20 EFFECTS OF WINDS AND OF 



Let the corresponding notation with reference to barometric gradients 

 along the meridian be used. That is, let b m , b ni , b nt , and b m be the amounts 

 by which (5-7) decreases in each of the several 12-hour periods which were 

 specified in connection with b m , b wi , b W2 , and b W3 , respectively; and let B n<> , 

 B ni , B n2 , and B H3 have meanings corresponding to those already specified for 

 B wa , B WI , B WI , and B W3 , respectively. By the same reasoning which was used 

 in connection with barometric gradients along parallels, it may be shown that 

 the decrease, due to change in barometric gradients along meridians, in the 

 mean elevation of the current day over the mean elevation of the preceding 



day will be b n .B na +b ni B ni +b n2 B n2 +b n3 B nt (29) 



On the assumptions thus far stated, the form of each observation equation, 

 one for each day, is as follows: 



1> w w t +l>nB m +b^^+bMB m +b^ m +b ni B ni +b n nt +b nt B fu +I = V (30) 



In equation (30), I is the observed rise in the elevation of the water sur- 

 face at the gage station that is, the mean observed elevation for the current 

 day minus the mean observed elevation for the preceding day. The second 

 member of the equation is a residual, v, which is the discrepancy between 

 theory and observation for the particular day. The least-square solu- 

 tion serves to determine the most probable values for the unknowns B w , 

 B m . . . B m , B nt . These values are the ones which will make the sum 

 of the squares of the system of residuals, v, a minimum. 



Note that B ng , B m . . . B n B U3 have values in terms of C w and C n which 

 are tabulated in the third line of table No. 1 (page 21) as derived from equa- 

 tions (27), (21), (23), and (25). When these values of B m , B Wl . . . B w 

 B ni have been determined by the least-square solution, it will then be pos- 

 sible to compute C w and C n . 



LAG IN BAROMETRIC EFFECTS. 



Thus far, in fixing the form of the observation equations (30), it has been 

 assumed that there is no lag in the response of the water to barometric 

 changes. 



Let it be assumed that the response occurs with a lag which is to be deter- 

 mined from the observations. The observation equations will remain as 

 before, as shown in (30), but certain modifications, which are about to be 

 indicated, will be necessary in interpreting the equations and in interpreting 

 the derived values of B m , B Wl , . . . B w B nt . 



Let it be assumed for a moment that the response of the water surface to 

 barometric changes lags 4 hours behind such changes. Then the responses 

 of the water surface are properly represented on the same basis as before by 

 the lines marked " B 1} 4"Lag," " B z , 4 h Lag," "# 3 , 4 h Lag," and "B , 4 h Lag" 

 on plate 3. 



Consider in detail the first of these cases. It is assumed in this case that 

 between 8 a.m. and 8 p.m. of the preceding day (6-8) increased by an amount 



