974 
MR. O. REYNOLDS ON THE MOTION OF WATER AND OF 
The determination of the relation between circumstances of motion and the 
physical condition of the water in such a general form was not contemplated 
when the experiments were undertaken, and must be considered as a result of the 
method of logarithmic homologues which brought out the relation in such a marked 
manner that it could not be overlooked. Nor is this all. 
It had formed no part of my original intention to re-investigate the law of resistance 
in pipes for velocities above the critical value, as this is ground which had been very 
much experimented upon, and experiments seemed to show that the law was either 
indefinite or very complex—a conclusion which did not seem inconsistent with the 
supposition that above this point the resistance depended upon eddies which might be 
somewhat uncertain in their action. But although it was not my intention to investi¬ 
gate laws, I had made a point of continuing the experiments through a range of 
pressures and velocities very much greater I think than had ever been attempted in 
the same pipe. 
Thus it will be noticed that in the larger tube the pressure in the last experiment 
is four thousand times as large as in the first. In choosing the great range of pressures 
I wished to bring out what previous experiments had led me to expect, namely, that 
in the same tube for sufficiently small pressures the pressure is proportional to the 
velocity, and for sufficiently great pressures, the pressure was proportional to the 
scpiare of the velocity. Had this been the case not only would the lowest portion of 
the logarithmic homologues up to the critical point have come out straight lines inclined 
at 45 degrees, but the final portion of the curve would have come out a straight line 
at half this inclination, or with a slope of two horizontal to one vertical. 
The near approach of the lower portions of the curve to the line at 45° led me, 
as I have already explained, to discover that the temperatures had risen at the lower 
velocities, and to make a fresh set of experiments, some of which are given in Table IV., 
in which, although the temperatures were not constant, they were sufficiently different 
from the previous ones to show that the discrepancy in the lower portions of the curves 
might be attributed to variations of temperature, and the agreement with the line of 
45° considered as within the limits of accuracy of experiment. 
When the logarithms of the upper portions of the curve came to be plotted, the 
straightness and parallelism of the two lines was very striking. 
There are a few discrepancies which could not be in any way attributed to tempera¬ 
ture, as with so much water moving this was very constant, but on examination it was 
seen that these discrepancies marked the changes of the discharge gauges. The law 
of flow through the orifices not having been strictly as the square roots of the heights, 
the manner in which the gauges had been compared forbade the possibility of there 
being a general error from this cause; the middle readings on the gauge were correct, 
so that the discrepancies, which are small, are mere local errors. 
This left it clear that whatever might be their inclination the lines expressed the 
laws of pressures and velocities in both tubes, and since the lines are strictly parallel, 
