16 EFFECTS OF WINDS AND OF 



and the (N-S gradient) was taken as 



(3-6) 



(15) 



(distance 3 to 6) 



The procedure outlined above involves assumption No. 2, which is stated 

 in the following paragraph : 



ASSUMPTION No. 2. 



It is assumed that the barometric gradients at any time on any lake along 

 parallels and meridians are the same as the barometric gradients derived, as 

 indicated above, from readings taken from the forecast maps at the selected 

 points 3, 4, 5, 6, 7, and 8, which lie on meridians and parallels through the 

 lakes. 



It is believed that this assumption is only a fairly good approximation, 

 that the barometric gradients over the shorter distances limited by the lake 

 surface vary through a larger range than the gradients over the longer dis- 

 tances between the reading points used on the forecast maps, and that the 

 variations of barometric gradients over the shorter and longer distances may 

 not be in step that is, one may in general be ahead of the other. It is be- 

 lieved, however, that the errors in assumption No. 2 are largely canceled out 

 in so far as the final values of the computed barometric effects are concerned. 

 This cancellation is believed to be affected in part by the device of introduc- 

 ing the proportionality factors P w and P n into the derivation of the observa- 

 tion equations as indicated later, and in part by the process of deducing, from 

 the results of the least-square computations, the lag of barometric effects 

 behind the changes in barometric gradients. 



For Lake Erie the expression for EI, the barometric effect at any point 1 

 on that lake, as shown in equation (11), may now be rewritten as follows by 

 means of expressions (12) and (13) : 



distance 6 to 8 / \ distance 5 to 7 



= + (6-8)12.+ (5-7)^ (16) 

 in which 



1.131/u, , p 1.13L ra , _, 



K w = - and K n = - (I/) 



distance 6 to 8 distance 5 to 7 



R w and R n are constants for any given point on Lake Erie. They differ for 

 different points but do not change with the lapse of time. 



PROPORTIONALITY FACTORS FOR BAROMETRIC EFFECTS. 



Equation (16) expressed the barometric effect on the elevation of the 

 water surface at any given point 1 on Lake Erie provided the water always 

 remained in equilibrium under the influence of gravity and barometric 

 pressure. The general conception thus far set forth, and including assump- 

 tion No. 1, is that the barometric pressures over Lake Erie are continually 



