THE LAW OF RESISTANCE IN PARALLEL CHANNELS. 
979 
were calculated for each tube, using the values of A and B as already determined, 
log i 0 and v 0 are the co-ordinates of O the intersection of the two straight branches of 
the logarithmic curves, so that the application of the formula to the results was simply 
tested by continuing the straight upper branches of the logarithmic homologues 
to see whether they passed through the corresponding point O. 
The agreement, which is shown in diagram III., Plate 74, is remarkable. There 
are some discrepancies, but nothing which may not be explained by inaccuracies, 
particularly inaccuracies of temperature. 
42. The effect of the temperature above the critical point. —It is a fact of striking 
significance, physical as well as practical, that while the temperature of the fluid has 
such an effect at the lower velocities that, cceteris paribus, the discharge will be double 
at 45° C. what it is at 5° C., so little is the effect at the higher velocities that neither 
Darcy or any other experimenter seems to have perceived any effect at all. 
In my experiments the temperature was constant, 5° C. at the higher velocities, so 
that I had no cause to raise this point till I came to Darcy’s result, and then, after 
perplexing myself considerably to make out what the temperatures were, I noticed 
the effect of the temperature is to shift the curves 2 horizontal to 1 vertical, which 
corresponds with a slope of 2 to 1, and so nearly corresponds with the direction of 
the curves at higher velocities that variations of 5° or 10° C. produce no sensible effect; 
or, in other words, the law of resistance at the higher velocity is sensibly independent 
of the temperature, i.e., of the viscosity. 
Thus not only does the critical point, the velocity at which eddies come in, diminish 
with the viscosity, but the resistance after the eddies are established is nearly, if not 
quite, independent of the viscosity. 
43. The inclinations of the logarithmic curves. —Although the general agreement 
of the logarithmic homologues completely establishes the relations between the 
diameters of the pipes, the pressures and velocities for each of the four classes of pipes 
tried, viz., the lead, the varnished pipes, the glass pipes, and the cast iron, there 
are certain differences in the laws connecting the pressures and velocity in the pipes 
of different material. In the logarithmic curves this is very clearly shown as a 
slight but definite difference between the inclination of the logarithmic homologues 
for the higher velocities. 
The variety of the pipes tried reduces the possible causes of this difference to a small 
compass. It cannot be due to any difference in diameters, as at least three pipes of 
widely different diameters belong to each slope. It is not due to temperature. This 
reduces the cause for the different values of n to the irregularity in the pipes owing 
to joints and other causes, and the nature of the surfaces. 
The effect of the joints on the values of n seems to be proved by the fact that 
Darcy’s three lead pipes gave slightly different values for n, while my two pipes 
without joints gave exactly the same value, which is slightly less than that obtained 
from Darcy’s experiments. 
