970 
MR. 0. REYNOLDS ON THE MOTION OF WATER AND OF 
32. The results of the experiments .—A considerable number of preliminary experi¬ 
ments were made until the results showed a liigb degree of consistency. Then a 
complete series of experiments were made consecutively with each tube. The results 
of these are given in Tables III. and V. 
33. The critical velocities .—The determination of these, which had been the main 
object of the experiments, was to some extent accomplished directly during the 
experiments, for starting from the very lowest velocities, it was found that the fluid 
in the differential gauge was at first very steady, lowering steadily as the velocity 
was increased by stages, until a certain point was reached, when there seemed to be 
something wrong with the gauge. The fluid jumped about, and the smallest adjust¬ 
ment of the tap controlling the velocity sent the fluid in the gauge out of the field 
of the microscope. At first this unsteadiness always came upon me as a matter of 
surprise, but after repeating the experiments several times, I learnt to know exactly 
when to expect it. The point at which this unsteadiness is noted is marked in the 
tables. 
It was not, however, by the unsteadiness of the pressure gauge that the critical 
velocity was supposed to be determined, but by comparing the ratio of velocities and 
pressures given in the columns v and i in the tables. This comparison is shown in 
diagram I., Plate 74, the values of i being abscissse and v ordinates. It is thus 
seen that for each tube the points which mark the experiments lie very nearly in a 
straight line up to definite points marked C, at which divergence sets in rapidly. 
The points at which this divergence occurs correspond with the experiments 
numbered 6 and 59, which are immediately above those marked unsteady. 
Thus the change in the law of pressure agrees with the observation of unsteadiness 
in fixing the critical velocities. 
According to my assumption, the straightness of the curves between the origin and 
the critical points would depend on the constancy of temperature, and it was the 
small divergences observed that suggested a variation of temperature which had been 
overlooked. This variation was confirmed by further experiments, amongst which 
are those contained in Table IV. These showed that the probable variation of the 
temperature was in Table III. from 12° C. to 9° C. at the critical point, and from 12° C. 
to 8° C. in Table V., which variations would account for the small deviation from the 
straight. 
It only remained, then, to ascertain how far the actual values of v c , the velocity at 
a p 
the critical points, corresponded with the ratio ^ or —. 
For tube 4 from the Table III. 
D = (P-00615 
v c — 0 ; "’4426 
at 9° C.; at this temperature 
P= *757 
see p. 952. 
