THE LAW OF POI SEVILLE

13

formula becomes V = K

pd*

For water at 10°C he found the

value of K to be quite exactly 2,495,224, p being expressed in
millimeters of mercury at 10° and I and d in centimeters. He
experimented with alc,ohol and mixtures of alcohol and water
and for these we obtain different values of K. Poiseuille did
not use the terms viscosity or fluidity, nevertheless these values
of K are proportional to the fluidity.

The Effect of Temperature on the Rate of Flow.—Girard had
given a formula to represent the flow of water in a pipe as a
function of the temperature, but the constants had to be deter-
mined for each pipe. Poiseuille gave a formula which was inde-
pendent of the instrument used,

r>d*
Q = 1,836,724,000(1 + 0.0336793Z7 + 0.0002209936r2) —

where Q represents the weight of water traversing the capillary
in a unit of time. The adequacy of this formula to reproduce
the observed values is shown in Table V.

TABLE V.—CAPILLARY A

I = 10.05 cm d = 0.0141125 cm p = 776 mm of mercury. Time of

flow 1,000 sec.

WEIGHT OF EFFLUX

WEIGHT OF EFFLUX CALCULATED BY

TEMPERATURE OBSERVED FORMULA

0.6
5.0
10.0
15.0
20.0
25.0
30.1
35.1
40.1
45.0

5.74376

6.60962

7.64649

8.74996

9.91530

11.14584

12.45631

13.80695

15.21866

16.67396

5.73955

6.60381

7.64435

8.74705

9.91191

11.13892

12.45423

13.80710

15.22184

16.66860

Since the values calculated are weights and not volumes, the
values of Q are not proportional to the fluidity. This formula
pd*
remains empirical, but the expression V = K —•r- can be readily
derived from the fundamental laws of motion.
Theoretical Derivation of the Law.—Hagenbach (1860) appears
to have been the first to give a definition of viscosity. He made