»oo,ooo goqooo -feet 



J)i5tancc- -from ImUiqI LviT ranee. 



Figure S3.— Progression of tide and current tlirough connecting canal. 



The height of the tide at the middle of the canal is then the mean 

 of the heights at the entrances, increased by the factor 1/cos jiy. 



The velocity at the middle of the canal is, similarly, from equation 



(230): 



Vm=(g/c)[Ao sin (at-\-ao)—Ai sin {at-^-ai)] cos ^T/sin 7 



= y2(g/c)[Ao sin (at+aoJ-A, sin ((7i+ai)]/sin }h (238) 



The total sm^face head between the two entrances to the canal is: 



hs—Ai cos (at-{-ai)—Ao cos (at-\-ao) 



If the effect of the tidal storage were neglected, the water surface 

 would have the uniform slope of: 



dy/dx=[Ai cos (ai+txi)— ^ cos {at-\-ao)]/L (239) 



And from equation (177) the velocity through the canal would be: 



Vi=-g\ idy/dx)(>t^ (g/aL)[Ao sin (ai+ao)-^ sin (at-^a,)] (240) 



The ratio of the velocity at the middle of the canal, when tidal 

 storage is considered, to the velocity through the canal without tidal 

 storage, is then, from equations (238) and (240): 



vJi, = ^^^^^l^=(aL/c)/2 sin K. = ./2 sin %y 



(241) 



In equation (241). 7 is measured in radians. Its relation to the 

 wave length, X, of the component is given by equation (236): 



7 = 27rL/X=i/(X/27r) 



331. The nature of the ratios, 1/cos ^27 and 7/2 sin Kt can perhaps 

 be shown more clearly on a diagram. 



