ox THE FLOW OF WATER IN PIPES, CONDUITS, ETC. 133 



the resistance head becomes 



7i = 



('+i'^)^^i;^- 



If we combine into a single symbol 



i kAR = t, 



then 



h 



V r / r 2g 



wliich is the form given to the value of the resistance head by the dis- 

 tinguished French engineer Darcy, in which Darcy assumed that i- and t 

 were certain constants. It is an injustice to Darcy to let it appear, as 

 is so often done in reference to his formula as above presented ia (13), 

 that he was not aware of the insufficiency of the expression 



m ^ fc -j (13) 



r ' 



to represent the coefficient of resistance. In fact he proposed the more 

 general expression 



m = fx -\ + — -f- — r- 



r V vr^ 



for this coefficient, in which a, ji, A, /x were certain positive constants.* 



5. Taking up again our expression (9), we observe that if Afi be con- 

 sidered arbitrarily small then equation (9) degenerates into Chezy's form 

 given in (6), but the result of experiment shows, as was indicated before, 

 that we had no right to pass to the limit of the continuum in the inte- 

 gration but should employ the finite summation and retain the vanishing 

 terms in the form (9). 



We shall, ais is the conventional custom, term the expression 



AR AR AR 



the coefficient of resistance, and in this expression we shall call 



AR 



"Ency. Brit., Ninth Ed., Hydromechanics, p. .510, Vo!. XII. 



