14 EFFECTS OF WINDS AND OF 



The well-known condition which locates the so-called center of gravity of 

 an area is that the integral over the whole area / LdA is zero with L reck- 

 oned from any line through the center of gravity. Hence, it is clear that 

 the nodal line under assumption No. 1 of isobars which are straight and uni- 

 formly spaced is a line parallel to the isobars passing through the center of 

 gravity of the area of the lake surface. 



The position of the center of gravity of the area of Lake Erie is indicated 

 in the lower part of plate 1 by the circle labeled "C. G. of lake area." It is 

 634,000 feet west and 276,000 feet south of the Buffalo gage station. Its 

 latitude is 42 07' and its longitude is 81 13'. 



For all conditions of equilibrium under the influence of gravity and baro- 

 metric pressures, under the restrictions of assumption No. 1, the elevation of 

 the lake surface at the center of gravity remains unchanged. 



Let H c be this fixed elevation of the water surface at center of gravity 

 that is, fixed and unchangeable in so far as changes of barometric pressure 

 limited by assumption No. 1 are concerned. Let M c be the barometric 

 pressure on the surface of the water at the center of gravity. Then equation 

 (4) may be rewritten thus: 



E 1 = H 1 -H C =-(M 1 -M C }(1.1^ (7) 



in which EI is the barometric effect, under the specific conditions, on the 

 elevation of the water surface at the point 1. 



For convenience in computation it is now proposed to express Hi H c in 

 terms of slopes of the water surface measured along parallels and meridians 

 and to express M\ M C similarly in terms of barometric gradients measured, 

 along parallels and meridians. 



The barometric gradient between two points is the difference in barometric 

 pressures at the two points divided by the distance between the points. 



Let the barometric gradient along a parallel be called the "W-E gra- 

 dient," and let it be called positive when the barometric pressure increases 

 to the westward. Similarly, let the barometric gradient along a meridian 

 be called the "N-S gradient," and let it be called positive when the baro- 

 metric pressure increases to the northward. 



Let the co-ordinates of point 1 measured from the center of gravity of the 

 lake along parallels and meridians be L w along a parallel and L n along a 

 meridian as indicated on the lower part of plate 1. Let L w be considered 

 positive to the eastward and L n positive to the southward. 



Then, keeping in mind that under assumption No. 1 the isobars are 

 straight and equally spaced, 



Mi-M e = - (W-E gradient) (L w ) - (N-S gradient) (L n ) (8) 



Similarly, 



#! - # c = - (W-E slope) (L w ) - (N-S slope) (L n ) (9) 



in which the slope of the water surface along a parallel is called the "W-E 

 slope," positive when it is upward to the westward, and the slope of the 



