Arched frame-work of bridges. Composition of the arches. Junction of the straight beams with the arches.

Cast-iron Bridges.—Different systems. General principles of their construction.

Aqueducts in masonry; in cast-iron.

14th. Suspension Bridges.—Equation of the curve of the chains and construction of this curve. Tension supported by the suspension cables, their thickness. Influence of the length of the flèche upon the tension of the cables. Inconveniences resulting from a long flèche. Vibrations and means of diminishing them. Limits of length of the flèche. Length of the curve of suspension. Causes operating to vary this length; means of obviating the effects produced by them. Length of the suspension rods. Number of supports to be adopted. Thickness of the piles. Points at which the fixing cables are to be attached. Advantages and disadvantages of chains composed of bars and of cables of iron wire. Some details of construction.

15th. Drawbridges.—Conditions which they must satisfy. General principle of their balance.

Drawbridges with Plyers.—Special theory of this bridge. Reduction of it to practice. Alteration of equilibrium and means of remedying it.

Disadvantages of the drawbridge with plyers.

16th. Spiral drawbridge of Captain Berché. Trace of the spiral. Determination of the radius of the chain-roller, and of the greatest radius of the spiral.

17th. Drawbridges with variable counterbalances, invented by M. Poncelet. Construction of the chains of the counterbalance. Establishment of the leverage. Calculation of the counterbalances for the special case of the pulleys in front corresponding to the axis of the platform. Influence of the nature of the chains. Method of allowing for the weight of the small chains. Definitive construction of the chains of the counterbalance. Provision of loose cords.

18th. Succinct ideas upon the motion of the sea, and its action on the shore.