McMath recommended the use of _C_ equal to 0.75, _i_ as 2.75 inches per hour, and _S_ equal to 15. The formula has been extended for use with all values of _C_, _i_, _S_, and _A_ ordinarily met in sewerage practice. Fig. 11 is presented as an aid to the rapid solution of the formula. [Illustration: FIG. 11.—Diagram for the Solution of McMath’s Formula, _Q_ = _Aci_⁵√_S_⁄_A_. ] Other formulas have been devised which are more applicable to drainage areas of more than 1,000 acres.[30] Such areas are met in the design of sewers to enclose existing stream channels draining large areas. Kuichling’s formulas, published in 1901 in the report of the New York State Barge Canal, were devised for areas greater than 100 square miles. The following modification of these formulas for ordinary storms on smaller areas was published for the first time in American Sewerage Practice, Volume I, by Metcalf and Eddy: _Q_ = 25,000⁄(_A_ + 125) + 15. [Illustration: FIG. 12.—Comparison of Empirical Run-off Formulas. ] It is to be noted that the only factor taken into consideration is the area of the watershed. It is obvious that other factors such as the rate of rainfall, slope, imperviousness, etc., will have a marked effect on the run-off. There are other run-off formulas devised for particular conditions, some of which are of as general applicability as those quoted. Two formulas which are frequently quoted are: Fanning’s, _Q_ = 200_M_^⅝ and Talbot’s _Q_ = 500_M_^¼, in which _M_ is the area of the watershed in square miles. A comprehensive treatment of the subject is given in American Sewerage Practice, Vol. I, by Metcalf and Eddy. A comparison of the results obtained by the application of a few formulas to the same conditions is shown graphically in Fig. 12. It is to be noted that the divergence between the smallest and largest results is over 100 per cent. As these formulas are not all applicable to the same conditions, the differences shown are due partially to an extension of some of them beyond the limits for which they were prepared.