THE LAW OF RESISTANCE IN PARALLEL CHANNELS. 
981 
of his smallest tubes, succeeded in attaining velocities at which the results were no 
longer in accordance with his law. 
When I first examined his experiments I expected to find these limiting velocities 
above the critical velocities as given by my formula. In all cases, however, they 
were very much below, and it was then I came to see that Poiseuille had taken no 
account of the pressure necessary to start the fluid. 
It then became interesting to see how far the deviations were to be explained in 
this way. 
In pipes of sensible size the pressure necessary to start the fluid lies between 
v 2 
and L505 tw 
2 9 
according to whether the mouthpiece is trumpet-shaped or cylindrical. Poiseuille 
states that he was careful to keep both ends of his pipe cylindrical, hence according 
to the law for mouthpieces of sensible size, the pressures which he gives should be 
v 2 
corrected by L505 
This correction was made, and it was then found that with all the smaller tubes 
Poiseuille’s law held throughout his experiments, and with the larger pipe it held up 
to the critical value and then diverged in exact accordance with my formula, as shown 
by the line CC. 
Darcy’s experiments in the case of three tubes F, G, I fall below the critical value, 
and in all these cases agree very well with the theoretical curve as regards both 
branches. 
This, however, must be looked upon as accidental, as at the lower velocities Darcy 
had clearly reached the limit of sensitiveness of his pressure gauges; thus, for instance, 
the experiment close by the letter F is the mean of two readings which are respectively 
7 and 15 ; there is a tendency throughout the entire experiments to irregularity in 
the lower readings which may be attributed to the same cause, and this seems to 
explain the somewhat common deviation of the one or two lower experiments from 
the line given by the middle dots. 
A somewhat similar cause will explain cases of deviation in the one or two upper 
experiments, for the discrepancy in the two gauges here again becomes considerable. 
For these reasons the intermediate experiments were chiefly considered in deter¬ 
mining the slopes of the theoretical lines. 
These slopes were obtained as the mean of each class of tubes 
Lead jointed. 
Varnished. 
Glass. 
New cast iron .... 
Incrusted pipe .... 
Cleaned pipe . . . . 
G iv 
179 
1-82 
179 
L88 
2 * 
1*91 
MDCCCLXXXIJT. 
