245 



ment, gives the value of m' =MqIM' . The coefficient lajg remains un- 

 changed. Since p= (Stt/S) {ajg) C-r its value after improvement is 



2?i=p(CV/CiVi) 



in which C and C\, r and Vi are the values of the Chezy coefficient and 

 the hydraulic radius before and after improvement. Often Ci may 

 be taken as the same as C, so that 



The value of ri should be computed by a procedure paralleling 

 that used in the computation of r. 



474. Completion of computation. — The primary currents that would 

 be produced in the iro.proved channel, if the tides were unchanged, 

 are first com.puted. If the values of /are not changed, the phases, /3, 

 are those already determined, and the amplitudes, B, are derived by 

 multiplying the values of Bjm,, previously found, by the new ratio m' ; 

 otherwise the values of I A sin a and lA cos a are recomputed from 

 the prim.ary tides at the storage stations and the values of {Bjm') 

 sin /3 and {Bjm') cos /3 found by their summation from the head of 

 tide. The coordinate amplitudes of the heads in the subsections cor- 

 responding to these currents are then computed from the values 

 ascertained for lajg and pi; the corrected coordinate amplitudes of the 

 tides derived therefrom; and the process repeated until the tides and 

 currents are in satisfactory concordance. The elevation of mean low 

 water after improvero.ent is then found by multiplying the mean semi- 

 range of the tide at the station, as established by comparison or other- 

 wise, by the ratio of the computed amplitudes of the primary tides 

 after and before improvement, and subtracting the result from es- 

 tablished half-tide level. 



475. Computation of changes in mean lower low water datum. — If the 

 tides are of the mixed type, and the adopted datum is mean lower low 

 water, the changes resulting from an extensive channel improvement 

 might be computed on the assumption that the ratio of the mean 

 range to the diurnal range will rem.ain the same after and before the 

 improvement. The primary tides after and before improvement could 

 then be computed as outlined in the preceding paragraphs. The ratio 

 of their amplitudes at a station would then give the ratio of the ele- 

 vations of mean lower low water below established half-tide level after 

 and before the improvement. 



476. Application to the approach to a sea-level canal. — The changes 

 that may be expected in the tides and currents in a confined approach 

 to a sea-level canal because of the fiow in and out of the canal entrance, 

 could best be computed by determining the subsection coefficients in 

 the approach channel from tidal observations made before the canal 



