102 A NEW METHOD OF ESTIMATING STREAM-FLOW 
(b) The first, second and third trial groupings showed a tendency for + resi- 
duals between wind velocities of 7.5 to 10.4 m.p.h. This was shown also in the 
original detailed tabulation, which is not presented here for want of space. 
(c) From the original tabulation and the four trial groupings there appeared but 
little — and certainly only inconclusive — evidence of any systematic groupings of 
signs in the residuals, and therefore of curvature in the evaporation curve. 
(d) For wind velocities of 7.1 m.p.h. or lower ((tqt; —2.4 J = —0.7 or less) the 
first trial grouping showed negative mean v's in four out of five groups, and three 
out of four of these negative means are larger than their own p.e. and the one 
positive value is only | of its own p.e. This evidence was also confirmed by the 
second and third trial groupings. 
The above faint evidence of curvature for wind velocities below 10 m.p.h. led 
to the test of that idea in Solution BB, with the results already noted. One other 
consideration, obtained largely from other Solutions than U,, led to the belief that 
the evaporation curve is concave upward. This has already been noted in connec- 
tion with Solution V,, and was the fact that with the best determinable values of 
Ei and E t from the straight-line form of evaporation equation, the computed 
evaporation for zero winds came out negative. 
The distribution of the residuals with respect to wind velocity in Solution Tc, 
shown in Table 36, indicates that, within the allowable limits of accuracy of that 
solution, it is probably impossible to determine any departure of the wind exponent 
from unity. 
The proper conclusions from these studies, and as embodied in equation (22), 
appear to be, (a) that the evaporation in terms of e is a constant for wind velocities 
up to 10.8 m.p.h., and (b) that it is a linear function of the wind velocity for winds 
higher than that. 
RUN-OFF INTO THE LAKE 
The method of obtaining a first approximation to the constant part of the 
run-off into the lake was stated on pages 16 to 19, and it was stated in connection 
with the discussion of the results of Solution V s on pages 84 to 86 and on page 
80 that the only method devised for evaluating the variable part of the run-off 
into the lake failed. 
It is now proposed to show how it was attempted in this investigation to 
evaluate the variable part of the run-off into each of Lakes Michigan-Huron and 
Superior, and to show how the first approximate values of /. were revised by the 
least-square computations by successive trials until more correct values were 
obtained. 
VARIABLE PART OF RUN-OFF INTO LAKE MICHIGAN-HURON 
One form of observation equation used in the attempt to evaluate simultane- 
ously the evaporation from the lake surface and the run-off into the lake from the 
adjacent drainage area is equation (27), which is here repeated for convenience as 
equation (28), namely 
efl,+ 
too-)J 
E 1 -riR l -r i R i -nR i -r i Ri-r i R i -rtR i +I = v (28) 
This is the same as equation (1), page 8, except in two particulars, namely, 
(a) that the run-off terms — r-iJB,, — r t R t , . . . rjt t , expressing the variable part of 
