4 A NEW METHOD OF ESTIMATING STREAM-FLOW 
of any one of the Great Lakes is measured by the change of elevation of the mean 
lake surface from day to day, since the area remains substantially constant. Each 
recording gage measures the change in elevation of the surface of the lake at the 
point at which the gage is located. At the beginning of this investigation the only 
feasible way to fix the elevation of the mean surface of the lake was to take it as 
equal to the arithmetic mean of the elevations at the one or more points on the lake 
at which first-class gages were operating. It soon became apparent, in the course of 
the investigation, that the most serious errors encountered were those due to the 
effects of winds and of barometric pressures in causing the recorded elevation of the 
lake surface at the gage to be different from that of the mean elevation of the whole 
lake surface. Accordingly, the first part of the investigation centered upon devising 
methods of evaluating the effects of winds and of barometric pressures upon the 
lake surface. This part of the investigation was published in 1922 by the Carnegie 
Institution as Publication No. 317, entitled Effects of Winds and of Barometric 
Pressures on the Great Lakes by John F. Hayford. For the complete exposition of 
that part of the investigation the reader is referred to that publication. 
As an outcome of that part of this investigation contained in Publication No. 
317, the mean elevation of the surface of the whole lake may be determined on any 
day by applying the known corrections for wind effects and barometric effects at 
any gage to the observed elevation for that gage. The proper weighted mean for 
the several gages may be taken and the few abnormal values may be detected and 
rejected by a definite criterion. In the place, then, of the former values of mean 
elevation of the whole lake surface, of a certain degree of accuracy, as an outcome of 
the part of this investigation contained in Publication No. 317, one has now avail- 
able values of a much higher degree of accuracy. It appeared at the time of 
publishing Publication No. 317 that from observations at Mackinaw alone the 
mean elevation of the whole of Lake Michigan- Huron on any day may possibly be 
determined with a probable error less than =±= 0.010 foot. (See page 113, Publication 
No. 317.) From the three stations, Milwaukee, Harbor Beach and Mackinaw 
together, it was estimated that this probable error may be reduced still more. It 
appeared that the change in elevation of the mean surface of the whole of Lake 
Michigan-Huron in one day might possibly be determined with a probable error less 
than =±=0.007 foot. This estimate, =±=0.007 foot, was made at the culmination of 
Publication No. 317. It was not later to be realized. It was found in the evapora- 
tion study, the results of which are hereinafter presented, that the accuracy 
actually achieved is as follows: from readings at the three gages Milwaukee, Harbor 
Beach and Mackinaw, corrected for wind and barometric effects, and taking account 
of evaporation, the change in elevation from one day to the next, of the mean surface 
of the whole of Lake Michigan-Huron, can be determined with a probable error of 
=±= 0.014 foot, that is, the actual mean elevation on any day can be determined with a 
probable error of (=±=0.014-*-\/2 = ) =±=0.010 foot. 
It was estimated early in this investigation that the evaporation from Lake 
Michigan-Huron in a single day, measured in depth of water taken off the whole 
surface of the lake, probably varied between limits which are approximately 0.000 
foot and 0.021 foot. With the new accuracy obtained by applying corrections for 
winds and barometric effects, it became possible to evaluate the change in content 
of the lake from day to day with sufficient accuracy to segregate that part of the 
outgo which is evaporation. This has been done on Lake Michigan-Huron, and 
with a lesser degree of success also on Lake Superior. 
