222 



the length increases, the successive approximations converge more 

 slowly, and after a certain length is reached, run completely wild. To 

 compute the primary tides and currents in a long closed canal, the 

 amplitudes and initial phases of the currents produced by tides of 

 successive amplitudes at a station at a moderate distance from the 

 head of the canal may be determined by the method that has been 

 described. The tides and currents set up when another section is 

 added are derived therefrom. By continuing the process, the primary 

 tides and currents in a closed canal of any length may be computed. 

 429. Example. — The primary currents produced by tides of succes- 

 sive amplitudes at the entrance to a canal 60,000 feet in length, and 

 16 feet in mean depth, determined by the same procedure as that set 

 forth in figure 76, are: 



At entrance (station 60) 

 TIDE 



A a 



3.5 



3.0 



2.5 



CURRENT 

 B /S 



1.94 -4°o0' 



1.66 -4° 



1.40 -3°20' 



At head {station 0) 



TIDE 

 A a 



3.73 -6°10' 



3.21 -5°20' 



2.70 -4°30' 



The computation from this data of the primary currents at the 

 entrance to a canal 80,000 feet long and of the same mean depth, 

 when the tide at the entrance has an amplitude of 3 feet, is shown at 

 the bottom of figure 76. For the initial computation the tide at 

 station 60 is taken as the same as at station 40 of the 60,000 foot 

 canal, the amplitude of which is 3.12 feet and the initial phase is 

 — 3°50'. The corresponding amplitude of the current is, by inter- 

 polation from the tabulated data, 1.73 feet per second, and its initial 

 phase, for a zero phase of the tide at station 60 is — 4°10'. Since 

 the phase of the tide at station 60 is — 3°50', the phase of the current 

 at this station is — 4°10' — 3°50'=— 8°. The coordinate amplitudes 

 of the velocity at station 60 are then : 



1.73 sin (-8°) = -0.240 1.73 cos (-8°) = 1.710. 



The current at station 70 is derived by adding the velocity increment, 

 stations 60 to 70, determined by the tide at station 65, and the resulting 

 coordinate heads, stations 60 to 80 derived therefrom. The recom- 

 putation from the corrected tides at station 60, develops heads in 

 satisfactory agreement with those first found. In the final computa- 

 tion, the current at station 80 is determined by adding to the corrected 

 velocity components at station 60 the storage due to the tide at 

 station 70. The current at the entrance to the 80,000 foot canal is 

 found to have an amplitude of 2.27 feet per second, and an initial 

 phase of — 10°30'. 



The final determination of the amplitude of the tide at station 60 

 of the 80,000-foot canal is 3.13 feet and its phase is -8°20'. The 



