948 
MR. 0. REYNOLDS ON THE MOTION OF WATER AND OF 
the well known experiments of Darcy on pipes ranging from 0'014 to 0'5 metre in 
diameter. 
Taking no notice of the empirical laws by which Darcy had endeavoured to 
represent his results, I had the logarithmic homologues drawn from his published 
experiments. If my law was general then these logarithmic curves, together with 
mine, should all shift into coincidence, if each were shifted horizontally through 
TD 3 
P 3 
and vertically through 
D 
P 
In calculating these shifts there were some doubtful points. Darcy’s pipes were 
not uniform between the gauge points, the sections varying as much as 20 per cent., 
and the temperature was only casually given. These matters rendered a close 
agreement unlikely. It was rather a question of seeing if there was any systematic 
disagreement. When the curves came to be shifted the agreement was remarkable. 
In only one respect was there any systematic disagreement, and this only raised 
another point ; it was only in the slopes of the higher portions of the curves. In 
both my tubes the slopes were as 1722 to 1 ; in Darcy’s they varied according to the 
nature of the material, from the lead pipes, which were the same as mine, to 1‘92 to 1 
with the cast iron. 
This seems to show that the nature of the surface of the pipe has an effect on the 
law of resistance above the critical velocity. 
16. The critical velocities .—All the experiments agreed in giving 
1 P 
Vc ~ 278 D 
as the critical velocity, to which corresponds as the critical slope of pressure 
. _ 1 P 3 
l °~ 47700000 D 3 
the units being metres and degrees centigrade. It will be observed that this value is 
much less than the critical velocity at which steady motion broke down; the ratio 
being 437 to 278. 
17. The general law of resistance .-—The logarithmic homologues all consist of two 
straight branches, the lower branch inclined at 45 degrees and the upper one at n 
horizontal to 1 vertical. Except for the small distance beyond the critical velocity 
these branches constitute the curves. These two branches meet in a point on the 
curve at a definite distance below the critical pressure, so that, ignoring the small 
portion of the curve above the point before it again coincides with the upper branch, 
the logarithmic liomologue gives for the law of resistance for all pipes and all velocities 
