HYDRAULIC INVESTIGATIONS. |07 



bd 



and e zz ~r, v 7, 4- 2ev — bk t whence v = -/ (6/t + <?*) — e. 



In order to adapt this formula to the ease of rivers, we T n riTers. 



d d h 



must make /infinite; then b becomes —rand bh zz — hr 



(ti (I I 



52 ~, s being the sine of the inclination, and d four times 



c 



the hydraulic mean depth ; and since e is here zz~-,«zz 



v/ {ads + cc) -~ - c 



_, ^ anc j in m0B t nvers, v becomes nearly */ 



(i>0000^). 



In order to show the agreement of these formulae with Various exp*. 

 the result of observation, I have extracted, as indiscrimi- "^Withthe 

 nately and impartially as possible, forty of the experiments formula. 

 made and collected by Dubuat; I have added to these some 

 of Gerstner's, with a few of my own ; and I have compared 

 the results of these experiments with Dubuat's calculations, 

 and with iny own formula^ in separate columns. There are 

 six of Dubuat's experiments, which he has rejected as irre- 

 gular, apparently without any very sufficient reason, since 

 he has accidentally mentioned, that some of them were made 

 with great care: I have therefore calculated the velocities 

 for these experiments in both ways, and compared the re- 

 sults in a separate table. 



Tabular 



