The shape of the drop-down curve can be expressed, in some cases, by mathematical formulas of more or less simplicity, dependent on the shape of the conduit. The formula for a circular conduit is complicated. Due to the assumptions which must be made in the deduction of these formulas, the results obtained by their use are of no greater value than those obtained by approximate methods. A method for the determination of the drop-down curve is given by C. D. Hill.[32] In this method it is necessary that the rate of flow past all sections shall be the same; that the depth of submergence at the outlet shall be known; and that the depth of flow at some unknown distance up the stream shall be assumed. The shape and material of construction of the sewer and the slope of the invert should also be known. The problem is then to determine the distance between cross-sections, one where the depth of flow is known, and the other where the depth of flow has been assumed. This distance can be expressed as follows: _L_ = ((_d__{2} − _d__{1}) − (_H__{1} − _H__{2}))⁄(_S_ − S_{1}) = (_d_′ − _H_′)⁄_S_′, in which _L_ = the distance between cross-sections; _d__{1} = the depth of flow at the lower section; _d__{2} = the depth of flow at the upper section; _H__{1} = the velocity head at the lower section; _H__{2} = the velocity head at the upper section; _S_ = the hydraulic slope of the stream surface; _S__{1} = the slope of the invert of the sewer. In order to solve such problems with a satisfactory degree of accuracy the difference between _d__{1} and _d__{2} should be taken sufficiently small to divide the entire length of the sewer to be investigated into a large number of sections. The solution of the problem requires the determination of the wetted area, the hydraulic radius, and other hydraulic elements at many sections. The labor involved can be simplified by the use of diagrams, such as Fig. 19, or by specially prepared diagrams such as those accompanying the original article by C. D. Hill. The solution of the problem can be simplified by tabulating the computations as follows: DROP-DOWN CURVE COMPUTATION SHEET Uniform discharge. Varying depth