1484

THEORY AND PRACTICE OF ENGINEERING.

Rook II.

very great difference between the quantity of water which flows at cither place: we mayvalue by approximation this difference, by comparing the superficies of the basins, whichsupply the water at Mirabeau and Bonpas, and we find the latter surpasses the other aboutone-sixteenth ; hence there must flow at Bonpas in a second a volume of water equal to 3838cube metres, which for a section of 1530 square metres gives a mean rapidity of 2-51 metres.The construction of the bridge in wood diminishes a very little from the superficies ofthe water-way, and we may remark that the rapidity of 2 51 metres per second, which cor-responds to a height of water of more than 3 metres in the bed of the river, scarcelysurpasses 2*44 metres of rapidity, which the river takes naturally at Mirabeau, for aheight of water of 2*92 metres. Thus the mean rapidity at Bonpas is less considerablethan in other parts of the course of the river, and the waters have there an easy discharge.

The discharge of the Rhone at the bridge of St. Esprit is about 3580 square metres ; thatis to say, a little more than double that of theDurance at Bonpas, whilst the superficies of thebasins, the waters of which flow to the Rhone at St. Esprit, is more than five times greaterthan that of the basins which flow into the Durance at Bonpas : thus, although the rapidity ofthe Rhone is very considerable under the arches of the bridge of St. Esprit, it would ap-pear that the discharge given to the Durance is much too great. But we must observethat this river at Bonpas, being only 25 myriametres from its source, is still a torrent, whilstthe Rhone at St. Esprit is no longer such.

It is then very essential in regulating the water-way of bridges to distinguish the torrentsof rivers, and to have regard, in comparing the superficies of the basins, to the nature of thesoil, and to the time which the waters take to flow : it may happen, as we have said above,to be necessary to construct over a river a bridge larger at a little distance from the source,than at a place farther distant, although it may have received in the interval several tribu-tary streams.

Of the Form of Arches used in Bridges . — The arches of bridges are divided relatively totheir form into three principal kinds: semicircular ; those generally described by several arcsof a circle of different radii, and the form of which approaches to a demi-cllipsis ; and archeswhich form the part of a circle, more or less. Semicircular arches are the most ancient; thereis scarcely any ancient bridge in which this form is not employed, and during a long time itwas generally adopted in Europe ; it has the advantage of greater solidity and more facilityin construction, hut the inconvenience of considerably obstructing the passage of the water.Flat arches were not introduced until the end of the seventeenth century, and their adoptionarose from the necessity of giving as much water-way as could be obtained without con-siderably increasing the height of the arch : this it effects admirably, and presents besides,when the two diameters are not very unequal, almost as much solidity and facility in theconstruction as the semicircular.

Of arches forming a part of a circle there are two varieties : the first is that where thespringings are under water, as is the case in the first great bridge built in France , as theSt. Esprit, and the ancient bridge at Avignon ; but this form has the disadvantage ofgiving less water-way than the flattened one, and of requiring very massive tympanums.This latter defect appears to have been recognised by the first builders, for the backs of thearches are almost always simply filled with earth, or discharged by means of a number ofsmall arches. In the second case the springing of the arches are raised on piers nearly theheight of the greatest rise of the river, as at the Pont Louis XVI. at Paris , which generallyrequires the arch to be much flattened; hence it results that the lateral pressure of theveussoirs is very considerable, and great care is required in the construction, in order thatthe arch* should not sink after the striking of the centre, which has sometimes occurred.The manner in which the thrust of arches of this kind exerts itself is different from that inwhich it acts in others; they do not generally tend to overthrow their abutments, but tomake them slide horizontally; we shall indicate hereafter the means for resisting this thrustwithout incurring any considerable expense. We shall also find that the resistanceopposed by the springing of the arches to the current when they are plunged in it, is oneof the principal causes of the wearing away that takes place at the foot of the piers:bridges with circular arches have in this particular a great advantage over others, whentheir springing is not reached by the waters of the river.

It is not possible to give general rules for the selection of these different kinds of arches;the decision must be made in each particular case according to local circumstances, asthe width of the water-way, the height with regard to either high or low water, the heightat which the surface of the pavement of the bridge may be placed, the obligation whichsometimes occurs of destroying one arch, and consequently making the piers perform thefunctions of abutments, are the principal considerations: due regard must also be paid tothe nature of the materials and the degree of resistance they may offer.

To the three species of arches mentioned, which are those now in use, we may add theforms employed by the Arabs , and above all the Gothic, composed of two arcs of a circle,and known under the name of O G: this latter has the inconvenience of considerablydiminishing the water-way j but this defect is easily remedied by making openings in the