THE LAW OF RESISTANCE IN PARALLEL CHANNELS. 
949 
D 3 I) 
where n has the value unity as long as either number is below unity, and then takes 
the value of the slope n to 1 for the particular surface of the pipe. 
If the units are metres and degrees centigrade 
A=67,700,000 
B=396 
P = (1+0-0336 T+0-000221 T 2 ) -i 
This equation then, excluding the region immediately about the critical velocity, gives 
the law of resistance in Poiseuille’s tubes, those of the present investigation and 
Darcy’s, the range of diameters being 
from 0•000013 (Poisettille, 1845) 
to 0’5 (I)arcy, 1857) 
and the range of velocities 
from 0'0026 1 
^ >■ metres per sec., 1883. 
This algebraical formula shows that the experiments entirely accord with the 
theoretical conclusions. 
The empirical constants are A, B, P, and n; the first three relate solely to the 
dimensional properties of the fluid summed up in the viscosity, and it seems probable 
that the last relates to the properties of the surface of the pipe. 
Much of the success of the experiments is due to the care and skill of Mr. Foster, 
of Owens College, who has constructed the apparatus and assisted me in making the 
experiments. 
Section II. 
Experiments in glass tubes by means of colour bands. 
18. In commencing these experiments it was impossible to form any very definite 
idea of the velocity at which eddies might make their appearance with a particular 
tube. The experiments of Poiseuille showed that the law of resistance varying as 
the velocity broke down in a pipe of say 0'6 millim. diameter ; and the experiments 
of Darcy showed this law did not hold in a half-inch pipe with a velocity of 6 inches 
per second. 
These considerations, together with the comparative ease with which experiments on 
a small scale can be made, led me to commence with the smallest tube in which I 
MDCCCLXXXIII. 6 F 
