in which _P_ = lateral pressure in pounds per square inch; _R_ = rate of filling forms in feet per hour; _H_ = head of fill. Ordinarily taken as ½_R_, but in cold weather or when continuously agitated it may be as high as ¾_R_; _C_ = ratio, by volume, of cement to aggregate; _S_ = consistency in inches of slump. Earlier investigators have usually concluded that the pressures were equal to those caused by a liquid weighing 144 pounds per cubic foot, but the tests of the United States Bureau of Public Roads, from which the above formula was devised, show the pressures to be decidedly below this amount under certain conditions. [Illustration: FIG. 133.—Centering for Large Forms. ] With these units and formulas the design of the lagging becomes a matter of substitution in, and the solution of, the equations produced.[102] The forces acting on the ribs are indeterminate. No more satisfactory design can be made for the ribs than to follow successful practice, or what is seldom done, to determine the stresses in the forms by the application of one of the theories for the solution of arch stresses. The sizes of the lumber used in the ribs varies from 1½ × 6 inches to 2 × 10 inches, depending on the size of the sewer. If vertical posts are used at the ends to support the arch forms they are computed as columns taking the full weight of the arch. If the span is so wide that radial supports are used as shown in Fig. 133 the load at the center is assumed as one-fourth of the weight of the arch. =192. Wooden Forms.=—Norway and Southern pine, spruce, and fir are satisfactory for form construction. White pine is satisfactory but is generally too expensive. The hard woods are too difficult to work. The lumber should be only partly dried as kiln-dried lumber swells too much when it is moistened, warping the forms out of shape or crushing the lagging at the joints. Green lumber must be kept moist constantly to prevent warping before use and when it is used it does not swell enough to close the cracks. The lumber should be dressed on the face next to the concrete and at the ends. Either beveled or matched lumber may be used for lagging. The joint made by beveled lumber shown in Fig. 134 is cheaper but less satisfactory than a tongued and grooved joint. [Illustration: FIG. 134.—Beveled Joint for Wood Fords. ] [Illustration: FIG. 135.—Collapsible Wooden Invert Form for Concrete Sewers. ] [Illustration: FIG. 136.—Support for Arch Centering. ] [Illustration: FIG. 137.—Wooden Forms Used in Tunnel, North Shore Sewer, Sanitary District of Chicago. Journal Western Society of Engineers, Vol. 22, p. 385. ] Types of wooden forms are shown in Figs. 135 and 136 for use in sewers to be built as monoliths or in two portions. Fig. 137 shows the details of a built-up wooden form used in tunnel work for a 42½ inch egg-shaped sewer.