24 A NEW METHOD OF ESTIMATING STREAM-FLOW 
veloped in this investigation (see Publication No. 317) the wind effect varies 
inversely as the cube of the depth. 
A nodal line on the lake surface is a line which remains unchanged in elevation 
for a wind of any velocity, but constant direction. All parts of the lake surface to 
leeward of the nodal line are raised, and all parts to windward are lowered. (For 
full discussion see Publication No. 317, pages 48-54.) 
The center of gravity of the area of Lake Superior, shown on Plate 3, is 
359,510 feet north and 85,200 feet west of the Marquette gage. 
The unit of time used in the observation equation, (1), is one day. To com- 
pute the wind effect at a gage for a day requires the computation of the effect for 
each hour for each wind direction by equation (18) by the proper substitution 
therein of h and Sx for that hour and wind direction, respectively, and the total 
effect for the 24 hours divided by 24 to get the mean effect for the day. To thus 
compute the daily wind effect at each gage for each day of the 1,500-odd days 
of observation at each gage used in this investigation would be an unnecessarily 
slow process. As a device for saving time in the computations of daily wind effects, 
w 
a table was constructed for each gage, giving the values of ~j in terms of the two 
arguments h and 2%- With the Weather Bureau records of wind velocity and 
direction and such a table before one, it is a simple matter to take out the tabular 
values, one for each hour, to the nearest 0.001 foot, and enter them into the compu- 
tations. (This computation becomes further simplified by virtue of the fact that 
for the gages under consideration a large percentage of the winds are too feeble to 
produce an effect as much as 0.001 foot.) The total of these values for any day 
gives the daily wind effects at the gage in question for that day. 
In concluding these statements on the method of computing I x for use in 
equation (1), it may again be convenient to note its definition (page 9). For Lake 
Superior the only available, reliable gage being at Marquette, and the daily wind 
effects being so small as to be neglected, 7i for any day is the mean observed 
elevation at Marquette corrected for barometric effects on the current day minus 
the mean observed elevation at Marquette corrected for barometric effects on the 
preceding day. In obtaining 7 X for any day for Lake Michigan-Huron, the pro- 
cedure is as follows: (a) the observed elevation at each of the gages Milwaukee, 
Harbor-Beach and Mackinaw is corrected for wind and barometric effects in the 
manner described in the preceding pages; (6) the weights 1.9, 2.9 and 5.1 are 
assigned to the elevations corrected as stated in (a) at the three stations there 
mentioned, respectively, and the weighted mean elevation obtained of the whole 
lake surface corrected for winds and barometric effects; (c) the difference current 
minus preceding is taken of the values obtained in (b) as the Ii for Lake Michigan- 
Huron for the current day. 
The method of computation of i\ will be made specific later by a numerical 
illustration. Note that a complete illustration of steps (a) and (b) in the computa- 
tion of 7i for Lake Michigan-Huron is given in Publication No. 317, of which the 
statements in these pages is an abstract, and is here included merely for convenience 
in reference and to make the publication a self-contained entity. 
The weights assigned to the elevations corrected for wind and barometric 
effects, namely 1.9, 2.9 and 5.1, at the three gages Milwaukee, Harbor Beach and 
Mackinaw, respectively, were obtained by dividing the square of the probable 
error of the observed elevation at the gage by the square of the probable error of 
