BAROMETRIC PRESSURES ON THE GREAT LAKES 77 



At Cleveland, six least-square solutions for wind effects were made, in 

 which the assumed values of the exponent were 2.0, 2.2, 2.3, and 2.4. Com- 

 parisons were made between these solutions, in pairs, to determine as far as 

 feasible the effect of the assumed change of exponent between the two 

 solutions of each pair. The change of exponent from 2.0 to 2.2 reduced Zv 8 

 by 3 per cent, and other kinds of internal evidence showed clearly that 2.2 

 is nearer the truth than 2.0. The expression 2z; 2 is used to indicate the sum 

 of the squares of the residuals in a solution. It is evident that the closer 

 the approach to the truth in all assumptions the smaller will be Sv 2 . The 

 change of the assumed exponent from 2.2 to 2.3 reduced Si> 2 only 1 per 

 cent, and from 2.3 to 2.4 reduced it again only 1 per cent. In these last 

 two steps the other evidence than that given by 2i> 2 was not clear. 



At Buffalo, seven least-square solutions for wind effects were made, in 

 which the assumed values of the exponent were 2.0, 2.3, 2.4, and 2.5. There 

 was decisive evidence that the change from 2.0 to 2.3 was an approach to the 

 truth. But among the six of the seven solutions which were based on the 

 assumed values 2.3, 2.4, and 2.5 for the exponent, the apparent change in Sv 2 

 due to change of exponent over this range of 0.2 was only 1 per cent or less. 

 Other evidence was not clear in favor of any choice between 2.4 and 2.5. 



Hence, the conclusions reached from a consideration of the evidence as a 

 whole are (a) that the most probable value of the exponent is 2.4, (6) that 

 the true value may be as low as 2.3 or as high as 2.5, and (c) that the error 

 in the assumed value 2.4 probably produces a very small otherwise-avoidable 

 error in the final computed daily wind effects, provided the one value of the 

 exponent is carried consistently throughout the whole computation. 



The fact that a change of 0.1 in the exponent either way from 2.4 pro- 

 duces a change of only 1 per cent or less in S^ 2 is the main basis for conclusion 

 (c) above, which is applicable primarily to daily wind effects. Such a daily 

 effect is the mean of 24 hourly effects, which usually involve winds of a con- 

 siderable range of velocity and usually a change of direction. It is conceded 

 that the computed wind effect for the hour of maximum velocity may be 

 appreciably in error on account of the error in the exponent, but the other 

 values for lighter winds during the day will tend normally to have much less 

 error from this cause, and for the extremely light winds the error tends to be 

 reversed in sign. The net result is a daily wind effect based on 24 hourly 

 values having little error due to the cause in question. 



The adopted exponent, 2.4, depends on deductions from observations, 

 not primarily on theory, and is believed to be as good an approximation to 

 the truth as is needed for the prime purpose of this investigation. 



The evidence as set forth on pages 72-77, mainly from the four final least- 

 square solutions for wind effects, is abundantly corroborated by the many 

 earlier least-square solutions made in series on the general plan indicated 

 on pages 6-8. There were in all 29 least-square solutions devoted en- 

 tirely to a study of wind effects, and 37 other solutions in which the wind 

 effects were studied in conjunction with other matters. 



