BAROMETRIC PRESSURES ON THE GREAT LAKES 



63 



Each solution gives one value for C x = C p -\-C a . 



The probable error of each value of d from one solution is, with sufficient 

 accuracy for the present purpose, the square root of the sum of the squares 

 of the separate probable errors of C p and C a from that solution. 



Table No. 13 shows the four values of C x and their probable errors, the 

 weight assigned to each value of C x , the weighted mean and its probable 

 error, and the residuals of the four separate values from this weighted mean. 

 The assigned weights are inversely proportional to the squares of the probable 

 errors of C x , corresponding to the assumption that all errors in computed 

 values of C x are of the accidental character. Unit weight corresponds to a 

 probable error squared of 0.001. 



TABLE No. 13. 



Sum of weights 25.2. Weighted mean +0.088. Probable error of weighted mean=0.006. 



The value +0 . 088 . 006 for C x is adopted as the best that can be derived 

 from the present investigation. Accordingly, equation (51), expressing 

 the total effect of the wind upon the elevation of the water surface at any 

 gage, may now be written thus: 



Tf = +0.088 



(69) 



In (69), W is expressed in units of 0.01 foot, h is the wind velocity at the 

 gage as determined by observations at the nearest Weather Bureau station 

 which makes such observations. I> x is a quantity dependent upon the 

 location of the gage with reference to the lake, the shape of the lake, the 

 depth in every part of the lake, and the direction of the wind. The meaning 

 of S x and the manner of computing it are fully stated on pages 43-54. 





COMPUTATION OF WIND EFFECTS. 



The wind effects at each hour at any gage might be computed by the use 

 of formula (69) by making the proper substitutions for each hour of h and 

 S x . Such a substitution might be made systematically by a tabulation such 

 as the first six columns of table No. 11 on page 59, supplemented by the 

 last column of that table, which is headed W. Each value in that last 



