system increases with the length of the storm up to the time when the run-off from the most distant part of said area reaches the point of observation; after which the run-off very nearly equals the rainfall upon said area while the rate of fall remains constant. That the percentage of imperviousness of the surface may vary from 0% to 100%, being the first in the case of very porous soil under natural conditions at the beginning of a rain, and the last in an urban district where streets, sidewalks, and yards are all paved, or occasionally where a dense clay soil is saturated by previous rainfall. ART. 19. FORMULAS FOR STORM-WATER RUN-Off. Many attempts have been made to construct a simple general formula for obtaining the run-off from any area. The best known of these are as follows: Craig: Dredge: Dickens: Fanning: D= 440BN hyp. log D= 8 L' discharge in cubic feet per second; D= discharge in cubic feet per second; = = Q discharge in cubic feet per second; = c = constant-0.75 for paved streets, 0.31 for R = average rate during heaviest fall in cubic S= general fall of area per 1000; 2 cubic feet per second per acre reaching = Maximum rainfall of one inch, one half running off. Hawksley: log D = D= diameter of sewer in inches; A number of acres to be drained; N = length in feet in which sewer falls one Terms as in Bürkli-Ziegler; R taken at St. Louis as 2.75 inches. The following, known as Roe's tables, gives the number of acres of urban surfaces which can be drained by sewers of different diameters and at different grades. It is no longer in general use. The formulas of Craig, Dredge, Dickens, and Fanning apply to natural surfaces and have the shape and extent of the drainage-area as the only variables. The Bürkli-Ziegler, Kirkwood, and McMath formulas take into account also the slope of the surface. The Bürkli-Ziegler and Kuichling allow for varying conditions of surface, and, together with the McMath, for varying rates of rainfall. All these formulas. except the three last mentioned are based on an assumed maximum rate of rainfall. Roe's tables give the diameter of sewer necessary to meet various conditions of area and sewer grade. As in a level sewer the surface of the water must have some fall if there is to be any flow, the quantities given for a level grade can apply only to a limited length of sewer. None of these formulas is satisfactory for all cases, because none takes into account all the variable conditions. Those which are probably the most frequently used are the Bürkli-Ziegler, McMath, and Kuichling, and these are seen to be the ones containing the most variables. The proper test of any formula is to calculate by it from known data quantities which are also known. Many such tests of all these formulas have been made, and it has been found that there are few, if any, cases in which all will give results practically identical or equal to the actual quantities as measured. Such a comparison is given of Roe's tables, Hawksley's, Kirkwood's, and Bürkli-Ziegler's formulas, and the actual gaugings of a sewer in Washington made in 1884 (from paper by Capt. R. L. Hoxie read before the Am. Soc. C. E. July 2, 1886): The discrepancies are largely due to the causes already referred to that factors are taken as constants which are really variables, and hence each formula can give correct results for certain cases only. In most the constant is supposed to be derived from maximum rates of rainfall, but such data were until recently incomplete and inaccurate. Also, since the authors of the older formulas were Europeans or derived their data from European sources, the maximums were those for Europe and are not applicable to this country. Also the character of the majority of city-street surfaces has changed since that time. The Kuichling, Bürkli-Ziegler, and McMath formulas recognize the variableness in drainagesurfaces. It is possible that a formula can be devised which shall represent by variable factors all the conditions which have been shown to affect the run-off. But it can hardly be expected that such a formula can be other than cumbersome, and it is probable that the shortest method which is at all rational and accurate in all cases is that of subdividing the calculation, and adapting a general method rather than a general formula to the peculiar conditions of each case. Such a method is recommended and will be outlined further on. Many engineers, however, use some one of the formulas given, and a large majority of the storm-sewers built in this country are probably so designed-in spite of the fact that McMath considers his formula (which is probably the most popular) as adapted to large areas only, and that it is derived in an entirely empirical manner from St. Louis data only; and that Kuichling has “finally abandoned the attempt to establish a general formula for run-off," although the one bearing his name is largely general in application and rational in origin and construction. ART. 20. EXPEDIENCY OF PROVIDING FOR EXCESSIVE STORMS. An examination of rainfall records shows no apparent law of frequency of excessive storms. It can be said as a general statement, however, that a rate of fall within certain limits. may be expected almost any month; one within higher limits five or more times in ten years (these are the storms referred to in Art. 17); and a phenomenal downpour at most irregular intervals, usually many years apart. Should the sewer be designed to carry the run-off from storms of the first class |