80 A NEW METHOD OF ESTIMATING STREAM-FLOW 
The coefficient of E 2 , the product of e and f j™ — 2.6 V enters only rarely. 
By actual count there are 145 in the 755 equations given. As some of these are 
for combined dates, it may be said that the mean wind velocity over two-day 
periods exceeds 10.8 miles per hour for somewhat more than 20 per cent of the 
time (i| = 0.192). 
The absolute term, in units of 0.001 foot, is that part of the directly observed 
rise in the lake surface, which is — as far as has been possible in this investigation 
to render it so — due only to evaporation from the lake surface. The absolute 
term for any day represents the rise from the preceding day to the day to which 
the observation equation refers. 
If it had been possible to eliminate all of the influences except evaporation 
upon the change in elevation of the mean surface of the whole lake from each day 
to the one next following, the absolute terms would all be negative; that is, they 
would all be negative rises — or falls — of the lake surface from each day to the 
next following. The influences which were eliminated as far as possible were 
wind effects, barometric effects, inflow, outflow, rainfall on the lake surface, and 
the run-off into the lake, which last was taken as constant. There remain two 
principal influences which were not eliminated, and which are primarily responsible 
for the fact that the absolute terms are sometimes plus and sometimes minus 
instead of consistently minus. These two influences are the effects of seiches, 
and the effects of the variable part of the run-off into the lake. 
Seiche effects are largely accidental in character. They could probably not 
be eliminated by any process. Because of their accidental character, they prob- 
ably affect the final results but little. 
By assuming the run-off into the lake to be constant, an error of a systematic 
character is introduced into the equations, the effect of which is to increase the 
probable error of a single observation and of the derived values of E, and E 2 . If 
the constant part of the run-off into the lake is correctly evaluated, however, the 
actual error in the E x and E 2 will be small. The adopted value of 0.006 foot per 
day on the surface of Lake Michigan-Huron for the constant part of the run-off 
is probably very near the truth. The variable part of the run-off was not taken 
into account in this investigation because the only feasible way devised for evalu- 
ating it failed. This last will be discussed more fully later on. 
The residuals, or v's, represent the discrepancies between the observed rise 
of the mean lake surface corrected for wind and barometric effects, inflow, outflow, 
rainfall on the lake and run-off into the lake on the one hand (the / of equation (1)), 
and the computed fall of the lake surface due to evaporation, -j-eE^ey y — — 2.6 jE 2 , 
on the other hand. The closer the agreement between the observed facts and 
the approximate theory, the smaller the v's tend to be, and the more perfectly 
they approach the law of distribution of accidental errors. 
NORMAL EQUATIONS AND VALUES OF THE UNKNOWNS FROM THE TWO FINAL LEAST SQUARE 
SOLUTIONS FOR DETERMINING E l AND & 
In this investigation, made by methods stated on pages 6 and 7 of Publi- 
cation No. 317, a total of 24 least-square solutions was made in the investigation 
of the laws of evaporation proper, and of the run-off into the lake, but the 74 
