44 EFFECTS OF WINDS AND OF 



if the strip under consideration lay along the line BE in figure 1, plate 4, on 

 the actual Lake Erie, the slope at point F on the strip is that fixed by 

 formula (56) if one uses for D not the depth at F but the mean depth 

 along the line CC", which is at right angles to BB through the point F. 



Under assumption No. 4, formula (59) applies to any strip parallel to the 

 wind direction on any actual lake provided one uses for each point on the 

 strip a depth D which is a mean depth along such a line as CC' at right 

 angles to the strip through the point. 



The values of 2 X , the summation indicated in (59), have been computed 

 for 8 wind directions for the Buffalo and Cleveland gages on Lake Erie and 

 for the Milwaukee, Harbor Beach, and Mackinaw gages on Lake Michigan- 

 Huron. The way in which formula (59) and assumption No. 4 have been 

 applied in these computations will be illustrated by selected portions of the 

 computations. 



EXAMPLE OF COMPUTATION OF Z. 



The whole area of Lake Erie, as shown on a chart of Lake Erie issued by 

 the United States Lake Survey, was divided up into strips parallel to CC' 

 on figure 1, plate 4, the axis of each strip being in the meridian. The widths 

 of the strips varied from 2,000 feet to 50,000 feet. The strips were wide 

 where the depths were large and comparatively regular, and were narrow in 

 shallow water and where the depths were irregular. The division lines 

 having been drawn on the chart, the separate depths were estimated from 

 the chart and entered in the computation illustrated by selected portions in 

 table No. 8. 



In table No. 8 the strip limits are given, in the first column, in thousands 

 of feet measured westward from the Buffalo gage. The first strip shown in 

 the table has for its eastern limit a meridian line which is 50,000 feet west 

 of the Buffalo gage, and for its western limit one which is 100,000 feet west 

 of the Buffalo gage. The approximate location of each of the strips may be 

 seen on figure 1 of plate 4, on which a scale of distances westward from the 

 Buffalo gage is shown. 



With the chart before one, and with dividers in hand, it is a matter of 

 easy routine to visually divide any strip across the lake into ten equal parts, 

 to estimate the mean depth in each part, and to enter it in the computation 

 as shown in the second to the eleventh columns of table No. 8. The mean 

 depth shown on each line in the twelfth column is the mean of the depths 

 entered in the next preceding ten columns on that line. 



The values of D 3 as shown in table No. 8 are rounded off to three sig- 

 nificant figures. That gives sufficient accuracy. 



Each L is a distance parallel to the wind under consideration an east 

 wind in this case. It is in each case the same as the width of the strip, which 

 is the difference between the two figures given in the first column as strip 

 limits. For convenience, L is given in thousands of feet in the table. 



The first group of strips shown in table No. 8 includes the deepest part of 



