INVESTIGATION OF FLOW OF WATER IN UNIFORM CHANNELS. 375 
velocity and the temperature of the water, the relative fluidity’ of 
the water for each experiment is stated, since it is preferable to 
introduce the fluidity, rather than the temperature, into an 
expression for the rate of flow. In the experiments of this series 
the mean hydraulic radius was in each case almost exactly ‘9 cm. 
and the velocities have therefore been reduced to that common 
value instead of to an hydraulic radius of 1 cm. 
The logarithims of the velocity and the fluidity are co-ordinated 
in Fig. 4, and the relationship between the two quantities may be 
represented roughly by a straight line curve having an inclination 
q=°3 approximately, or in symbols 
Cag 
This was the expression made use of in reducing the velocities in 
Series LI. to a common temperature. 
15. Comparison of results obtained by the use of the formula 
of Kutter and Ganguillet.—Since the formula of Kutter and» 
Ganguillet is probably that most used for the determination of 
the velocity of flow in open channels, an interesting comprarison 
may be made between the actual results of the present experi- 
ments and those compiled by means of the formula. 
In the formula 
V=c V(RkT) 
the coéfficient is, in metric measure, 
23 4 + Bea 3 
c= eit 
1 + (3. + AON N 2 ) a 
The value of the coéfficient of roughness, , in this expression 
may probably be assumed to be 009 for the circumstances of the 
present experiments. On this assumption, the velocity has been 
determined at various slopes throughout the range embraced 
by Series II., and the resulting curve is shown in Fig. 3, (K 
and @), 
1 See pp. 318, 319 of this Volume. 
