980 
MR. 0. REYNOLDS ON THE MOTION OF WATER AND OF 
Darcy’s pipes were all of them uneven between the gauge points, the glass and 
the iron varying as much as 20 per cent, in section. The lead were by far the most 
uniform, so that it is not impossible that the differences in the values of n may be due 
to this unevenness. 
But the number of joints and unevenness of the tarred pipes corresponded very 
nearly with the new cast iron, and between these there is a very decided difference in 
the value of n. This must be attributed to the roughness of the cast iron surface. 
44. Description of Diagram III. 
Diagram III.—In this diagram the experiments of Poiseuille and Darcy are 
brought into comparison with those of the present investigation. 
In consequence of the number of lines, the general aspect of the diagram is 
somewhat confused, but such confusion vanishes so soon as it is clearly perceived that 
each line of dots indicates the logarithmic homologue for some particular pipe as 
determined by experiment, reduced and plotted in exactly the same manner as for 
diagram II. ; DD and EE being exact repetitions of the logarithmic homologue for 
pipes 4 and 5, on a somewhat smaller scale. 
It is at once apparent from diagram III. how, for the most part, the experiments 
have been well below or well above the critical values. In the small pipes of 
Poiseuille the velocities were below the critical values, and hence lie in straight lines 
inclined at 45°. 
The smallest pipe on which Poiseuille’s experimented had a diameter of CFO 14 
millim.; only one experiment, marked A, is shown in the diagram, as the remaining 
three extended outside the range of the plate. They fall exactly on the dotted line 
through A, and do not reach the critical value. 
The same is true of all the rest of Poiseuille’s experiments except those made on a 
much larger pipe, diameter 0'65 millim., hence it is thought sufficient to plot only one, 
namely BB. 
CC shows the experimental results obtained with the pipe 0'65 millim. diameter, 
and these reach the critical value as given by the formula, and then diverge from the 
line. 
It is important to notice, however, that the points are not taken directly from 
Poiseuille’s experiments, which have been subjected to a correction rendered 
necessary by the fact that Poiseuille did not measure the resistance by ascertaining 
the pressure at two points in the pipe, but by ascertaining the pressure in the vessels 
from which and into which the water flowed through the pipe, so that his resistance 
includes, besides the resistance of the pipe, the pressure necessary to impart the initial 
velocity to the water. This fact, which appears to have been entirely overlooked, had 
a very important influence on many of Poiseuille’s results. Poiseuille endeavoured 
to ascertain what was the limit to the application of his law, and, with the exception 
