143 



And in a section of channel so short that the change in slope in 

 the section is negligible : 



by/bx=hJl={H^/l) cos {imt + H°) + (H2/I) cos (sa^ 

 =/i cos (m,t+H,°)^l2 cos (s2^+-?:^2°) + - • ' 



(178) 



289. The slopes, 7i, I2, etc., in this equation quite evidently approach 

 definite limits as the length, I, of the section is reduced. 



Substituting in equation (177) and integrating: 



v=-g \ (dy/dx)dt 

 = -{I,glm,) sin {m,t+H,°)-{hgls2) sin {s^t+H^'')— ■ • + K (179) 



The constant of integration, K, is readily interpreted as an adven- 

 titious constant current through the channel, apart from the currents 

 due to tidal fluctuations, and may be disregarded. 



If then the flow in a tidal channel is essentially frictionless, the 

 velocity of the current at any point in the channel is the resultant of 

 component velocities with the speeds of the tidal components. 



290. The inference should not be drawn from equation (179) that 

 the amplitudes of the components of the velocity are proportional to 

 the ratios of the amplitudes of the tidal components to their respective 

 speeds ; for the component heads and slopes, from which the velocities 

 are derived, are determined by the changes in the amplitudes and 

 phases of the tidal components at successive points along the channel, 

 and not by the magnitude of these amplitudes. 



COMPONENT CURRENTS 



291. As shown in paragraph 289, when the tidal flow is essentially 

 frictionless the current may be resolved into component currents, 

 fluctuating at the same speeds as those of the tidal com^ponents. If 

 the flow is not frictionless, each fluctuation of a tide of the semidiurnal 

 type has been shown to produce a primary current with a sim.ple 

 harmonic fluctuation, to which minor corrections are to be applied. 

 The am,plitude of the primary current must vary from, day to day 

 with the variation in the amplitude of the resultant tide. The primary 

 current should then be resolvable into components of fixed amplitudes, 

 with the speeds of the tidal components. The corrections to the pri- 

 mary current, and its distortions due to overtides, are repeated almost 

 identically in each successive tidal fluctuation, and are then reproduced 

 by overcnrrents whose speeds are integral multiples of the speeds of the 

 principal tidal component. 



