176 SEWER DESIGN 



age lines were then drawn through the points thus plotted. 



Then, since the expression c equals - , can be trans- 



x 



l+ VR 



formed by taking the reciprocal of each side, the expression 

 becomes 



i i . x i 



c 



or it has the form of an equation of the first degree and of a 

 straight line in which if values of i/c are plotted as ordinates 

 and of i/\/R as abscissae, then i/y must be the constant term 

 and x/y the tangent of the angle of inclination. If i/y is 

 constant, it will appear by all the lines passing through the 

 same point on the axis of y. Far from doing this, the lines 

 plotted cut the axis at points unmistakably far apart, and 

 the divergence was especially noticeable when small flows 

 with steep grades and large flows in rivers with low grades 

 were compared. It seemed then that, in the formula, y must 

 be made a variable as well as x. After repeated trials to get 

 the plotted points to agree with the curves drawn by the 



formula, y was made equal to <H , and x to a-n, so that C 



n 



equals 



n 



. an 

 i+- 



VR 



the above values or relations being determined by series of 

 gagings made with the same slope as nearly as possible. Up 

 to this point in the development, c had been made to vary 

 with R and with n, and it remained to make it vary with 5. 

 It was known from the experiments of Bazin and from those 

 of Humphreys and Abbot that it must be brought in in such 

 a way that c would increase as the slope decreased for large 



