STEADY FLOW OF WATER IN UNIFORM PIPES AND CHANNELS. 331 
of log J as abscissee, and the corresponding values of log U as 
ordinates : and = will be the tangent of the angle which the line 
makes with the axis of abscisse. There are slight variations of 
temperature in Reynolds’ and Darcy’s experiments, hence the 
velocities must first be corrected to the one temperature, which [ 
have taken generally to be about the mean for the series. For 
this purpose, Reynolds’ formula—see (7) § 6—has, after some 
partial justification, been asumed to be true in so far as its theory 
of temperature correction is concerned ; and the very small required 
correction’ has been applied from approximate values of m, in the 
manner indicated in the discussion of this question hereinafter. 
It may be remarked that on the scale of the figures, the effect of 
the temperature correction is hardly noticeable. 
On looking over Figs. 2 to 6, it will be observed that not only 
is the relation evidently linear; but the precision of that relation 
is very remarkable. Moreover, it is evident that it is not possible 
to make the index of U, 2, without involving appreciable error, 
except in three instances, viz., those of lines 14, 18 and 20 of 
Table A. hereinafter, in which all the results are entered for the 
sake of easy reference. 
Again, the practical difficulty of computing the velocity of flow 
is rendered apparent, since for the same material and class of pipe 
there are sensible differences in the index nm. It appears to be 
certain that m increases with the roughness of the pipe, but it 
varies between wide limits, as for example in lead pipes, from 
1-695 to 1-784: in new cast iron—rejecting 1-861 as a doubtful 
case—from 1-917 to 1-957, and in incrusted cast iron from 1-908 
to 1-985. In the light of this evidence it is beyond question that, 
in calculations of velocity from fall in pressure, precision depends 
upon a nice discrimination of the eats of the boundary, so 
as to correctly estimate the value of n. 
1 Reynolds’ temperature ‘correction, if in error, is too small. However 
the results are more nearly comparable after ae correction has been 
lied. 
