BAROMETRIC PRESSURES ON THE GREAT LAKES 39 



the hourly barometric effects, and thence the daily barometric effects, by 

 step (1) involves a smoothing out of the discrepancies between the values of 

 BUO, B w i, . . . B n2 , B n3 as derived from the least-square solution, and 

 therefore does not agree exactly with the computations made from formulae 

 (46) to (50) . The rule stated in the preceding paragraph was adopted, as a 

 result of experience, as probably giving the best balance between extreme 

 accuracy, on the one hand, and large expenditure of time in computation, 

 on the other hand. 



THEORETICAL BASIS FOR WIND OBSERVATION EQUATIONS. 



The formula for wind effect which has been adopted as the basis for the 

 observation equations is as follows : 



W is the effect, at a given time, of the wind, at a given gage station, in 

 elevating the water surface at that station above the mean elevation of the 

 whole surface of the lake, h is the velocity of the wind at that station. 

 "2 X is a quantity appropriate to the station, for each wind direction, which 

 expresses the relation between the effect of a wind of a certain velocity, on 

 the one hand, and the depth of the lake at every point, the shape of the 

 bottom, the horizontal dimensions of the lake, and the shape of its shore, on 

 the other hand. 



A wind blowing across a lake drives the surface water to leeward at every 

 point on the surface at a rate dependent upon the wind velocity. This 

 surface water delivered toward the lee shore tends to raise the surface 

 elevation of that part of the lake. As soon as this action has established a 

 surface slope downward to windward, gravity tends to set up a current to 

 windward, which current extends to the full depth of the lake, from the sur- 

 face to the bottom. Said return current to windward is a function of the 

 surface slope, tending to be greater the greater the slope. When a steady 

 regime has been established for a wind of a certain direction and velocity, 

 the total volume of water per unit of time delivered to windward across any 

 line which may be drawn completely across the lake is necessarily equal to 

 the total volume of surface water delivered per unit of time to leeward 

 across that line. If it were otherwise, the surface elevations at some parts 

 of the lake would necessarily be changing and the regime would not be steady. 



Formula (51) expresses the wind effect after the steady regime has been 

 established for a wind of any given direction and velocity. 



The explanation of the theoretical basis of formula (51) is given in the 

 following successive steps: 



(1) For an assumed wind of constant direction and constant velocity, and 

 for a narrow strip of the lake parallel to the direction of the wind, the 

 relation at each point of the strip, during a steady regime, between the 



