BAROMETRIC PRESSURES ON THE GREAT LAKES 13 



must now, under assumption No. 1, substitute other isobars coinciding as 

 nearly with the actual isobars as is consistent with the condition that they 

 must everywhere over Lake Erie be straight and uniformly spaced. The 

 corresponding contours on the lake surface, for the conditions of equilibrium, 

 will be straight and uniformly spaced as indicated in the lower part of plate 1. 



The total amount of water in Lake Erie is not affected by the barometric 

 pressure, or its distribution. The effect of the greater barometric pressure 

 on the southwestern part of the lake as compared with that on the north- 

 eastern part of the lake is to subtract water from the southwestern part and 

 add it to the northeastern part. Some line on the surface of the water, such 

 as that marked as the nodal line on the lower part of Plate 1, is not changed 

 in elevation. What is the location of that line? The direction of the nodal 

 line is evidently parallel to the contours. It remains to fix one point on the 

 nodal line. 



Consider an elementary portion of the lake surface as shown on the lower 

 sketch on plate 1 of which the two dimensions are 8L at right angles to the 

 contours and SW parallel to the contours, of which the area is 8LdW = 8A 

 and of which the distance from the nodal line is L. Let the slope of the 

 water surface be called S. 



The volume of water which had been added at this area by the barometric 

 influence is D ept h o f added water ( area ) =SL8L8W = SL8A 



SL is the depth of water added at the particular area. 

 The total amount of water added to the northeastward of the nodal line 

 is the integral over that portion of lake of these elementary volumes, namely: 



JSL8L8W = JSL8A = S JL8A (5) 



S may be placed outside the integral sign, as it is the slope which has been 

 assumed to be constant. 



Consider the portion of the lake which lies to the southwestward of the 

 nodal line, from every portion of which water is subtracted by the barometric 

 influence. Use the same notation as before, but let L be counted as negative 

 when measured to the southwestward from the nodal line. Then for this 

 portion of the lake the total amount of water subtracted is the same integral 



as before, namely, f 



S I L8A (6) 



in which, however, all values of L are negative and the integral is negative. 



As the total amount of water in the lake has not been changed, the sum of 



integrals (5) and (6) must be zero that is, the amount of water added on one 



side of the nodal line must equal that subtracted from the other side. In 



other words the integral S I L8A over the whole of the lake surface must be 

 zero, the distance L being reckoned from the nodal line as indicated. Hence, 

 S being a constant, / L8A over the whole area of the lake must be zero. 



