BAROMETRIC PRESSURES ON THE GREAT LAKES 17 



changing but always in such manner that the isobars over the lake are 

 straight and uniformly spaced, and that the fluctuations in the elevations of 

 different parts of the water surface take place at once in such a manner that 

 the water is always in equilibrium. 



It is obvious that the effects of friction and of inertia will tend to modify 

 the response of the water to changing barometric pressures. 



Friction will tend in general to reduce the range of fluctuation of water 

 surface and to produce a lag of the response behind the barometric changes 

 which produce it. 



Inertia will tend to produce an initial lag in the response of the water 

 surface to any change in the barometric pressure. But when the water has 

 once started from one part of the lake toward another, as the water surface 

 is approaching a new condition of equilibrium after some relatively sudden 

 change of barometric gradients, inertia will tend to cany the water past the 

 position of equilibrium and thereby to make the fluctuations of elevation of 

 the water surface greater than those corresponding to continuous equilibrium. 



If friction is relatively large, so that all motions of the water produced by 

 inertia, all free oscillations, are quickly damped out, the fluctuations in the 

 elevation of the water surface at any point would tend to be considerably 

 less in range than those which would be computed from equation (16). On 

 the other hand, if friction is relatively ineffective in damping out free oscilla- 

 tions of the water of the lake under the influence of inertia, and if the natural 

 periods of oscillation of the lake happen to bear certain relations to the 

 periods of change in the barometric gradients, the actual fluctuations in the 

 elevation of the water surface at a point might largely exceed those com- 

 puted from equation (16). 



Hence, aside from providing later for an assumed lag to be determined by 

 the observations themselves, through the least-square solution, it is also 

 advisable to introduce into equation (16) proportionality factors P w and P n , 

 to be determined from the observations. 



Hence, equation (16) is now rewritten thus for Lake Erie: 



E l = + (6-8) R W P W + (5-7) R n P n = + (6-8) C w + (5-7) C n (18) 



in which P w and P n are proportionality factors not necessarily assumed to 

 be equal, and ^ = R ^ ^ ^ = R ^ (19) 



It is desirable to note that the proportionality factors P w and P n , to be 

 derived from the observations, tend to take into account several effects: (1) 

 certain effects arising from friction and free oscillations just referred to; (2) 

 errors of certain kinds in assumption No. 2, to which attention has already 

 been called (on page 16). There may also be some tendency for the wave 

 produced by barometric influences to be modified by the configuration of 

 the shores and bottom as it progresses in such wise that the wave may be 

 accentuated or modified and given a larger, or possibly smaller, range at the 

 gage station than it otherwise would have. This will also be taken into 



