Frictional Resistance: in Artificial Waterways 47 
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and 14, derived from the data from which Figs. 30, 31, 32 and 33 
were constructed, the discharges indicated by the several methods 
are compared on a percentage basis, taking the multiple point de- 
teamination as 100 per cent. This procedure is also applied in 
Table 15, which summarizes the determinations of flow in ten 
flumes, rating flumes and canals, including the four previously 
stated. The channels are all comparatively shallow, ranging from 
1.0 to 5.7 feet in mean depth of water, with mean velocities of from 
1.3 to 4.3 feet per second. It will be observed from the relative 
percentages of the aggregate discharge, given at the bottom of Table 
15, that the multiple point method gives the least value and that the 
vertical integration, the 0.2 and 0.8 depth, and the 0.6 depth 
methods give higher values by percentages of 0.8, 2.2, and 5.6 
respectively. These data, and general observations, apparently 
warrant the following statements: 
1. The multiple point method, whereby the velocity is ob¬ 
tained by holding the meter successively at points relatively close 
together in a vertical plane, gives the closest determination of the 
actual mean velocity. Where accuracy is more essential than time, 
and where the 'condition of flow will not change during the time 
required to make the rating, the multiple point method should be 
used. The greater the number of points taken, the more accurate 
will be the determination. 
2. The vertical integration method, in which the mean veloc- 
tiy at each station in the cross-section is determined by moving 
the meter slowly upward and downward, is particularly applicable 
where reasonable accuracy is desired in a comparatively short time. 
The water should not be too deep nor too swift to permit of the 
meter being moved with a uniform, slow motion in a vertical line. 
It is very essential that a sufficient number of complete trips be 
made from top to bottom, and as previously stated, that the motion 
be slow and unvarying. Under suitable conditions this method 
gives results next in accuracy to the multiple point, but the accuracy 
depends largely upon the skill of the operator. Some hydrograph- 
ers allow a little longer time when near the top and the bottom, 
but since these points are the most unreliable in the section, such 
practice is questionable, for it has a tendency to give them too 
much weight in the average result. 
3. The 0.2 and 0.8 method, which consists in taking separate 
velocity measurements at two-tenths and at eight-tenths of the 
depth of water at each station, and using their average as the 
mean velocity for the vertical section, is third in point of accuracy. 
This method is more rapid than either of the previous ones, but 
