982 
MR. 0. REYNOLDS ON THE MOTION OF WATER. 
and then in the cases in which the temperature was given, I. J, L, M, N, the points 
O having being determined by the formula, 
Log i 0 — 2 log P — 3 log D — 7’851 
Log v Q — log P— log D—2‘598 
the lines having the respective slopes were drawn through these points and in all 
cases agreed closely with the experiments. 
In the cases where the temperature was not given the values of log i 0 and log v 0 
were calculated for 5° C., these are shown along the line marked “line of intersections 
at 5°,” through these points lines are shown drawn at an inclination of 2 to 1, which 
are the lines on which O would lie whatever might be the temperature. These with 
the respective slope lines were drawn so as most nearly to agree with the experiments, 
these intersect the lines at 2 to 1 in the points 0 which indicate the temperatures, and 
considering the extremely small effect of the temperature these are all very probable 
temperatures with the exception of G, H, and S, in which cases 0 is above the line 
for 5° C. This indicates strongly that in these cases there must have been a small 
error, 2 or 3 per cent., in determining the effective diameter of the pipes. 
It seemed very probable that roughness in the pipes, such as might arise from 
incrustation or badly formed joints, would affect the logarithmic homologues, and for 
this reason only the smoother classes of pipes were treated; but with a view to test 
this idea, the homologues Q and It, which related to the same incrusted pipe before 
and after being cleaned were drawn, and their agreement is such as to show that 
for such pipe the effect of incrustation is confined to the effect on the diameter of the 
pipe, and on the value of n which it raises to 2. This, however, was a large pipe and 
the velocities a long way above the critical velocity, so that it is quite possible that 
the same incrustation in a smaller pipe would have produced a somewhat different 
effect. 
The general result of this diagram is to show that throughout the entire range— 
from pipes of 0’"'000014 to 0' m 5 in diameter, and from slopes of pressure ranging from 
1 to 700,000—there is not a difference of more than 10 per cent, in the experimental 
and calculated velocities, and with very few excejrtions the agreement is within 2 or 
3 per cent., and it does not appear that there is any systematic deviation whatever. 
