50 EFFECTS OF WINDS AND OF 



Equation (64) identifies the value of S as shown in the fifth and sixth 



D s 



columns of the computation illustrated in table No. 9, at which the nodal 

 point lies. In table No. 9 the seventh column shows the value for each 

 strip of one of the products indicated in the numerators of the second 

 member of (64). The continuous summation of these products is shown in 

 the eighth column. This summation (eighth column) at the end of the 

 computation, covering the whole lake, is the numerator of the second 

 member of (64) . The denominator of the second member of (64) , the area 

 of the lake, is the sum of the separate areas of the strips as shown in the 

 fourth column of table No. 9. 



In the concrete case illustrated in table No. 9 the value of the numerator of 

 the second member of (64) was found to be 45,500,000. The area of the 

 lake was found from the computation to be 276,000. Hence, the value of 



_,L , , 45,500,000 1CK u ,. 



S at the nodal point was found to be - - : - = 165. By inspecting 



D 3 276,000 



the fifth and sixth columns of the computation illustrated in table No. 9 it 



was found that this value of S occurred at 1,027,000 feet west of the 



Buffalo gage and that therefore the nodal point and nodal line are in that 

 location, as indicated in figure 1, plate 4. 



The preceding derivation of certain formulae and of the location of the 

 nodal point has been written for a definite case, for an east wind over Lake 

 Erie, and for an initial point at the extreme eastern part of Lake Erie, where 

 the water will be lowest under the influence of an east wind. The demon- 

 stration and the corresponding methods of computation are of general 

 application, with certain obvious minor changes in statement, for any lake, 

 for any initial point on that lake, and for any wind direction. 



The computations have been made for eight wind directions for Lake 

 Erie and for Lake Michigan-Huron. 



As already noted (page 46), in making the computations for an east 

 wind over Lake Erie it was found that a special auxiliary computation of 

 the general character shown in table No. 8 must be made for Sandusky Bay. 

 In the corresponding auxiliary computation for Sandusky Bay of the charac- 

 ter illustrated by table No. 9 the computation was started with the value 



of S found at the entrance of the bay, at the first strip in the bay 

 D 3 



which is found to be cut off from the corresponding strip in the main lake by 

 intervening land. 



Many such auxiliary computations were found to be necessary for bays 

 cut off from the main lake by intervening land, so far as certain strips of 

 the character used in the computation are concerned. 



In what precedes, the expression "nodal point" has frequently been used, 

 having in mind a profile view of the water surface at right angles to the 



