BAROMETRIC PRESSURES ON THE GREAT LAKES 57 



ing station between 9 a.m. and 10 a.m. In such a case the velocity applies 

 more strictly to 9.30 a.m. than to 10 a.m., or, in other words, it is the velocity 

 of one-half hour before the time specified. So the statement of the preceding 

 paragraph would apply strictly if the wind effect lagged one-half hour 

 behind each change in the wind. 



Compare the second of the three terms in the first member of observation 

 equation (66), namely, 



\(> 



LVioo 



with equation (51). It appears from the comparison that in the same 

 manner that the first term expresses the computed fall in the water surface 

 if the lag is one-half an hour, so the second term would properly express it if 

 instead of lag there is an anticipation of one-half an hour. An anticipation 

 means in this case merely that the water surface at the gage station changes 

 before the change in wind occurs at the Weather Bureau station at which 

 the wind is recorded, which may be a mile or even several miles away, and 

 not that the effect on the water preceded the cause which produced it. It is 

 desirable, also, if one tends to be skeptical of an anticipation in the sense 

 indicated in the formula, to consider that an effect at the gage may precede 

 the arrival of the wind change at the gage, since the wave of water piled up 

 by an approaching wind may outrun the progressive change in the wind. 



If, then, the least-square solution shows derived values of C p and C a which 

 are equal, the meaning is that the wind effect at the gage (a change of 

 elevation of water surface) is, upon an average, simultaneous with the change 

 in the wind at the Weather Bureau station, if C p is finite and C a zero the lag 

 is 0.5 hour, and if C p is zero and C a finite there is an anticipation of 0.5 

 hour. For intermediate cases the lag or anticipation has intermediate 

 values. 



Studies and various least-square solutions made in this investigation be- 

 fore the final form of the observation equations as shown in (66) was adopted 

 showed that the discoverable lag, if any, in the wind effects is probably very 

 small, a few minutes only. Hence, (66), based on the supposition that the 

 lag is very small, is deemed to be the best form for the observation 

 equations. 



If the computed fall of the water surface, represented by the first two 

 terms of the first member of equation (66), were exactly equal to and opposite 

 in sign to the observed rise, L, then the whole first member of (66) would be 

 zero, and the computed residual, v, in the second member would be zero. 

 This would be the case if both the theory and all the observations were 

 absolutely perfect. In the actual case, each v, a discrepancy between 

 computation and observation, is a residual for a particular hour between 

 theory and computation on the one hand and observation on the other. A 

 large group of such residuals from many observation equations furnishes a 

 measure of the accuracy of the theory and the computation based upon it. 



