MATHEMATICAL FORMULAE 79 



various attempts have been made at different times to express 

 in mathematical terms the relation existing between the rain- 

 fall, the general slope of the surface, the drainage-area, and the 

 storm-water discharge, but experience has proved them all more 

 or less unsatisfactory. Could the coefficients of these formulae 

 be well known by experiment, and then could they be used 

 by the same investigator on similar territory, doubtless the 

 results would be sufficiently accurate; but the coefficients are 

 made by one engineer and their values used by another, whose 

 knowledge of the original conditions can be at best very limited. 

 As to the density or character of the district, often nothing 

 more is known than that the territory is " urban." 



The best-known formulae are those of Hawksley, Biirkli- 

 Ziegler, Adams, and McMath. The following analytical com- 

 parison is taken from a lecture by Emil Kuichling delivered 

 before the Association of Civil Engineers of Cornell University 

 in 1893.* 



Hawksley's formula was probably established some time 

 between the years 1853 an d 1856, and was the result of an 

 endeavor to find the relation existing between the diameter 

 of a circular sewer and the other factors above named, on the 

 assumptions of a rainfall of i inch per hour, one-half reaching 

 the sewer, with the sewer-grade parallel to that of the street. 

 This formula expressed analytically the relations brought out 

 in a table prepared by John Roe, showing the measured dis- 

 charges from a number of sewers in the city of London, during 

 and after rain-storms of different intensities and under other 

 different conditions. An intensity of i inch per hour was 

 regarded as the maximum for which provision should be made, 

 as rains yielding more than that are exceedingly rare in Lon- 

 don. Hawksley considered that this rate was general, and 

 concluded, therefore, that a formula based on the measurements 

 made would serve for any other sewer to be constructed in 

 that vicinity a fair conclusion, except that it omits any con- 

 sideration of the character of the soil or of the relative amount 



* See also Trans. Am. Soc. C. E., Vol. LVIII, p. 458. 



