3. This per cent increases rapidly and directly or uniformly with the duration of the maximum intensity of the rainfall until a period is reached which is equal to the time required for the concentration of the drainage waters from the entire area at the point of observation, but if the rainfall continues at the same intensity for a longer period this per cent will continue to increase at a much smaller rate. 4. This per cent becomes larger when a moderate rain has immediately preceded a heavy shower on a partially permeable territory. Gregory’s formulas have not been generally accepted and are not widely used in practice. Marston stated:[28] All that engineers are at present, warranted in doing is to make some deduction from 100 per cent run-off ... the deduction ... being at present left to the engineer in view of his general knowledge and his familiarity with local conditions. Burger states[29] in the same connection: In its application there will usually be as many results (differing widely from each other) as the number of men using it. In spite of these objections the Rational Method is in more favor with engineers than any other method. =32. Empirical Formulas.=—The difficulty of determining run-off with accuracy has led to the production by engineers of many empirical formulas for their own use. Some of these formulas have attracted wide attention and have been used extensively, in some cases under conditions to which they are not applicable. In general these formulas are expressions for the run-off in terms of the area drained, the relative imperviousness, the slope of the land, and the rate of rainfall. The Burkli-Ziegler formula, devised by a Swiss engineer for Swiss conditions and introduced into the United States by Rudolph Hering, was one of the earliest of the empirical formulas to attract attention in this country. It has been used extensively in the form _Q_ = _CiA_∜(_S_⁄_A_), in which_Q_ = the run-off in cubic feet per second; _i_ = the maximum rate of rainfall in inches per hour over the entire area. This is determined only by experience in the particular locality, and is usually taken at from 1 to 3 inches per hour; _S_ = the slope of the ground surface in feet per thousand, _A_ = the area in acres; _C_ = an expression for the character of the ground surface, or relative imperviousness. In this form of the expression _C_ is recommended as 0.7. The McMath formula was developed for St. Louis conditions and was first published in Transactions of the American Society of Civil Engineers, Vol. 16, 1887, p. 183. Using the same notation as above, the formula is, _Q_ = _CiA_⁵√(_S_⁄_A_),