978 
MR. O. REYNOLDS ON THE MOTION OF WATER AND OF 
it, and as his pipes, 300 metres long, were in the open air, the effect of the sun on the 
pipes would have led to still larger differences. 
The effect of these various causes on his results may be seen, as he took the pre¬ 
caution to use two pressure gauges on separate lengths of 50 m of his pipes, and the 
records from these two gauges by no means always agree, particularly for the lower 
velocities. In one case the results are as wide apart as 15 and 7, and often 10 
or 1 5 per cent. In arriving at tabular values for i he has taken the mean of the 
two gauges. 
Taking these things into account, I could not possibly expect any close agreement 
with my results; still, as experiments on pipes of such large diameters are not likely 
to be repeated, at any rate with anything like the same care and success, they offered 
the only chance of proving that my law was general. 
40. Reduction of the experimented results. —Rejecting all the experiments on rusty 
and rough pipes, i.e., selecting the lead, the varnished, the glass, and new cast iron 
pipes, which ranged from half-an-inch to twenty inches diameter, I had the log¬ 
arithmic homologues drawn. These are shown on diagram III., Plate 74. In the case 
of two of the smaller pipes the smallest velocity is well below the critical point, and 
in several of the other pipes the smallest velocity is near the critical velocity. This 
accounts for the lower ends of the logarithmic curves being somewhat twisted; for the 
remainder of the logarithmic homologues are nearly straight; some are slightly bent 
one way and some another, but they are none of them more bent than may be attri¬ 
buted to experimental inaccuracy. 
The inclinations of the upper ends of the lead and bituminous pipes is 1'746, 
slightly greater than mine ; but in the cases of the glass pipes and the cast iron pipes 
the slopes are 1*82 and l - 92 respectively. 
So much appeared from the logarithmic homologues themselves, but the most 
important question was, would the curves agree with the results calculated from the 
formula 
b5A 
41. Comparison with the law of resistance. —-In applying this test I was at first 
somewhat at a loss ou account in some cases of the want of any record of the tempe¬ 
rature, and the doubt as to such temperatures as had been recorded being the 
temperature of the water in the pipes between the gauges. 
The dates at which the experiments were made to a certain extent supplied the 
deficiency of temperature, the temperatures given fixing the law of temperature, so 
that the probable temperature could be assumed where it was not given. 
Assuming the temperature, the values of 
• _ p2 
?0 ~AD 3 
r 
V ° BD 
