186 Mr. C. Marett on the causes of the Intervals 



when the series will recommence. We have therefore in C — 



Tide flowing from 3 till 9 

 ... ebbing from 9 till 3 

 ... rising from till 6 

 ... falling from 6 till 12 



which is the system usually called tide and half-tide, and is ex- 

 plained (Encijc. Metr. 'Tides and Waves/ §§ 184, 507) upon 

 independent considerations founded on the motions of water 

 in waves. 



Explanation of High-water occurring before the turn of tide. 



Let us now suppose that R is of limited area, which seems to 

 be the ordinary case of a river or channel, and that the water 

 flowing through C in six hours will affect the level of the water 

 in R 6 feet ; for the sake of simplicity let us suppose the rising 

 and falling of the water in R to be uniform, viz. one foot per hour. 

 Then at low water in A, the height of the water in R will be 4 ft. 

 6 in., as I shall proceed to show ; for, assuming it to be so and 

 the time to be 0*^, the water in A will then begin to rise, 

 and the water in R will fall, ebbing through C, till 1^ 30"», at 

 which time the levels will be the same in both, having fallen 

 1 ft. 6 in. in R and risen 3 ft. in A. The stream in C will 

 then turn and flow into R, the water in R rising at the same 

 time till 6^, at which time the height of the water in R will 

 be 7 ft. 6 in., in A 12 ft. The water in A and C will then begin 

 to fall, but still flow through C till 7^ 30"^, when the water in 

 A and R will be at the same level, viz. 9 feet : the stream in C 

 will then turn and ebb, and will continue to ebb and also to fall 

 till 12 hours, when it will be low- water in A and 4 ft. 6 in. in R. 

 The series will then recommence, and the original hypothesis, 

 that at low water in A the height would be 4ft. 6 in. in R, is 

 therefore correct, as it is the only permanent system. We shall 

 have therefore in C,— Tide flowing from 1^^ 30°^ to 7^ 30"^, 

 ... ebbing ... 7^^ 30"^ to 11^30^, 

 ... rising ... 0^ 0^ to 6^ 0^, 

 ... falling ... 6^ 0^ to 12^ 0°^, 

 high-water and low- water each occurring one hour and a half 

 before slack- water. Similarly, if R were smaller, it might 

 be shown that high-water would be nearer slack-water, and 

 ultimately, when R becomes nothing, or at the end of the chan- 

 nel C, high- water would coincide with slack-water. — Tides and 

 Waves, §335. 



Now if we take any section of a river, we may regard that 

 section as C, and the portion of the river above it as R, and we 

 have an explanation of the phsenomenon observed in rivers^ 



i 



