192 



371. Placing for brevity: 



Mo/M=m (281) 



aU/Mo=I (282) 

 equations (279) and (280) may be written: 



(B/m) sin /3=5o sin /So + S/yl sin a (283; 



{B/m) cos ^=Bo cos /3o + S/A cos a. (284) 



In equations (283) and (284), m is the ratio of the areas, at mean 

 tide, of the cross section at the middle velocity station to that at the 

 given station, A sin a and A cos a are the coordinate amplitudes of the 

 tides at the intervening storage stations, and the values of I are deter- 

 mined from the surface- areas, U, at mean tide, between the successive 

 intervening velocity stations and the speed, a, of the primary tidal 

 fluctuations, whose usual value is 0.0001405 radians per second. 



372. If the canal has a uniform width and cross section, and con- 

 sequently a uniform mean depth, D, at mean tide; 771 = 1, and 

 I—azAx/AIo=aAx/D. If, further, all of the sections are of the same 

 length, the value of / is the same for all. 



The computations indicated in equations (283) and (284) establish 

 the first values of the amplitudes B, and the initial phases, /3, of the 

 currents in the subsections of the canal, 



373. Heads corresponding to computed velocities in subsections. — The 

 relations between the amplitude, B, of the primary current in a short 

 section of channel of length, I; its angular lag, cj), and the amplitude, aS*, 

 of the slope in the section, have been developed in chapter V. From 

 equation (153) in that chapter: 



tan ct>= (37r/8) (a/g)C'rlB. (285) 



It is convenient to place: 



p={3Tl8){a/g)C'r (286) 



in which a is the speed of the fluctuation, in radians per second, 

 ^=32.16, and C and r the Chezy coefficient and hydraulic radius in 

 the section at mean tide. 



If the speed of the primary tidal and current fluctuations has its 

 usual value of 0.0001405 radians per second, equation (286) becomes: 



:P = 0.000,005,148 C'r. (287) 



The logarithm of the coefficient is 4.71 160 — 10. 

 From equations (285) and (286): 



tan <i>^plB. (288) 



