56 EFFECTS OF WINDS AND OF 



The form of each observation equation is as follows: 



/7? 2 - 4 \ 



- 



K 





= - (66) 



/i is the wind velocity, in miles per hour, at the station to which the equation 

 refers, ending at the hour specified by the subscript. 



The subscript c refers to the current hour the hour by which the equa- 

 tion is designated. The subscript p refers to the preceding hour. The 

 subscript c+1 refers to the hour following the current hour. 



C p and C a are unknown constants to be derived from the observations by 

 means of the least-square solution. 



L is the elevation of the water surface at the gage at the current hour 

 minus the elevation of the water surface at the gage at the preceding hour, 

 the elevations being first corrected for any known effects for which it is 

 feasible to apply reliable corrections. The only such correction applied in 

 this investigation was the correction for hourly barometric effects, computed 

 as indicated on pages 32-36. 



The symbol 2* stands for the appropriate value from table No. 10 for the 

 gage station under consideration Buffalo gage, Cleveland gage, etc. and 

 for the wind direction at that station for the hour specified by the subscript 



. 



of the term ( - ) into which this particular S x is multiplied. 

 VlOO/ 



Compare (66) with (51) on page 39. It appears that if C p , an unknown 

 constant to be determined, is considered to be the C x of equation (51), then 



Cp in (66) is the effect of the wind at the preceding hour in elevat- 



1007 p 



ing the surface of the water at the gage. Similarly, ( )(2 Z )C P , on the 



\1007c 



same supposition, is the effect of the wind at the current hour in elevating 

 the surface of the water at the gage. The difference shown as the first of 

 three terms in the first member of the observation equation (66), namely, 



r//)2-4\ / J,2 



( ) (Sx)-( ) (Sx)|C, 



lAioo/v Vioo/y 'J 



is the computed fall in the water surface from the preceding to the current 

 hour on the supposition that C p is the C x of equation (51). 



One modification should be made of the statement in the preceding 

 paragraph, in which it is implicitly assumed that there is no lag in the re- 

 sponse of the water to a change of wind. It should be noted that h, as 

 defined just below equation (66), is the wind velocity at the hour ending at 

 the time specified. If, for example, the hour specified is 10 a.m., the velocity 

 h is the velocity for the hour from 9 a.m. to 10 a.m. This velocity is in 

 fact ordinarily obtained by counting up the number of miles of wind, as 

 shown on an automatic record from an anemometer, that passed the record- 



