199 



The primary tides and currents at the entrances and at tlie middle of 

 the canal are shown in figaire 73, page 218. 



385. Shape of instantaneous profiles. — The characteristic shapes of 

 the instantaneous profiles developed by the successive approxima- 

 tions is readily shown by plotting the values of ^4 sin a and ^ cos a 

 successively derived in figure 62, since A cos a is the tidal height at a 

 station at hour and A sin a=A cos (—90° + a) is that at —3 lunar 

 hours. The instantaneous profiles at hour are shown by the lines'- 

 marked — in figure 63. The dift'erences between the first and second; 



4i o 



4^ 

 Lu 



I- 



0-1 



5roL 



40 so 180 I60 



Figure 63. — Instantaneous profiles at and HI hour. 



eoo 



recomputations are too smaU to be distinguishable. The successive 

 determinations at —3 lunar hours are shown by the lines marked 

 III — III on the figure. 



386. Sufficiency of suhdirision: — The question may arise whether 

 subsections 40,000 feet in length, in a canal having a mean depth of 

 30 feet, are suflEiciently short to afford a reliable determination of the 

 currents. An independent computation, based on a subdivision into 

 9 subsections, each 22,222 feet in length, afl'ords the follo^\dng com- 

 parative figures in the ef^uations of the currents at the entrances: 



Computed from 9 subsections 



Computed from 5 subsections 



At initial entrance. 

 At other entrance.- 



;;= 1.12 sin W+47°10'). 

 11=3.65 sin (a?+20°40')- 



!)=1.14sin (a?+47°20'). 

 »= 3.57 sin (a/+20°50'). 



It is apparent, therefore, that the results are but little improved 

 by using the shorter sections. 



