110 



EFFECTS OF WINDS AND OF 



evident, throughout this investigation, that the observations at any one gage, 

 considered as an attempt to secure the mean elevation of the whole lake 

 surface, are subject to systematic errors which are not small in comparison 

 with the accidental errors, and that, therefore, the computed probable 

 error of a single observed elevation, such a probable error as those shown in 

 table No. 28, is unreliable as an indication of relative accuracy at different 

 stations. Among the systematic errors to which the observed elevations 

 are subject are the barometric effects and wind effects. It is not at all 

 certain that these and other systematic errors would be more thoroughly 

 eliminated from the mean observed elevations by using weights based on 

 the probable errors than by using equal weights at the different stations. 

 In fact, which procedure would give the best elimination depends largely 

 upon the relations to each other of the systematic errors at the various sta- 

 tions as well as upon the accidental errors. Incidentally, it is interesting 

 to note here that evidence developed very late in this investigation as to the 

 barometric effects on Lake Michigan-Huron shows clearly that the alge- 

 braic sum of the barometric effects at the three stations Milwaukee, Harbor 

 Beach, and Mackinaw tends to be nearly zero on each day.* Therefore, 

 it is clear that equal weights assigned to the three observed elevations on 

 any day at these stations tends to give a much better elimination of the 

 principal systematic error that from barometric effects than if unequal 

 weights were used. 



TABLE No. 28. Probable error of a single daily elevation of the water surface computed 



from the residuals shown in tables 19 to 28. 



On the other hand, when one tests the corrected elevations in various 

 ways, little evidence is found of systematic errors. The errors in these 

 values seem to be mainly of an accidental character. Hence, for corrected 

 elevations each station has been given a weight inversely proportional to the 

 square of its probable error as shown in table No. 28. Unit weight was 

 assigned to Buffalo, where the probable error is 0.036 foot. The weights 

 assigned on this basis for other stations are stated on pages 100, 104. 



* Consult table No. 7, page 33, and note that the algebraic sum of the three values of 

 C w for Milwaukee, Harbor Beach, and Mackinaw, namely, 4.97, +6.94, and 2.54, is 

 only 0.57. Similarly, note that the algebraic sum of the three values of C n is only +3.62. 

 The smaller these two sums the smaller the sum of the barometric effects at the stations 

 tends to be on each day. 



