BAROMETRIC PRESSURES ON THE GREAT LAKES 41 



sideration. The exact relation between these various arrows is not claimed 

 to be known, and for the purpose of this investigation it is not necessary to 

 know it. The illustration figure 3 is meant merely to show the general 

 conception. 



As the wind delivers water toward the lee shore, as an east wind would 

 deliver water along the line BB, figure 1, plate 4, on Lake Erie toward the 

 western shore of the lake, it raises the elevation of the water surface on that 

 leeward portion of the lake. In due time, if the wind remains constant in 

 velocity and direction, a surface slope will be established everywhere on the 

 strip, along BB, downward to windward such that the return current to 

 windward, set up by the action of gravity, will deliver the water to windward 

 at the same rate, Q, that the wind delivers it to leeward. During the con- 

 tinuance of this steady regime, after it is once established, the elevation of 

 the water surface at every part of the strip will remain fixed, the volume of 

 water delivered by the wind past each point of the strip per unit of time 

 to leeward will be Q, and the volume delivered per unit of time past any 

 point by the return gravity current to windward will also be Q. 



The return current is illustrated by figure 4, plate 4. As this current is 

 produced by gravity, the Chezy formula (52) expresses the relation neces- 

 sarily existing between the velocity and the slope. This return current, 

 being produced by gravity, extends throughout the depth, and with suf- 

 ficient accuracy for the present purpose may be considered as being the same 

 at all depths as shown in the illustration. 



As the wind current indicated in figure 3, plate 4, to leeward and the 

 return gravity current to windward, figure 4, exist at the same time, the 

 actual velocities of the water at various depths are properly represented by 

 figure 5, in which each arrow is the algebraic sum of the two corresponding 

 arrows in figures 3 and 4. During the steady regime under consideration 

 the sum of the arrows in figure 3 is the same as the sum of the arrows in 

 figure 4, and in figure 5 the sum of the arrows which point to the left is the 

 same as the sum of the arrows which point to the right. According to these 

 figures, the net delivery of water past the point is zero, the separate volumes 

 delivered per unit of time in opposite directions each being Q. 



As the Chezy formula (52) holds for the return current produced by 

 gravity, the following relations (53) to (59) are true during the continuance 

 of the steady regime: 



At each point of the strip of unit width under consideration, 



R = D = depth of water at that point of the strip. (53) 



This follows from the fact that the only part of the perimeter of the cross- 

 section of the stream under consideration which encounters resistance at a 

 solid boundary is the bottom. The two sides of the stream are in contact 

 with water of adjacent strips. The strip being of unit width and the wetted 

 perimeter unity, the area of the cross-section of the stream flowing along the 

 strip is numerically the same as the depth. 



