110 A NEW METHOD OF ESTIMATING STREAM-FLOW 
computation, the first estimate obtainable of the run-off is I e -\-Riri+ R,r t -\-R i r i -\- 
R t r>+R,r % , or 6+(0.07)(-8) + (0.17) (- 21) + (0.80) (+2) + (0.20) (0) + (0.27) (+4) 
= 6-1-4+2+0+1 = +4. The first estimate of -r, is +4+8-l = +ll, with 
which a first estimate of -\-Rirt for that day can be computed, viz, (0.01)( — 11) = 
0, in the units used. Since this, added to the first estimate of the run-off, +4, 
does not change it, the first estimate of —r t for April 18, +11, remains unchanged 
at that value. 
After April 18, to the end of October 31, 1911, the last day for which an ob- 
servation equation is written in that year, — r, for any day is computed as for 
April 18; that is, the first estimate of the run-off is always 7 < ,+i? a 7- J +i2,r,+iJ 4 r 4 + 
Rtft+Rtft. The first estimate of —r t is [(/,+i22r J +JK,r,+E4r«+i2 4 r,+jR,r,) + 
(Estimated Ei) — (Observed rainfall)]. With this value, the first estimate of 
+R<ri is obtainable, which added to the first estimate of the run-off, gives the 
second estimate. If this second estimate of the run-off now fails to change the 
first estimate of — r,, the computation is carried forward to the next day. 
If the first estimate of the -\-R x rt for any day differs from zero, this will change 
the first estimate of the run-off, 7 e +jR 2 r a +J?,r, . . . R t r t , for that day by the 
amount -\-RiTl This, in turn will change the first estimate of — r, by the same 
amount. Using this second estimate of — r x , a second estimate of -\-R x r x may be 
obtained. If this agree with the first estimate of -\-R x ri the computation may 
proceed to the next day. If it differ from the first estimate of +R x r x , the cycle 
must be repeated, and this repetition must continue until the nth estimate of — r, 
is the same as the (n — l)th estimate of it. Note that, in this particular case, 
since J?i = 0.01, the first estimate of — r x will have to be numerically greater than 50 
in order to make a second estimate of it necessary. Thus, a second estimate is 
rarely necessary (note the range in value of — r x , in Table 37), and the computation 
proceeds more rapidly than might be supposed from the above explanation. 
It should be apparent that the estimated run-off, beginning with an approxi- 
mation on April 2, rapidly converges toward the true run-off; that is, the true 
run-off in so far as the assumed law of run-off and the assumed constants make 
possible the evaluation of the true run-off. The first date in 1911 for which an 
observation equation is written is May 2. By starting the computation of r x , r a , 
r t , . . . r e one month earlier, the convergence is approximately complete by May 2. 
Careful study will show that the convergence is not complete on April 18, as at 
first might be supposed. 
If the proper conception of the run-off terms, I e -\-R x r x -{-R,r t + . . . -\-R t r», 
has been obtained, it should be clear that they represent the flow of a composite river 
emptying into the lake. These terms represent not only the flow into the lake 
through all of the rivers except the St. Mary's River, but also that part of the flow 
which reaches the lake directly by underground travel. 
EXAMPLE OF OBSERVATION EQUATIONS FOR DETERMINATION OF EVAPORATION AND RUN-OFF 
The method of computing all of the quantities in equation (28) should be clear 
from preceding examples. As a sample of the observation equations, those for 
May 2 to 10, 1911, are shown in Table 38. In that table the unknowns E x , E lf 
Rt, Ri, . . . Rt shown at the tops of the columns in parentheses should be con- 
sidered as repeated down the columns. 
The coefficients of the unknowns may be verified as follows : The coefficient of 
Ei, e, from Table 24. The coefficients of R x , R 2 , R», . . . R«, viz, — r,, — r,, — r,, 
. . . r„ from Table 37. The absolute term, I, from Table 23. 
