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large as that required to protect cribs sunk upon the natural bed; they would not however, spread to such a distance from the channel-side of the pier as to be an obstruction to navigation.

A clearer understanding of the subject will perhaps be derived through the following illustrations, the first of which exhibits the end view of a crib set horizontally upon a natural sand-bed in a depth of 14 feet of water. The width of the crib is 20 feet; the height is represented as being 15 feet. It is shown in a proper position before having been subjected to the action of the water.

Fig. 2 is not an exaggerated exhibition of the same crib after having been subjected to the action of the water. Many instances are known of cribs having settled much more seriously.

In this representation it is shown that a portion of the sand-bed has been washed from under the crib, aud that the stone filling has settled down with it, and run through the grillage; but in the discussion of the relative cost of cribs, sunk with and without artificial foundations, the quantity of stone which may have actually run into the sand below the crib will not be estimated for a greater depth than is shown by the sketch, nor will the detrimental effect produced by the distorted position of the crib, nor the imperfect construction involved through the necessary insertion of wedgeshaped timbers to provide a proper bearing for the superstructure, be taken into the account of dollars and cents.

Fig. 2 represents the stone as having settled into the sand below the natural bed, on the outer or seaward side, to a depth of 4 feet, and on the inner or channel side, to a depth of 2 feet. It also shows the crib itself as having settled 3 feet on the outer, and 1 foot on the inner sides.

The quantity, therefore, contained in the prism of stone which has subsided below the natural bed, for a crib of dimensions 32 by 20 feet, approximates 32 by 20 by 3 feet = 1,920 cubic feet, or 15 cords, and the mean subsidence of the crib equals 2 feet, or two courses of timbers 12 by 12 inches square.

Two middle courses of a crib of the above dimensions contain, as per bill of materials used, 276 linear feet of framed timber, and 346 pounds of iron bolts. The average cost of these materials, with the framing, would be approximately as follows, the prices being taken from the contracts awarded by the Government in 1871, viz:

For 15 cords of stone ballast, at $8.25..

For 276 linear feet of framed timber, at 31 cents.
For 346 pounds of iron bolts, at 4 cents....

Total cost involved by subsidence of crib......

$123 75

85 56

13 84

223 15

Fig. 3 represents the same crib as being set upon a foundation of loose stone, in the same natural depth of water. The stone are shown as having been pressed downward to a distance of 3 feet below the natural bed of the lake by the superincumbent weight of the stone in the crib, and after its having been subjected to the action of the water. For the convenience of computation, it is shown in a more symmetrical shape than it would actually assume.

The quantity of stone contained in this artificial foundation, having a mean dimension of 28 by 4 by 32 feet, equals 3,584 cubic feet, or 28 cords, of 128 cubic feet, which, at $3.25 per cord, would cost $231, showing an excess of $7.85 over the cost involved by the subsidence of crib placed upon the natural lake-bed. But it is assumed that the crib which is set upon a foundation of stone rests in a horizontal position, with its two upper courses above water-surface, while, in the first case, it has settled and tilted so that the seaward side is 2 feet below the surface, and the inner side at water-level, a mean horizontal of which would show it to be 1 foot below the surface of the water. It is clear, then, that a gain is effected by adopting the system of stone foundation, which is equivalent to three courses of crib-construction in value at the prices above specified, as follows, viz:

414 linear feet of framed timber, at 31 cents.

520 pounds of iron drift-bolts, at 4 cents..

10 cords of stone ballast, at $8.25..

Amount gained..

Minus excess of....

Total amount gained by using an artificial foundation of stone......

Or a saving of about $7 per running foot of pier.

$128 34

20 80

82 50

231 64

7 85

2:23 79

Besides which, the cost of furnishing and driving the necessary piles for carrying the superstructure, the loss of timber occasioned by cutting wedge-pieces for leveling up the work, and the extra framing of the wedge-timbers, have not been taken into the

account.

Independent of these necessary considerations of means, the effectiveness and general appearance of the work should receive a proper share of consideration.

Various expedients will readily be suggested for placing the stone properly before setting a crib.

The advantage derived through this combined system has been fully demonstrated by practical experience at the harbor of Sheboygan, Wisconsin, during the present working season.

SEPTEMBER 5, 1871.

W. H. HEARDING, Assistant United States Engineer.

In order to secure a nearly level bearing for the cribs, I would recommend that the stones be placed as shown in the cross-section below, i. e., in two ridges, the crest of each ridge being placed about 3 feet outside of the sides of cribs. It will be easy to place the stone so that the crest of each ridge will be nearly level. The crib being placed between these two ridges will by its weight bring the stones nearly to a level bearing, and not be liable to be undermined.

In very bad bottoms it would be an improvement to place the stone in a broad matting, made of brush. This matting can be made of fascines bound together by withes. The fascines should be made of loose brush, including small branches and leaves, which have the effect of collecting the sand.

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OFFICE OF THE CHIEF OF ENGINEERS,

Washington, D. C., December 16, 1871. MAJOR: Your letter of November 29, submitting for the approval of the Chief of Engineers a modified cross-section for the breakwater at Chicago, has been received.

By reference to the annual report of the Chief of Engineers for 1870 and 1871 it will be seen that the appropriations for the breakwater at Chicago are based upon a plan of the Engineer Department, which was submitted to Congress. It is consequently not deemed advisable to make any radical alteration or modification in this plan, which has received the sanction of the Chief of Engineers after having been approved and recommended by a board of engineer officers.

In regard to the question of proper form of cross-section for pier and breakwater, it has been fully discussed in previous reports, and the weight of authority is largely in favor of a structure with almost vertical face on the seaward or exposed side. (Vide Report Chief Topographical Engineer, December 30, 1839, Doc. No. 2, Twenty-sixth Congress, first session, House of Representatives, and also Message and Documents, 1853--254, part 3, and Message and Documents, 1854-55, part 2, and also

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