the sides of the pentagon, in the proportion of 47 to the other two equal sides, the length of each of these being 40.

3. Hexagonal redoubt.

From a central point with a chain, or line, construct, and lay down, with pickets, six equilateral, and contiguous triangles, the bases of which will form the required hexagon.

4. Octagonal redoubt.

Construct a square (vide No. 1), from the centre of each side of which erect perpendiculars outwards, in length proportional to the side as 13 to 60 (nearly 1 to 5); join the extremities, or termination of the perpendiculars, to the angles of the square, which will determine the sides of the octagon.

Note 1.-The directions for the construction of the pentagonal, and hexagonal redoubts are on a small scale; but the redoubts may be increased by the equal extension of the interior sides of the triangles, until the bases are sufficiently long for the periphery of the work required.

Note 2.-By means of the pocket sextant, prismatic compass, or reconnoitring protractor, the pentagonal, hexagonal, and octagonal redoubt may be thus traced on the ground. From a central point place pickets at the requisite distance from each other, and in the direction of lines drawn from the angle of the centre of the intended work. (Vide PRACTICAL GEOMETRY. To find the angles at the centre, and circumference of a polygon.) Extend these radii equally until the relative distances between them are of the length required to form the sides of the proposed equilateral redoubt.

5. Front of fortification, for a Field fort.

Place pickets in a straight line, of the length required for the front of the proposed field work; from the centre of which drop a perpendicular inwards, making it for a square, pentagon, or hexagon, respectively one-eighth, one-seventh, or one-sixth of the exterior side. Direct the lines of defence from the termination of the exterior side to the end of the perpendicular, making the faces of the bastions two-sevenths of the exterior side, and constructing the flanks perpendicular to, and joining the lines of defence. Other fronts are traced by laying down the exterior sides, at the angle of the circumference of the intended polygon (vide PRACTICAL GEOMETRY) by means of the prismatic compass, &c., and then proceeding as directed for the former front.

PART XIII.

BRÍDGES, AND PONTOONS.

BRIDGES.

1. To find the number of planks required to form a float, to support a given weight.

1st. Find the content of one plank (vide PRACTICAL GEOMETRY, Part 15), and multiply it by the specific gravity of the wood; the product will be the weight of the timber.

2nd. Multiply the same solid content by the specific gravity of water: the product will be the weight of an equal bulk of water.

Then take the difference of these two products, or weight, and it will be the weight one piece of timber will support without sinking. Hence by Proportion, the number required to support the given weight may be found.

Note.-A fir tree, 1 foot square and 25 feet long, will float about 703 pounds. 2. To find the number of casks required to form a raft to support a given weight.

1st. Find the solid content of one cask in cubic inches (vide PRACTICAL GEOMETRY), and multiply it by the specific gravity of water; the product will be the weight of a quantity of water of equal bulk with the cask.

2nd. From this product, or weight, subtract the weight of the cask, and the remainder will be the weight it will support without sinking. Then by Proportion, the number required for the formation of the raft may be found.

3. To find the number of boats, or pontoons, required to support a given weight.

The burthen a boat, or pontoon, will support without sinking beyond a given depth (the form of the boat, or pontoon being known) must first be found, thus

1st. Find the solid content of the part to be sunk, in cubic feet (vide PRACTICAL GEOMETRY, Part 15), and multiply it by the specific gravity of water (vide GRAVITY, Part 15).

2nd. Subtract this product from the weight of the boat, or pontoon, and the remainder will be the burthen it will support without sinking beyond the required depth.

Then by Proportion, the number required to support the given weight may be computed.

Note. In the construction of bridges, should a rope require to be extended across a rapid river, the coil should be placed in the boat (instead of on shore), and be paid out as the boat advances.

PONTOONS.

Those called Blanshard's (from their inventor, M. General Blanshard, Royal Engineers) are of two descriptions.

1.-LARGE PONTOONS.

Displacement of water, 97 cubic feet, equals 6088 lb., or 54 cwt. The buoyant power of a raft of two pontoons, its own weight deducted, is 77 cwt., about one-half of which is a safe load. Each raft,

or one carriage load, forms 2 bays, or 20 ft. 8 in. of bridge: its own weight will sink it about 7 or 8 inches. The crew of a raft consists of 6 rowers, and 1 steersman.

At open order the bridge will pass cavalry, field artillery, or infantry with closed files.

At close order the bridge will pass any part of a heavy train.

Dimensions, and weight of cylindrical pontoons, manufactured in the Arsenal at Woolwich.

Five pontoons, with their appurtenances, form the load of one carriage. Length, 15 feet; diameter, 1 foot 7 inches; displacement, 27 cubic feet; buoyancy, 1718 lb., or 154 cwt., from which deduct 2 cwt. for the weight of pontoon, and share of superstructure. A bridge of this nature is so light that it may be made on shore, and carried by hand entire. It will support as many men as can be placed on it, and, by removing the chesses over the gunnels, it may bent so as to be passed without difficulty down a steep bank, or counterscarp.

be

* The length includes the hemispherical ends.