted connexions in preference to pins, and in any case to use pins for tension members only.

On the first English railways cast iron girder bridges for spans of 20 to 66 ft. were used, and in some cases these were trussed with wrought iron. When in 1845 the plans for carrying the Chester and Holyhead railway over the Menai Straits were considered, the conditions imposed by the admiralty in the interests of navigation involved the adoption of a new type of bridge. There was an idea of using suspension chains combined with a girder, and in fact the tower piers were built so as to accommodate chains. But the theory of such a combined structure could not be formulated at that time, and it was proved, partly by experiment, that a simple tubular girder of wrought iron was strong enough to carry the railway. The Britannia bridge (fig. 16) has two spans of 460 and two of 230 ft. at 104 ft. above high water. It consists of a pair of tubular girders with solid or plate sides stiffened by angle irons, one line of rails passing through each tube. Each girder is 1511 ft. long and weighs 4680 tons. In cross section (fig. 17), it is 15 ft. wide and varies in depth from 23 ft. at the ends to 30 ft. at the centre. Partly to counteract any tendency to buckling under compression and partly for convenience in assembling a great mass of plates, the top and bottom were made cellular, the cells being just large enough to permit passage for painting. The total area of the cellular top flange of the large-span girders is 648 sq. in., and of the bottom 585 sq. in. As no scaffolding could be used for the centre spans, the girders were built on shore, floated out and raised by hydraulic presses. The credit for the success of the Conway and Britannia bridges must be divided between the engineers. Robert Stephenson and William Fairbairn, and Eaton Hodgkinson, who assisted in the experimental tests and in formulating the imperfect theory then available. The Conway bridge was first completed, and the first train passed through the Britannia bridge in 1850. Though each girder has been made continuous over the four spans it has not quite the proportions over the piers which a continuous girder should have, and must be regarded as an imperfectly continuous girder. The spans were in fact designed as independent girders, the advantage of continuity being at that time imperfectly known. The vertical sides of the girders are stiffened so that they amount to 40% of the whole weight. This was partly necessary to meet the uncertain conditions in floating when the distribution of supporting forces was unknown and there were chances of distortion.

Fig. 16.—Britannia Bridge.

Fig. 17.—Britannia Bridge (Cross Section of Tubular Girder).

Wrought iron and, later, steel plate web girders were largely used for railway bridges in England after the construction of the Conway and Menai bridges, and it was in the discussions arising during their design that the proper function of the vertical web between the top and bottom flanges of a girder first came to be understood. The proportion of depth to span in the Britannia bridge was 1/16. But so far as the flanges are concerned the stress to be resisted varies inversely as the depth of the girder. It would be economical, therefore, to make the girder very deep. This, however, involves a much heavier web, and therefore for any type of girder there must be a ratio of depth to span which is most economical. In the case of the plate web there must be a considerable excess of material, partly to stiffen it against buckling and partly because an excess of thickness must be provided to reduce the effect of corrosion. It was soon found that with plate webs the ratio of depth to span could not be economically increased beyond 1/15 to 1/12. On the other hand a framed or braced web afforded opportunity for much better arrangement of material, and it very soon became apparent that open web or lattice or braced girders were more economical of material than solid web girders, except for small spans. In America such girders were used from the first and naturally followed the general design of the earlier timber bridges. Now plate web girders are only used for spans of less than 100 ft.

Three types of bracing for the web very early developed—the Warren type in which the bracing bars form equilateral triangles, the Whipple Murphy in which the struts are vertical and the ties inclined, and the lattice in which both struts and ties are inclined at equal angles, usually 45° with the horizontal. The earliest published theoretical investigations of the stresses in bracing bars were perhaps those in the paper by W.T. Doyne and W.B. Blood (Proc. Inst. C.E., 1851, xi. p. 1), and the paper by J. Barton, "On the economic distribution of material in the sides of wrought iron beams" (Proc. Inst. C.E., 1855, xiv. p. 443).

Fig. 18.—Span of Saltash Bridge.

The Boyne bridge, constructed by Barton in Ireland, in 1854-1855, was a remarkable example of the confidence with which engineers began to apply theory in design. It was a bridge for two lines of railway with lattice girders continuous over three spans. The centre span was 264 ft., and the side spans 138 ft. 8 in.; depth 22 ft. 6 in. Not only were the bracing bars designed to calculated stresses, and the continuity of the girders taken into account, but the validity of the calculations was tested by a verification on the actual bridge of the position of the points of contrary flexure of the centre span. At the calculated position of one of the points of contrary flexure all the rivets of the top boom were cut out, and by lowering the end of the girder over the side span one inch, the joint was opened 1/32 in. Then the rivets were cut out similarly at the other point of contrary flexure and the joint opened. The girder held its position with both joints severed, proving that, as should be the case, there was no stress in the boom where the bending moment changes sign.

Fig. 19.—Newark Dyke Bridge and Section of Newark Dyke Bridge.

By curving the top boom of a girder to form an arch and the bottom boom to form a suspension chain, the need of web except for non-uniform loading is obviated. I.K. Brunel adopted this principle for the Saltash bridge near Plymouth, built soon after the Britannia bridge. It has two spans of 455 ft. and seventeen smaller spans, the roadway being 100 ft. above high water. The top boom of each girder is an elliptical wrought iron tube 17 ft. wide by 12 ft. deep. The lower boom is a pair of chains, of wrought-iron links, 14 in each chain, of 7 in. by 1 in. section, the links being connected by pins. The suspending rods and cross bracing are very light. The depth of the girder at the centre is about one-eighth of the span.

Fig. 20.—Fink Truss.

In both England and America in early braced bridges cast iron, generally in the form of tubes circular or octagonal in section, was used for compression members, and wrought iron for the tension members. Fig. 19 shows the Newark Dyke bridge on the Great Northern railway over the Trent. It was a pin-jointed Warren girder bridge erected from designs by C.M. Wild in 1851-1853. The span between supports was 259 ft., the clear span 240½ ft.; depth between joint pins 16 ft. There were four girders, two to each line of way. The top flange consisted of cast iron hollow castings butted end to end, and the struts were of cast iron. The lower flange and ties were flat wrought iron links. This bridge has now been replaced by a stronger bridge to carry the greater loads imposed by modern traffic. Fig. 20 shows a Fink truss, a characteristic early American type, with cast iron compression and wrought iron tension members. The bridge is a deck bridge, the railway being carried on top. The transfer of the loads to the ends of the bridge by long ties is uneconomical, and this type has disappeared. The Warren type, either with two sets of bracing bars or with intermediate verticals, affords convenient means of supporting the floor girders. In 1869 a bridge of 390 ft. span was built on this system at Louisville.

Amongst remarkable American girder bridges may be mentioned the Ohio bridge on the Cincinnati & Covington railway, which is probably the largest girder span constructed. The centre span is 550 ft. and the side spans 490 ft.—centre to centre of piers. The girders are independent polygonal girders. The centre girder has a length of 545 ft. and a depth of 84 ft. between pin centres. It is 67 ft. between parapets, and carries two lines of railway, two carriageways, and two footways. The cross girders, stringers and wind-bracing are wrought iron, the rest of mild steel. The bridge was constructed in 1888 by the Phoenix Bridge Company, and was erected on staging. The total weight of iron and steel in three spans was about 5000 tons.

Fig. 21.—Typical Cantilever Bridge.

Fig. 22.

10. (e) Cantilever Bridges.—It has been stated that if in a girder bridge of three or more spans, the girders were made continuous there would be an important economy of material, but that the danger of settlement of the supports, which would seriously alter the points of contrary flexure or points where the bending moment changes sign, and therefore the magnitude and distribution of the stresses, generally prevents the adoption of continuity. If, however, hinges or joints are introduced at the points of contrary flexure, they become necessarily points where the bending moment is zero and ambiguity as to the stresses vanishes. The exceptional local conditions at the site of the Forth bridge led to the adoption there of the cantilever system, till then little considered. Now it is well understood that in many positions this system is the simplest and most economical method of bridging. It is available for spans greater than those practicable with independent girders; in fact, on this system the spans are virtually reduced to smaller spans so far as the stresses are concerned. There is another advantage which in many cases is of the highest importance. The cantilevers can be built out from the piers, member by member, without any temporary scaffolding below, so that navigation is not interrupted, the cost of scaffolding is saved, and the difficulty of building in deep water is obviated. The centre girder may be built on the cantilevers and rolled into place or lifted from the water-level. Fig. 21 shows a typical cantilever bridge of American design. In this case the shore ends of the cantilevers are anchored to the abutments. J.A.L. Waddell has shown that, in some cases, it is convenient to erect simple independent spans, by building them out as cantilevers and converting them into independent girders after erection. Fig. 22 shows girders erected in this way, the dotted lines being temporary members during erection, which are removed afterwards. The side spans are erected first on staging and anchored to the piers. From these, by the aid of the temporary members, the centre span is built out from both sides. The most important cantilever bridges so far erected or projected are as follows:—

Fig. 23.—Forth Bridge.

(1) The Forth bridge (fig. 23). The original design was for a stiffened suspension bridge, but after the fall of the Tay bridge in 1879 this was abandoned. The bridge, which was begun in 1882 and completed in 1889, is at the only narrowing of the Forth in a distance of 50 m., at a point where the channel, about a mile in width, is divided by the island of Inchgarvie. The length of the cantilever bridge is 5330 ft., made up thus: central tower on Inchgarvie 260 ft.; Fife and Queensferry piers each 145 ft.; two central girders between cantilevers each 350 ft.; and six cantilevers each 680 ft. The two main spans are each 1710 ft. The clear headway is 157 ft., and the extreme height of the towers above high water 361 ft. The outer ends of the shore cantilevers are loaded to balance half the weight of the central girder, the rolling load, and 200 tons in addition. An internal viaduct of lattice girders carries a double line of rails. Provision is made for longitudinal expansion due to change of temperature, for distortion due to the sun acting on one side of the structure, and for the wind acting on one side of the bridge. The amount of steel used was 38,000 tons exclusive of approach viaducts. (See The Forth Bridge, by W. Westhofen; Reports of the British Association (1884 and 1885); Die Forth Brücke, von G. Barkhausen (Berlin, 1889); The Forth Bridge, by Philip Phillips (1890); Vernon Harcourt, Proc. Inst. C.E. cxxi. p. 309.)

(2) The Niagara bridge of a total length of 910 ft., for two lines of railway. Clear span between towers 495 ft. Completed in 1883, and more recently strengthened (Proc. Inst. C.E. cvii. p. 18, and cxliv. p. 331).

Fig. 24.—Lansdowne Bridge.

(3) The Lansdowne bridge (completed 1889) at Sukkur, over the Indus. The clear span is 790 ft., and the suspended girder 200 ft. in length. The span to the centres of the end uprights is 820 ft.; width between centres of main uprights at bed-plate 100 ft., and between centres of main members at end of cantilevers 20 ft. The bridge is for a single line of railway of 5 ft. 6 in. gauge. The back guys are the most heavily strained part of the structure, the stress provided for being 1200 tons. This is due to the half weight of centre girder, the weight of the cantilever itself, the rolling load on half the bridge, and the wind pressure. The anchors are built up of steel plates and angle, bars, and are buried in a large mass of concrete. The area of each anchor plate, normal to the line of stress, is 32 ft. by 12 ft. The bridge was designed by Sir A. Rendel, the consulting engineer to the Indian government (Proc. Inst. C.E. ciii. p. 123).

(4) The Red Rock cantilever bridge over the Colorado river, with a centre span of 660 ft.

(5) The Poughkeepsie bridge over the Hudson, built 1886-1887. There are five river and two shore spans. The girders over the second and fourth spans are extended as cantilevers over the adjoining spans. The shore piers carry cantilevers projecting one way over the river openings and the other way over a shore span where it is secured to an anchorage. The girder spans are 525 ft., the cantilever spans 547 ft., and the shore spans 201 ft.

Fig. 25.—Quebec Bridge (original design)

(6) The Quebec bridge (fig. 25) over the St Lawrence, which collapsed while in course of construction in 1907. This bridge, connecting very important railway systems, was designed to carry two lines of rails, a highway and electric railway on each side, all between the main trusses. Length between abutments 3240 ft.; channel span 1800 ft.; suspended span 675 ft.; shore spans 562½ ft. Total weight of metal about 32,000 tons.

Fig. 26.—Jubilee Bridge over the Hugli.

(7) The Jubilee bridge over the Hugli, designed by Sir Bradford Leslie, is a cantilever bridge of another type (fig. 26). The girders are of the Whipple Murphy type, but with curved top booms. The bridge carries a double line of railway, between the main girders. The central double cantilever is 360 ft. long. The two side span girders are 420 ft long. The cantilever rests on two river piers 120 ft. apart, centre to centre. The side girders rest on the cantilevers on 15 in. pins, in pendulum links suspended from similar pins in saddles 9 ft. high.

Fig. 27.—Coalbrookdale Bridge.

11. (f) Metal Arch Bridges.—The first iron bridge erected was constructed by John Wilkinson (1728-1808) and Abraham Darby (1750-1791) in 1773-1779 at Coalbrookdale over the Severn (fig. 27). It had five cast iron arched ribs with a centre span of 100 ft. This curious bridge is still in use. Sir B. Baker stated that it had required patching for ninety years, because the arch and the high side arches would not work together. Expansion and contraction broke the high arch and the connexions between the arches. When it broke they fished it. Then the bolts sheared or the ironwork broke in a new place. He advised that there was nothing unsafe; it was perfectly strong and the stress in vital parts moderate. All that needed to be done was to fish the fractured ribs of the high arches, put oval holes in the fishes, and not screw up the bolts too tight.

Cast iron arches of considerable span were constructed late in the 18th and early in the 19th century. The difficulty of casting heavy arch ribs led to the construction of cast iron arches of cast voussoirs, somewhat like the voussoirs of masonry bridges. Such a bridge was the Wearmouth bridge, designed by Rowland Burdon and erected in 1793-1796, with a span of 235 ft. Southwark bridge over the Thames, designed by John Rennie with cast iron ribs and erected in 1814-1819, has a centre span of 240 ft. and a rise of 24 ft. In Paris the Austerlitz (1800-1806) and Carrousel (1834-1836) bridges had cast iron arches. In 1858 an aqueduct bridge was erected at Washington by M.C. Meigs (1816-1892). This had two arched ribs formed by the cast iron pipes through which the water passed. The pipes were 4 ft. in diameter inside, 1½ in. thick, and were lined with staves of pine 3 in. thick to prevent freezing. The span was 200 ft.

Fig. 28.—Arch of Bridge at Coblenz

Fig. 28 shows one of the wrought iron arches of a bridge over the Rhine at Coblenz. The bridge consists of three spans of about 315 ft. each.

Fig. 29.—St Louis Bridge.

Of large-span bridges with steel arches, one of the most important is the St Louis bridge over the Mississippi, completed in 1874 (fig. 29). The river at St Louis is confined to a single channel, 1600 ft. wide, and in a freshet in 1870 the scour reached a depth of 51 ft. Captain J.B. Eads, the engineer, determined to establish the piers and abutments on rock at a depth for the east pier and east abutment of 136 ft. below high water. This was effected by caissons with air chambers and air locks, a feat unprecedented in the annals of engineering. The bridge has three spans, each formed of arches of cast steel. The centre span is 520 ft. and the side spans 502 ft. in the clear. The rise of the centre arch is 47½ ft., and that of the side arches 46 ft. Each span has four steel double ribs of steel tubes butted and clasped by wrought iron couplings. The vertical bracing between the upper and lower members of each rib, which are 12 ft. apart, centre to centre, consolidates them into a single arch. The arches carry a double railway track and above this a roadway 54 ft. wide.

The St Louis bridge is not hinged, but later bridges have been constructed with hinges at the springings and sometimes with hinges at the crown also.

The Alexander III. bridge over the Seine has fifteen steel ribs hinged at crown and springings with a span of 353 ft. between centres of hinges and 358 ft. between abutments. The rise from side to centre hinges is 20 ft. 7 in. The roadway is 65½ ft. wide and footways 33 ft. (Proc. Inst. C.E. cxxx. p. 335).