100 A NEW METHOD OF ESTIMATING STREAM-FLOW 
The terms eE h e(:r^r— 2.4) \e 2 and I of equation (27) have already been 
denned. The first two terms are the same as the corresponding terms in Solutions 
V t and BBi. The absolute term, I, is the same as in all the V — and BB — solutions 
shown in Table 30, and is denned on page 9. 
The other terms in equation (27), viz, — r 1 R ] , — r 2 R 2 , — r s R 3 , . . . r e R s , repre- 
sent the variable part of the run-off into the lake in one day. As it is the intention 
at present to limit the attention to the wind term, the definitions of the run-off 
terms will be reserved for a later place. 1 
The analysis of the residuals of Solution U, is shown in Table 35, and of Solu- 
tion Ts in Table 36. The third column in these tables shows the number of resi- 
duals which occurred in the solution for the wind velocity shown in the second 
column, corresponding to values of L-^jTr— 2.4J in the first column. The alge- 
braic sum of all of the residuals corresponding to each wind velocity is shown in the 
fourth column. The mean residual is shown in the fifth column, and the probable 
error of the mean residual appears in the sixth column. This is computed from the 
relation r = ~7=, in which r is the probable error of the mean residual, r the prob- 
able error of a single observation for the solution (±20.5 for Sol. U 3 and =*= 16.4 for 
Sol. Ti, in units of 0.001 foot), and n equals the number of residuals in the group. 
After the first trial grouping, the residuals were grouped in larger groups as 
shown in the second (and subsequent) trial groupings, in order to make the analysis 
more powerful. In order to avoid bias in deciding which residuals to include in 
the larger groups in the trial groupings higher than the first, the rules adopted were 
as follows: 
In the second trial grouping, the maximum number of residuals which shall constitute 
any one group shall not exceed the maximum number of residuals for any single wind 
velocity in the first trial grouping. 
In the third and fourth trial groupings, the maximum number of residuals which shall 
constitute any group shall not exceed the maximum number of residuals obtainable by 
combining any two adjacent groups in the next earlier trial grouping. 
As an illustration of the first rule, it was found that the maximum number of 
residuals for any single wind velocity in the first trial grouping in Table 35 was 23 
for a wind velocity of 9.2 m.p.h. Hence in the second trial grouping the number of 
residuals combined into a single group was not allowed to exceed 23. 
. In illustration of the second rule, it was found that the maximum number of 
residuals obtainable by combining any two adjacent groups of residuals in the 
second trial grouping was 45. Hence in the third trial grouping, the number of 
residuals which were combined into a single group were not allowed to exceed 45. 
The residuals from Solution U 3 , considered as a whole, tabulated with respect 
to wind velocity as an argument, showed but little departure from the laws of 
accidental error. On the other hand the following considerations tended to indicate 
that the evaporation curve, plotted with respect to wind velocities as abscissas, is 
concave upward — at least for wind velocities below 10 m.p.h. 
(a) All four groupings as shown in Table 35 showed a tendency for more large 
residuals than would occur if the errors were all in the accidental class. 
1 See page 104 . 
