193 

 Again, from equation (151): 



S sin (j)=aB/g 

 whence: 



H=lS=l(a/g)B /sin 4>. (289) 



If a=0.0001405 and ^=32.162, the value of a/g is 0.000,00437 and 

 its logarithm is 4.64042 — 10. 



The relation between the initial phase, H°, of the head and the 

 initial phase, /3, of the primary current is, from equation (150): 



S'° = /3 + <^+90°. (290) 



The values of H and H°, derived from equations (288), (289), and 

 (290) give the values of the coordinate amplitudes, H cos H° and 

 H sin H°, of the heads in the subsections corresponding to the first 

 computation of the currents. 



374. Corrected tides and velocities. — The computed coordinate ampli- 

 tudes of the heads in the subsections are so adjusted that their sums 

 are equal to the differences between the coordinate amphtudes of the 

 tides at the entrance. The corrected coordinate amplitudes of the 

 tides at the ends of the subsections produced by the adjusted coor- 

 dinate amplitudes of the heads are computed from equations (269) 

 and (270). The coordinate amplitudes, Bo sin /3o and Bq cos jSq, 

 of current in the middle subsection are next recomputed from the 

 adjusted head in the subsection, but the recomputation may be 

 somewhat abbreviated. Let H and H' be the initial and adjusted 

 values of the amplitude of the head, and S=Hll and S'=H' jl the 

 corresponding values of the amplitude of slope in the subsection. 

 The ratio of the corrected value of P' = 1.0854 C-^tW (par 245) to 

 the value, P= 1.0854 C-^rS, initially computed, is: 



P7P= /S'/-ylS= ^H'l^H 

 So that: 



log P'=log P+)Klog H'-\og H) (291) 



and similarly: 



log (P7^')=log (P/^)-K(log £P-log H). (292) 



The corrected values of 0, Bq and 183 are determined from the corrected 

 values of P'/S' and P' as explained in paragraph 246. 



The currents in the other subsections are then recomputed from 

 equations (283) and (284). In applying these equations, the coordi- 

 nate amplitudes of the tide at any storage station which does not 

 coincide with the end of a subsection are interpolated between the 

 corrected values at the ends of the subsection in which it lies, on the 

 assumption that the instantaneous profiles iii each subsection are sub- 



