Moseley's Theory of Steady Flow. 113 



velocity-formula, and therefore fails as a rational theory along 

 with it, It might, however, happen that the other results 

 might prove to be good empirical formula?. The only others 

 admitting of test are the formulas for Discharge, which are 

 given in several forms, as suited for pipes of various sections 

 (circular, rectangular, &c.) flowing full and for open chan- 

 nels. A large number of the discharge-measurements of 

 MM. Darcy and Bazin in circular pipes flowing full and in 

 small rectangular and trapezoidal open channels, are compared 

 in the original essay with the results computed from the for- 

 mulas ; and here, again, there is a remarkable approximation 

 in the results. This turns out, however, to be no criterion of 

 approximation on the large scale, as will appear below. 



Some extensive large-scale experiments on flow of water in 

 large canals of various widths up to 200 x and depths up to 13/, 

 and various discharges up to 7000 cubic feet per second, made 

 under the author's superintendence near Roorkee in Northern 

 India, in 1874-79, and recently published*, afford a test for 

 the formula for discharge in open channels on the large scale. 

 The formula given is 



Discharge in cubic 1 Jy _ 1 W ■ 



metres per second ] u ~ * R' ' i L v 1 + ** ) • « } • » o, 



where 



B' = wetted border, 11' = hydraulic mean depth, both in 



metres; 

 v' = central surface-velocity in metres per second; 

 W = discharge in cubic metres per second. 



The formula is a very laborious one for computation; but its 

 failure on the large scale can be readily shown, without com- 

 plete computation, as follows: — It is obvious that the quantity 

 (1 + 2R/) . e _2R ' is always a + quantity, rapidly decreasing as 

 R/ increases : hence the above expression gives a result always 



less than \ =^ 7 . v f cubic metres per second, and therefore 



(changing to British measures) the 



Discharge, in cubic ) -^ . , 

 feet per second j ^ is alway= 



(3-281) 3 B 

 <- — ^ — — x 



2 R 3-281' 



< 5-382 ^-.r , 



where B, R, v are here measured infect, 



'. * Roorkee Hydraulic Experiments, 1681, 3 vols, (published at Tho* 

 mason C. E. College, Roorkee, N.W. P., India, 1881). 

 PhiL Mag. S. 5. Yol. 14. No. 86. Aug. 1882. I 



