A NEW EVAPORATION FORMULA 109 
method of computation of the estimated run-off for the first few days in Table 37 
is as follows: On April 2, 1911, the only known part of the run-off is the constant 
part, 6. Hence —r\ for that day= —2+1+6= +5, shown in column 15. This is 
an approximation to the true — r,, for April 2 in the sense that the variable pari of 
the run-off has been omitted because it is unknown. This approximate — /•,, for 
April 2, by definition, becomes — r s for April 3, and — r, for April 4, shown in the 
sixteenth and seventeenth columns, respectively, Table 37, opposite April 3 and 4. 
On April 3, the product of — (— ft) and R 2 , viz, +R,r t = 0.07X — 5 = —0.35 = 
— 0.00035 foot, is that part of the change in storage on April 2 which is assumed to be 
delivered to the lake on April 3. As this is less than 0.5 of 1/1000 foot, the unit used 
in the equations, it is entered as zero in the -\-R 2 r 2 column on April 3. Thus far on 
April 3 our total knowledge of the run-off is given by the sum of the constant part, 6, 
and that part of the variable part, +jR a r s = 0. The sum of these two is 6, which, 
added to the evaporation and rainfall for that day, +4 — 2, gives 8 as the estimated 
value of — r, for April 3, which is an approximation in the sense that that part of 
the variable part of the run-off for April 3 represented by the R 3 r 3 +.R 4 7- 4 +R6?" 6 + 
ReTs terms can not be known, and the Rir x part can not be known at the beginning 
of April 3 because r, is not known at that time. With the estimated value of 
— r,= +8, we now obtain the product -\-R 1 r l = (0.01) ( — 8) for April 3. This is zero 
in the units used and is so recorded in the Rir x column for April 3. Since the 
addition of this quantity has not changed the first estimate of the run-off for April 
3, +6, the value of — n for that date, +8, stands as the best obtainable. This 
becomes, by definition, — r 2 for April 4, — r, for April 5 and combines with r, for 
April 4 to give — r, for April 6 which is in units 10-times as large, or +1.3. 
On April 4 the first estimate obtainable for the run-off is I e +-R*r«+jBi»*« or 
6 + (0.07)(-8) + (0.17)(-5) or +4, and of -r„ +4+3-17= -10. With this 
first estimate, we compute the quantity Rir 1 = (0.01)(10) =0 in the units used. 
This now makes the second estimate of the run-off +6 + — 1 — 1=4, still. Hence 
the first estimate of —i\ remains unchanged at —10. This becomes — r 2 for April 
5, — r, for April 6 and added to +8 and divided by 10 gives the — r 4 = —0.2 of 
April 7. 
On April 5 the first estimate obtainable of the run-off is 7 c +i? 2 r 2 +R 3 r 3 , or 6 
+ (0.07)(10) + (0.17)(-8), or +6, and of -r„ +6+3-40= -31. With this 
first estimate, an approximate -\-R i r 1 can be computed, viz, (0.01) (+31) =0 in 
the units used. This now makes the second estimate of the run-off +6 + + 1 — 1 = 
+6, still. Hence the first estimate of — r x remains unchanged at —31. This 
becomes, by definition, — r 2 for April 6, — r 8 for April 7; added to —10 and divided 
by 10 gives — r 4 of April 8, viz, —4.1; and added to —10+8+5 and divided by 
10 gives — r 5 of April 10, viz, —2.8. 
On April 6 the first estimate obtainable of the run-off is 7 e +jR 2 r s +i2 8 r»+ 
R<r<, or 6 + (0.07)(31) + (0.17)(10) + (0.80)(-l), or 6+2+2-l = +9, and of -r„ 
+ 9 + 4 — 43= —30. With this first estimate, an approximate -\-Rii\ can be com- 
puted, viz, (0.01)(+30) =0, in the units used. This now makes the second esti- 
mate of the run-off +6+0+2+2 — 1 = +9, still. Hence the first estimate of — r, 
remains unchanged at —30. This is written into the table, according to definition, 
as — r's for succeeding dates. 
The process indicated is carried forward day by day. On April 10 it becomes 
possible to compute all —r's to — r 6 inclusive, and on April 18 all of the —r's can 
be computed. Beginning with April 18, the sixteenth day after starting the 
