294 The N.Z. Journal of Science and Technology. [Sept. 
Table II. 
1. 
Name of River. 
2. 
Drainage 
Area, in 
Square Miles. 
3. 
Mean Velocity 
of Flood-water, 
in Feet per 
Second. 
4. 
Discharge, 
in Cusecs. 
5. 
Discharge, in 
Cusecs per 
Square Mile. 
6. 
Inches 
of 
Rain 
per Hour 
. 
1. Waikerikeri 
' 
2-8 
5-93 
5,692 . 
2,032 
3-16 
2. Mangakorari 
4-5 
10-70 
8,025 
1,782 
2-80 
3. Haha 
6-5 
13-20 
10,930 
1,681 
2-62 
4. Opouteke 
12-0 
11-10 
19,738 
1,646 
2-57 
5. Opouteke 
19-0 
13-95 
24,691 
1,299 
2-03 
6. Opouteke 
30-0 
15-72 
36,659 
1,222 
1-91 
7. Waimamaku 
30-0 
11-17 
31,136 
1,038 
1-60 
8. Utakura . . 
38-0 
10-76 
32,587 
850 
1-33 
9. Mangakahia 
98-0 
13-88 
71,200 
726 
1-13 
In column 2 is given the drainage area of each river measured, and in 
column 4 the discharge in cusecs (cubic feet per second) at the highest stage 
of flood. 
The mean velocity of the flood-water was calculated after obtaining 
the hydraulic mean depth and the surface slope of the flood-water, by 
means of Kutter’s well-known formula, V = c y/RS 
In column 5 the discharge in cusecs per square mile is given, and in 
column 6 the discharge in cusecs per acre, which is very nearly equal to 
the inches of rain per hour, giving an equal momentary discharge. 
The figures in column 5 are very high, and give phenomenal records 
for run-off of rainfall per square mile of drainage area. It is noticeable 
how the discharge per square mile decreases with the increase of the 
drainage area. It is now quite generally admitted that the discharge per 
square mile is inversely proportional to the catchment area, and that it 
varies in the ratio of A* where A is the drainage area in square miles. 
In the diagram are shown the records of the rivers mentioned in 
Table II, plotted with inches of rain per hour as ordinates and the 
drainage areas as abscissae. 
On this figure is drawn the curve of an equation in which the discharge 
in cusecs per acre varies as A* where A is the drainage area in square miles. 
This diagram shows that the flood-discharges per acre obtained by the 
author correspond very closely to the above equation. A close relationship 
being established between the generally accepted idea of the ratio of flood- 
discharge to drainage area and the records obtained by the author, which 
seems to prove, at least, that the records are fairly reliable, the results of 
the run-off are still remarkably high. The author has very little reliable 
information regarding run-off per square mile of rivers in other districts 
in New Zealand, but those that are available are very much lower than 
any he has here recorded. 
It was estimated that in a flood in November, 1908, in the eastern 
province of Cape Colony, when much damage was done at Port Elizabeth, 
the maximum rate of flood was 640 cusecs per square mile for a drainage 
area of 35 square miles. This figure, however, does not equal that 
shown in Table II for a nearly equal area, the Utakura River, where 
the run-off is 850 cusecs per square mile from a drainage area of 38 square 
miles. 
