KUTTER'S FORMULA 177 



rivers, and would decrease as the slope decreased for small 

 channels and pipes. In other words, there must be a point 

 or a certain value of R or a certain sized stream in which the 

 slope had no effect on c, but that for that size the value of S 

 could increase or diminish without affecting the value of c. 

 From the available data a series of points were plotted with 

 values of c and R as variables, and all with the same slope 

 as near as possible. In this way a series of lines were obtained, 

 each representing a certain slope, and it was found without doubt 

 that they intersected at a point whose value for i/V^R was one 

 metre approximately, or whose value of i/c was .027 in metric 

 units. The element of slope was introduced, arbitrarily, by 

 making y equal to a+l/n+m/S\ then, preserving the relation 



x = n y i f x was made equal to (a,+}n. Then, to deter- 



\ V 



mine the values of /, points were plotted from streams whose 

 value of i/VR was i, and the roughness of whose channels 

 was similar, and the value of / was found to be i.oo. Then, 

 to get a, points were plotted with values of i/S as abscissae and 

 of y as ordinates, and the point where the line intersected the 

 axis gave a equal to 23, and m, or the tangent of the angle, 

 equal to .00155. The constants a, /, and m being determined, 

 it remained to find values for n for different channels. This 

 was done by again plotting points of actual gagings for differ- 

 ent streams and finding corresponding values of n. In this 

 way the values were found to range from .009 to .040. 

 To sum up, then, from the original formula 



in which c equals 



_^ 



where y equals 



/ ,m 



