66 EFFECTS OF WINDS AND OF 



The number of rejections was much larger than one per thousand. As an 

 example, in solution L2, the final barometric solution for Buffalo, 13 days of 

 observation were rejected out of a total of 243 possible days in the months 

 used in the solution. This is at the rate of 54 observations per thousand. 

 In solution K2, the final barometric solution for Milwaukee, the rejections 

 were at the rate of 53 per thousand. 



The external evidence, obtained from a detailed study of the separate 

 cases, is strong in indicating that as a rule, in the rejected cases, the observed 

 change of elevation of the water surface on the day in question was abnormal 

 and due to the first oscillation of a new seiche affecting the gage record at the 

 station, or that it was abnormal because of extremely rapid and irregular 

 changes in the barometric gradients over the lake, which departed widely 

 from the conditions postulated in the approximate theory used in this in- 

 vestigation. Such rapid and irregular changes in barometric gradients were 

 associated ordinarily with the passage of a powerful storm center, a low- 

 pressure area, over the lake or near it. A discussion of the seiches will be 

 found in a later part of this publication. 



Throughout the investigation any observation which showed a residual 

 larger than 3.5 times the probable error of the observation was considered 

 as suspicious. In each such case a special study of the external evidence 

 was made. 



Early in the investigation it was found that such a residual was frequently 

 preceded or followed by a residual of the opposite sign, which was also of 

 considerable size. A study in detail of many such cases, using the evidence 

 which was external to the least-square solution, showed that very frequently 

 such a case was due to an abnormal effect, of one or the other of the two kinds 

 mentioned above in connection with rejections, which occurred mainly within 

 the limits of a single day. This effect made the observed elevation of the 

 water surface for that one day either abnormally high or abnormally low. 

 In the first case there was an apparently abnormal rise of the water surface 

 on one day, followed on the next day by an abnormal fall. In the second 

 case there was apparently an abnormal fall on one day, followed by an 

 abnormal rise on the next. After many such cases had been examined in 

 detail the following rule as to combining successive observation equations 

 was adopted and used thereafter throughout the investigation. 



RULE FOR COMBINING OBSERVATION EQUATIONS. 



Whenever any observation equation has a residual larger than 

 3.5 times the probable error of a single observation, and a residual 

 for an equation immediately preceding or immediately following in 

 time is of the opposite sign, the two observation equations shall be 

 combined to form one equation, provided the residual for the new 

 combined observation equation will be less than 3.5 times the 

 probable error of a single observation. 



Such a procedure rejects the observed elevation of the water surface on 

 one day and treats a two-day interval as the basis of observation instead of a 



