A NEW EVAPORATION FORMULA 73 
residuals were found to be associated, as a rule, with seiches produced by sudden 
wind effects or sudden changes in barometric gradient. Or they were found to 
exist during the passage of a well-defined storm center over the lake, during which 
the conditions probably depart widely from the approximate theory postulated 
in the study of wind and barometric effects. 
The rule adopted in combining two or more days of observation into a single 
observation equation covering the whole interval was as follows: 
Whenever any observation equation has a residual larger than 3.5 times the probable 
error of a single observation, and the residual for an equation immediately preceding or im- 
mediately following in time is of the opposite sign, the two observation equations shall be 
combined to form one equation, provided the residual for the new combined observation 
equation will be less than 3.5 times the probable error of a single observation. 
Such a procedure rejects the elevation of the water surface on one day and 
treats a two-day interval as the basis of observation instead of a one-day interval, 
so far as the one combined equation is concerned. It retains all of the observed 
facts as to changes in barometric gradients, wind effects, inflow, outflow, run-off 
and rainfall on the lake, and uses them in the combined equation. 
The combined equations were formed by adding the two or more separate 
equations term by term. 
In Solution F e , there was a total of 51 combined equations out of a possible 
849, which is at the rate of 60 per thousand. If the errors involved in the large 
residuals were all of the accidental character, only 18 residuals per thousand 
would be outside the limit, 3.5 times the probable error, and less than that number 
would occur immediately preceded or followed by a residual of the opposite sign, 
large enough to make the combined residual less than 3.5 times the probable 
error. The combinations, as in the case of the rejections, were justified on the 
basis of abnormalities not taken into account by the approximate theory used in 
the investigation. 
LIST OF OBSERVATION EQUATIONS OF THE FORM OF EQUATION (I), LAKE MICHIGAN-HURON 
The form of the observation equation used in the last least-square solution 
on each of the two Lakes, Michigan-Huron and Superior, has thus far been pre- 
sented in general terms, following which, specific examples taken from the Lake 
Michigan-Huron computations have been given, illustrating the methods of 
computation of the various quantities involved in it. 
The complete list of daily observation equations for the 28 months, July to 
October inclusive, 1909, and May to October inclusive, of 1910, 1911, 1912 and 
1913 is shown in Table 24. These are the observation equations from Solution V t , 
Lake Michigan-Huron. In each column, the symbols (Ei) and (E 2 ) should be 
considered as repeated down the column. 
The definitions of the quantities in the observation equations have already 
been given on pages 8 and 9. With the complete list of equations before one, 
it may be convenient to consider the known quantities further. 
The coefficient of Ei, e, the vapor-pressure potential (or sometimes called 
the "saturation deficit") is sometimes zero for individual stations near the Great 
Lakes, and even negative, but the mean e for the whole lake, as computed from 
the 10 stations around it, is rarely zero. Only two such cases are shown in the 
list of equations for Lake Michigan-Huron, viz, August 25, 1910, and July 24, 1913. 
