161 



The component of the current at a pomt distant x from the origin is 

 then: 



'o={glc)[Q COS (axlc) — P sin (ax/c)] cos at 



— (glc)[N cos (ax/c)—M sin (ax/c)] sin at. (215) 



The constants M, N, P, and Q in the equation of the current are the 

 same as those in the expression for the corresponding component of 

 the tide. 



322. Determination of the. constants. — The constants in equations 

 (211) and (215) may be determined from, the amplitudes and phases 

 of the corresponding- component of the tide at the two ends of the 

 canal. 



Let L be the length of the canal, Ao the amplitude and ao the phase 

 of the component at the initial end, and Ai and ,ai the amplitude and 

 phase of this component at the other end. 



The equation of the component tide at the initial end is then: 



yo=Ao cos (at-{-ao)=Ao cos at cos ao—Aa sin at sin ao (216) 



and at the other end: 



yi=Ai cos {at-{-ai)=Ai cos at cos ai—A^ sin at sin ai (217) 



At the initial end, x—O, and equation (211) becomes: 



2/o=M cos at-\-P sin at (218) 



Since this equation must be identical with equation (216) 



M=Ao cos ao (219) 



P=-Aosmao (220) 



At the other end of the canal, x=L and equation (211) becomes: 



2/i = [Mcos {aLlc)-{-N sin (aL/c)] cos at 



+ [P cos (a Llc)-^Q sin(aX/c)] sin at 



Therefore: 



M cos (aZ/c) +N sin {aLjc) =Ai cos a^ (221) 



P cos (aL/c)-\-Q. sin (aL/c) = -A^ sin ^i (222) 



It will be convenient to place: 



aL/c=y (223) 



