I&7 
Dr. Young’s Hydraulic Investigations. 
rence or diameter, the relative magnitude of the friction must 
also be inversely as the diameter, or nearly so, as Dubuat has 
justly observed. We shall then find that a must be .0000001 
43° +v 
1440 
1 80 
d-\- 1 2 
and c — .0000001 I 
goo dd , 1 
\dd - f 1000 * \J d 
(1050 + 7+I))’ Hence it is easy to calculate the velocity 
for any given pipe or river, and with any given head of water. 
For the height required for producing the velocity, indepen- 
dently of friction, is, according to Dubuat, or rather, as it 
appears from almost all the experiments which I have com- 
pared, ~ q ; and the whole height h is therefore equal to / -f- 
or h = ( a i - 4 - — — \ v 2 4 - ^ v ; and making b = ■■■■■ — , and 
e = — ,v 2 + 2<?u = bh, whence v = \/ ( bh -f- e 2 ) — e. In 
order to adapt this formula to the case of rivers, we must 
make l infinite ; then b becomes , and bh — - . - = — , s 
being the sine of the inclination, and d four times the hydraulic 
mean depth ; and since e is here = -,v and in 
most rivers, v becomes nearly 4^/(20000 ds ) . 
In order to show the agreement of these formula with 
the result of observation, I have extracted, as indiscriminately 
and impartially as possible, forty of the experiments 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 my own formulae, in separate columns. There are six 
of Dubuat’s experiments which he has rejected as irregular, 
apparently without any very sufficient reason, since he has 
accidently 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 results in a se- 
parate table. 
