134 



ation as well as the cross section of the channel. In any case the 

 effect of the correction 8 upon the velocity head may be neglected, 



271. Substituting in equation (131) the expressions derived for the 

 several heads: 



hs+h,+bAv±Fv-+b{5~8o)+28Fv=0 



and, placing: 

 it becomes: 

 whence : 



hs+h,+bAv±Fv'=-R 

 b(8-8o)+28Fv-R=0 



(173) 



8=^{8o+R/b)Kl+2Fplb) (174) 



It should be observed that if v and Av were the correct velocity and 

 its increment for the given time, R would be zero. R is then the 

 residual head which 8 is to remove. 



272. The computation of 8 from equation (174) is most readily ex- 

 plained by applying it to the concrete example of the final adjustment 

 of the currents produced by the average tides in the section of the Cape 

 Cod Canal between stations 180+30 and 225, as of September-October 

 1932. In the computation, these tides are referred to a datum 10 feet 

 below mean sea level, so that all tidal elevations are positive. At 

 mean sea level, elevation 10, the hydraulic radius of the section has 

 been taken as 22.7 feet, and C at 90 (par. 249). From the cross sec- 

 tions of the canal, the value of r at elevation 14 is found to be 24.6 

 feet, and at elevation 6 to be 20.9 feet. The corresponding values of 

 (7 will be taken as 91 and 89, respectively. Since ^=4,470, the values 

 of F=Z/(7Vare: 



A diagram prepared from this data gives the value of F for any 

 value of y between 6 and 14. 



The coefficient b, for intervals of a half lunar hour, is, from equation 

 (167): 



6=0.0000167X4470 = 0.0746 



The lag of the primary current has been found to be 10° 12', and its 

 equation, with a lunar transit as the origin of time, to be (par. 249) : 



?;=5.27 sin (m2^+124°02') 



273. The computation of the residuals, R, may be made in the form 

 illustrated in the following tabulation. 



