122 



S{cos H' sin iS-sin H' cos ,3) + (8/3x)(5V(7V)(sin^ ^ + 008^ ^)-0 



or: 



-S sin {W- 13) + (8/37r)B7CV=() (149) 



It is convenient to place: 



H''-^ = ct>^ir/2 (150) 



So that equations (148) and (149) become: 



S sin <^=aBlg (151) 



^cos</>=(8/3x)57CV (152) 



Whence 



BjCh^ (37r/8) {alg) cot (153) 



Ehminating B from equations (151) and (153): 



sin c/, tan 0= (37r/8) (a/gyC'r/S (154) 



And from equation (152): 



^^VStt/SCV^VcosI) (155) 



Or, from equation (151) : 



B=(g/a) S sin ct> (156) 



It may be seen from equations (151) and (152) that both sin </> and 

 cos 4> are intrinsically positive. is therefore an angle between 

 and 90°. 



245. Computation of and B. — Equation (154) may be written: 



(g/a)-^sm 4> tan <j, = ^3^-C^J^IS (157) 



Placing for convenience, 



P=^3^C-yJVs (158) 



= 1.0854 C^I7S 



This equation reduces to : 



{g/a)^lsm<l)tancf> = P/S (159) 



The numerical values of P and P/S are readily computed from 

 the amplitudes, *S', of the slope in the section during, the tidal cycle, 

 and the Chezy coefficient C and hydraulic radius, r, at mean tide. 



