972 
MR. O. REYNOLDS ON THE MOTION OF WATER AND OF 
34. Comparison with the discharges calculated by Poiseuille’s formula. — Poiseuille 
experimented on capillary tubes of glass between '02 and '1 minim, in diameter, and 
it is a matter of no small interest to find that the formula of discharges which he 
obtained from these experiments is numerically exact for the bright metal tubes 
100 times as large. 
Poiseuille’s formula is— 
Putting 
Q = 1836'724( 1+ 0'0336793 T+0'000220992 T 3 )—y 
T = temperature in degrees centigrade. 
H = pressure in millims. mercury. 
D = diameter in millims. 
L= length in mi llims. 
Q=discharge in millims. cubed. 
. 13-64H 
1 = T~ 
P=lff-(0'336793 T+0'000220992 T 3 ) -1 
v = 
4Q 
7 rD 3 
and changing the units to metres and cubic metres this formula may be written 
D 3 . D 
47700000 -*=278- v 
the coefficients corresponding to A c and B c . 
The agreement of this formula with the experimental results from tubes 4 and 5 
is at once evident. The actual and calculated discharges differ by less than 2 per cent., 
a difference which would be more than accounted for by an error of half a degree in 
the temperature. 
35. Beyond the critical point. —The tables show that, beyond the critical point, the 
relation between i and v differs greatly from that of a constant ratio; but what the 
exact relation is, and how far it corresponds in the two tubes, is not to be directly 
seen from the tables. 
In the curves (Plate 74, diagram I.) which result from plotting i and v, it appears 
that after a period of flatness the curves round off into a parabolic form; but whether 
they are exact parabolae, or how far the two curves are similar with different para¬ 
meters, is difficult to ascertain by any actual comparison of the curves themselves, 
which, if plotted to a scale which will render the small differences of pressure visible, 
must extend 10 feet at least. 
36. The logarithmic method. —So far the comparison of the results has been effected 
by the natural numbers, but a far more general and clearer comparison is effected by 
treating the logarithms of l and v. 
