126 
The N.Z. Journal of Science and Technology. 
[Mar. 
When the rate of outflow from the reservoir exceeds the inflow into 
the reservoir the reservoir-level will fall, and we have the following 
equation : — 
cum = Q + A— 
dt 
Let H be the head on the weir corresponding to the flow Q ; then 
Q = CLH3/2 
CL (m - H 3 /-) = A— 
dt 
CL ^ _ - dh 
T ' ^ (hW - IL/2) 
the solution of which is 
CL 
A 
where 
• < = 7f 1 
</>(M = log ( a/-° -- 1 - 1 log ( h ° + x/^ + 1 
\H/ |3 °V V H 3 ° \H V H 
+ tar, 
V 3 
'•'H 1 ■ )1 los W a-‘l-j ios (a + v"a + 1 
1. 2 V| + i] 
4- — tan 
V3 
Vs 
h Q is the head on the weir when t — 0, h is the head at any time t there¬ 
after, and H is the final value of the head towards which the level is 
tending and corresponding to the flow Q. 
This function has been evaluated for values of H from 5-8 ft. to 0 at 
intervals of 0-2 ft., and the curves plotted on D 68 and D 69. It is 
necessary in this case to assume a limiting value for h Q , and a value of 
6 ft. has been selected as an extreme limit. All the curves accordingly 
start from 6 ft. datum above the weir-level. Keferring to D 68, for 
example, if the lake or reservoir level be 6 ft. when t = 0, and if the 
inflow fall to a rate corresponding to a head of 2 ft. on the weir, the 
curve marked H — 2 shows the rate at which the lake-level falls. If the 
inflow ceases altogether the lake-level falls according to the curve H — 0. 
If the inflow varies it is sufficient, in order to draw a curve showing the 
time rate of fall of lake-level, to assume that the inflow varies by steps, 
and to proceed in the manner already described in case of increasing 
inflow and rising lake-level. 
When this principle is applied to the conditions represented by D 67 
we get the descending portion of curve 2 on that figure. 
The charts may be used in two ways : either they may be used as a 
table of functions from which the lake-level at any instant for any value 
of CL/A may be ascertained by inspection if the flow is steady and by 
