BAROMETRIC PRESSURES ON THE GREAT LAKES 67 



one-day interval, so far as the one combined equation is concerned. It 

 retains all of the observed facts as to changes in barometric gradients and 

 uses them in the combined equation. 



As already stated, page 25, the combined observation equation was formed 

 by adding the two separate equations term by term. 



If the residuals were due entirely to accidental errors, only 18 equations per 

 thousand would have residuals larger than the adopted suspicion limit, 3.5 

 times the probable error. Much less than 18 equations per thousand should, 

 if the residuals were due entirely to accidental errors, be subject to the com- 

 bination rule. For if all errors were accidental, only a few of the suspicious 

 residuals would be preceded or followed immediately by a residual of oppo- 

 site sign big enough to bring the combined residual within the suspicion 

 limit. 



In table No. 6 it is shown that the number of days of observation used in 

 each solution exceeded the number of equations from 6 per cent (at Mac- 

 kinaw) to 22 per cent (at Buffalo) . In a few cases two or more days were 

 used in one observation equation, because no record of the elevation of the 

 water surface was obtainable from the gage for one or more days. In each 

 such case an observation equation was ordinarily used covering the interval 

 during which the gage record was missing. After allowing for such cases, 

 without a definite count, it appears that the number of combinations made 

 under the above-stated rule for combining observation equations varied 

 from about 50 to about 200 per thousand. This is far in excess of the 

 number of such combinations which would occur if the residuals were entirely 

 due to accidental error. The external evidence supported the combinations, 

 of one or the other of the two kinds mentioned in connection with rejections, 

 as being justified by something peculiar to the one abnormal day. 



DISCREPANCIES BETWEEN PAIRS OF VALUES. 



Each least-square solution gives two values for C w and two values for C n , 

 as noted on page 23. The discrepancy between the two values of each pair 

 is a test of the accuracy of the adopted value of C w or C n . Table No. 14 

 gives the discrepancies of that character arising from the final solutions for 

 barometric effects which gave the adopted barometric constants shown in 

 table No. 6, page 32. The equations (36) to (39), referred to in the first 

 column, are shown on page 23. 



According to the laws of probability, the discrepancy between two values 

 should be upon an average about three times the probable error of their mean. 

 In table No. 14, 5 of the 10 discrepancies are less than 10 per cent of the 

 larger of the two C"s for that station. The extreme case is the discrepancy 

 of 1.94 between the two values of C n for Cleveland, which is 29 per cent of 

 the adopted value of C n at that station. Table No. 14 indicates, therefore, 

 that the errors in the computed values of C w and C n are probably less than 3 

 per cent of the larger of said values at each station. 



