BAROMETRIC PRESSURES ON THE GREAT LAKES 55 



much lighter grip upon or impact upon these roughnesses than it would have 

 if the roughnesses were stationary. The impact of the wind on the rear 

 surface of a moving wave is certainly rather light when the wave is moving 

 nearly as fast as the wind. During very high winds, say in excess of 40 

 miles per hour, the wind waves are high and expose a very rough surface to 

 the action of the wind, this roughness is traveling to leeward at a much 

 slower rate than the wind moves, and the drift of water to leeward is now 

 augmented by the large throw to leeward of the upper part of each wave as 

 it breaks. 



From such considerations as are indicated in the preceding few paragraphs 

 it appears that the wind exponent in such a formula as (51) is probably 2 

 (or more), but that the theory is so uncertain that it is best to derive the 

 exponent from observations rather than from theory. 



Accordingly, in early stages of the investigation of wind effects, a number 

 of least-square solutions were made in pairs, in which the two solutions of a 

 pair differed only or mainly in the exponent assigned to h, the wind velocity. 

 These solutions indicated that the more nearly the exponent was made to 

 approach to 2.4 from either side the closer was the agreement obtained be- 

 tween the computed results and the observed facts. In other words, more 

 accurately stating the matter, the sum of the squares of the residuals ap- 

 peared to be a minimum when the exponent 2.4 was used. A residual in 

 this statement is a discrepancy between the computed change of elevation 

 of the water surface at a gage during a given interval, on the one hand, and 

 the observed change of elevation recorded by the gage during that interval, 

 on the other hand. 



Hence, the exponent 2.4, derived thus from observations, was adopted for 

 the final formula for wind-effect investigations, as shown in (51), page 39. 



Some further information is given at an appropriate place later in this 

 publication, in the discussion of errors of computed wind effect, as to the 

 particular least-square solutions which served to establish 2.4 as the most 

 probable value of the exponent and as to the estimated accuracy of that 

 exponent. 



At this point attention is called especially to the fact that the value 2.4 

 is derived from observation rather than theory. It is the investigator's be- 

 lief, based on much study of the details of the investigation and some theo- 

 retical considerations, that an error of moderate amount in the adopted 

 exponent has but slight effect on the final outcome of the investigation 

 expressed in terms of daily corrections for wind effect, provided the expo- 

 nent, once adopted, is used consistently throughout the remainder of the 

 investigation. 



EXAMPLE OF OBSERVATION EQUATIONS FOR WIND EFFECTS. 



The least-square solutions for determining the wind effects are based 

 upon hourly observations of the water surface and upon formula (51), 

 shown on page 39. 



