i 66 Dr . Young’s Hydraulic Investigations. 
practical form. By comparing the experiments, which he lias 
collected, with some of Gerstner, and some of my own, I 
have ultimately discovered a formula, which appears to agree 
fully as well as Dubuat’s, with the experiments from which 
his rules were deduced, which accords better with Gerstner’s 
experiments, which extends to all the extreme cases with equal 
accuracy, which seems to represent more simply the actual 
operation of the forces concerned, and which is direct in its 
application to practice, without the necessity of any successive 
approximations. 
I began by examining the velocities of the water,discharged, 
through pipes of a given diameter, with different degrees of 
pressure; and I found that the friction could not be represented 
by any single power of the velocity, although it frequently 
approached to the proportion of that power, of which the ex- 
ponent is 1.8; but that it appeared to consist of two parts, the 
one varying simply as the velocity, the other as its square. 
The proportion of these parts to each other must however 
be considered as different, in pipes of different diameters, 
the first part being less perceptible in very large pipes, or in 
rivers, but becoming greater than the second in very minute 
tubes, while the second also becomes greater, for each given 
portion of the internal surface of the pipe, as the diameter is 
diminished. 
If we express, in the first place, all the measures in French 
inches, calling the height employed in overcoming the friction 
f, the velocity in a second v , the diameter of the pipe d, and 
its length /, we may make f = a 2 -|- 2 c^v; for it is ob- 
vious that the friction must be directly as the length of the 
pipe ; and since the pressure is proportional to the area of the 
section, and the surface producing the friction to its circumfe- 
