=156. Earth Pressures.[92]=—The various theories of earth pressure are so conflicting in their conclusions as to be confusing. Rankine’s theory, the most frequently used, assumes that the pressure increases with the depth, whereas Meem’s theory[93] leads to an opposite conclusion. The discussion following Meem’s article is very illuminating. It indicates that no matter how good the theory, practical experience together with the use of generous sizes and close spacing are the best guides for bracing trenches and coffer dams. All are not possessed with the desired practical experience and some basis on which to commence work is essential. Another factor affecting computations of sizes based on theory is the tendency in practice to use the same size material for rangers and braces on any one job for all except very deep trenches and other special cases. Occasionally where there is an independent brace for each end of each ranger, the brace is made thinner, but is of the same depth as the ranger. The application of Rankine’s theory of earth pressure to the computation of the sizes of rangers and braces will be shown. His formula for the active earth pressure against a retaining wall is: _P_ = _wh_ cosθ (cos θ − √(cos^2 θ − cos^2 φ))⁄(cos θ + √(cos^2 θ − cos^2 φ)) in which _w_ = the weight of earth in pounds per cubic foot; _h_ = depth in feet at point at which pressure is to be determined; θ = the angle of surcharge, or the angle which the surface makes with the horizontal; φ = the angle of repose of the earth. Usually taken as 33°–41′ = 1½ horizontal to 1 vertical; _P_ = the intensity of pressure in pounds per square foot on a vertical plane in a direction parallel to the surface of the ground. In studying the pressures for trenches the surface of the ground will be assumed as horizontal and the formula reduces to _P_ = (1 − sin φ)⁄(1 + sin φ)_wh_. =157. Design of Sheeting and Bracing=.—The trench shown in Fig. 111 is assumed to be constructed in moist sand weighing 110 pounds per cubic foot, with an angle of repose of 30 degrees. The material used for sheeting and bracing is yellow pine. The steps taken in the design of the sheeting and bracing for this trench are as follows: [Illustration: FIG. 111.—Diagram for the Design of Wood Sheeting. ] 1. _Earth Pressure._—Substituting the units given in the data, in Rankine’s formula for earth pressures, _P_ = 36.7_h_.