172 The N.Z. Journal of Science and Technology. [Aug. 
on the watershed. By taking a yield of 4, 5, 6, &c., cusecs successively in 
column 3 a series of points on the curve of perennial yield are obtained. 
A longer period of gaugings must be examined in each case. 
APPENDIX II.—ECONOMIC CAPACITY OF RESERVOIRS. 
It is obvious that on any given area a large reservoir produces a pro¬ 
portionally less improvement in stream-flow than a small one—that is, 
successive increments of capacity effect diminishing increments of yield. 
The problem is somewhat similar to that known to economists as the “ law 
of diminishing returns ” in agriculture, and the point to which development 
should be carried is that at which the enterprise is just able to return revenue 
sufficient to balance all its charges. To obtain a diagrammatic illustration, 
assume a watershed giving a yield curve similar to fig. 2, and consider in the 
first instance that the total cost of a scheme is simply proportional to the 
volume of masonry in the dam—that is, to the cube of its height. The 
power supplied (if the dam provides the whole of the head) is proportional 
to the product of the height of the dam and the yield. Consider the height 
and cost of a dam of 1 in. capacity as unity, and tabulate. The effect of 
capacity on the relative return of power to be obtained for a given cost is 
shown in column 6, plotted in fig. 3, curve A. 
1 . 
Capacity. 
2. 
Height. 
3. 
Yield. 
4. 
Power. 
5. 
Cost. 
6. 
Power 
7. 
Cost. 
8. 
Power 
Cost. 
Cost. 
0-5 
0-79 
0-77 
0-61 
0-5 
1-22 
: 
1-5 
0-41 
1 
1-00 
1-00 
1-00 
1 
1-00 
2 
0-50 
2 
1-26 
1-25 
1-58 
2 
0-79 
3 
0-53 
3 
1-44 
1-48 
2-13 
3 
0-71 
4 
0-53 
4 
1-59 
1-65 
2-62 
4 
0-65 
5 
0-52 
6 
1-82 
1-98 
3-60 
6 
0-60 
7 
0-51 
8 
2-00 
2-26 
4-52 
8 
0-58 
9 
0-50 
10 
2-15 
2-47 
5-31 
10 
0-53 
11 
0-48 
15 
2-47 
2-89 
7 13 
15 
0-48 
16 
0-45 
20 
2-71 
3-22 
8-73 
20 
0-44 
21 
0-42 
This illustrates the law of diminishing returns very effectively, but the 
accuracy of the assumptions may be improved. The cost of hydraulic plant 
is not quite proportional to the power, but is approximately aP + b, where 
P is horse-power and a and b are constants. The term aP does not influence 
the economic limit of construction, provided that a market is available for 
all the power generated, and so it may be neglected. In b are to be included 
all items of cost which do not vary with the capacity, e.g., constructional 
tram-lines, and so it may be of some magnitude. Taking b as equal to the 
cost of a dam of 1 in. capacity, the power y- cost ratio in column 8 and 
curve B is obtained, showing a well-defined maximum. This might appear 
to be the correct point of development. In a work undertaken in the national 
interest a larger dam, although it would return a smaller percentage of 
profits, might still show a credit balance and therefore be justified. This 
limit is clearly much higher if part of the cost of the work can be credited 
to navigation and flood-prevention than if undertaken for power alone. 
