DEVELOPMENT OF FORMULAE FOR FLOW 169 



liminary, he died, in 1860, and the carrying on of the experi- 

 ments and drawing up of the conclusions fell to his assistant, 

 M. Bazin. It was the latter who arranged and conducted the 

 gagings and extended them to several branches of the Canal 

 de Bourgogne, who collected and digested the numerous results, 

 and who has written an elaborate book on the subject, embody- 

 ing the results of years of investigation and study.* Bazin 

 made two general deductions: 



1. The coefficient c of the formula for the determination 

 of the mean velocity in canals and rivers of uniform flow varies 

 with the degree of roughness of the wetted surface. 



2. These coefficients c vary much more nearly with R than 

 with v. 



He further noticed a change in c corresponding to a change 

 in 5, but he did not consider it of sufficient importance to be 

 taken into account. 



From his study and the knowledge thus gained M. Bazin 

 established a new formula, making it applicable to his experi- 

 ments and having v change with the differences in the rough- 

 ness by having four classes of surfaces, with special coefficients 

 for each class, and putting every channel into one of these four 

 classes. He takes the abbreviated formula of Eytelwein, 



and makes the constant 



or 



*Wa+|Ror.= 



, To determine values of a and fi, M. Bazin plotted for con- 



* Recherches Hydrauliques, entreprises par M. H. Darcy: continues par 

 M. H. Bazin, 1865. 



