186 



and determine the currents due to these, as well as those produced by 

 the representative normal tidal fluctuations. 



359. Primary currents and tides in the canal. — If the selected repre- 

 sentative entrance tides are not simple harmonic fluctuations of the 

 same speed, they may be approximated more or less closely by such 

 fluctuations. These may be termed the 'primary entrance tides. The 

 primary currents and tides in the canal which would be produced by 

 the primary entrance tides are first computed. These computations 

 are based on the depth and width of the canal at mean tide, and omit 

 the effect of the minor components of the friction term (par. 226) . The 

 primary currents and tides may then be adjusted to develop the 

 deformations produced by the minor components of the friction term, 

 by the variation in the width, depth, and area of the cross section of 

 the water prism as the ride rises and falls, and by the entrance, recovery, 

 and velocity heads; and to develop also the variations because of a 

 departure of the representative entrance tides from the simple har- 

 monic fluctuations from w^hich the primary currents and tides were 

 derived. 



The primary currents and tides usually afford a fair representation 

 of the currents and tides to be expected in the canal because of the 

 ordinary tidal fluctuations; but their adjustment, although a laborious 

 procedure, may be warranted to give a more complete and assured 

 picture of the anticipated tidal flow. The effect of storm tides can 

 be ascertained only by going through the latter process. 



360. Determination of primary entrance tides. — The primary tides 

 most nearly conforming to the selected representative tides ordinarily 

 will have the speed of the M2 component, whose component hour is 

 the mean lunar hour of 1.035 mean solar hours. By taking off from 

 the representative tide curves the heights on 24 successive lunar hours 

 after any assumed origin of time, the amplitude A, and the initial 

 phase, a, of the primary tide at this origin of time, may be computed 

 from equations (56), (57), (47), and (48) developed in Chapter II, viz: 



12c2=(Ao cos + /^i cos 30°+h2 cos 60° + . . . + /i23 cos 330°) (56) 



12s2={ho sin 0+7^1 sin 30°+/i-2 sin 60° + . . .+^23 sin 330°) (57) 



tan f =S2/c2 A=.S2/sin f =C2/cos f (47) (48) 



In which ho, hi, etc., are thp tidal heights at the successive lunar hours, 

 and f =— a. 



The abbreviation of the computations is explained in paragraph 94. 



A consideration of the derivation of these equations show^s that if 

 the representative entrance tides are taken as a fluctuation which is 



