BAROMETRIC PRESSURES ON THE GREAT LAKES 49 



strip. From (58) it is clear that the quantity CiS- - at each strip is the 



D 3 



mean elevation of the water surface of that strip (in the disturbed condition) 

 referred to the initial point as a zero. Hence, the product of the area of the 



strip into CiS for that strip is the amount of water in that strip which 

 D 3 



lies above the elevation of the initial point, and it is clear that the grand 

 summation indicated in (60) is the total amount of water in the lake which 

 is above the initial point during the disturbed condition. 



When the surface of the lake is undisturbed its whole surface is at one 

 elevation, and the total amount of water in the lake then lying above the 

 elevation of the initial point under consideration is 



(Hi) (area of lake) (61) 



A wind blowing the surface of the lake does not change the total content of 

 the lake. Hence, the total amount of water above the initial point (which 

 was the lowest point of the disturbed surface) must be the same in the dis- 

 turbed and the undisturbed condition. Hence, (60) and (61) are equal. 

 By placing them so in an equation and solving for Hi there is obtained 



S (area of strip) (CiS ) CiS (area of strip) (S ) 

 \ D 3 / \ D 3 / 



area of lake area of lake 



Equation (62) is an expression for the disturbance of elevation of the water 

 surface at the initial point referred to the nodal point, of which the location 

 is as yet unknown. Ci may be taken outside both summation signs as shown 

 because it is a constant which is the same for all strips. 



Equation (59) is an expression for the disturbance of elevation of any point 

 on the lake. Hence, applying this formula (59) to the initial point under 

 consideration, there is obtained 



Hi=C& (63) 



D 3 



in which the summation 2 extends from the nodal point to the initial 



D 3 



point. 



By placing the two expressions for Hi of (62) and (63) equal to each other 

 and dividing each side of the equation by C\ there is obtained, as an equation 

 applicable at the nodal point only, 



, L _ S (area of strip) ( S ) 

 '~^ = \ D 3 / 



2= \ D 3 / (64) 



D 3 



area of lake 



