150 U. S. COAST AND GEODETIC SURVEY 
or 
(H,,/H,) sin (G.—G,+180°) 
1+ (H,/H,) cos (G.— G,+180°) 
Formulas (472) and (474) are to be used when the ratio H,/H, does not 
exceed unity. In this case take argument’r of the tables=H,,/H,, and 
argument 2=(G),—G,+180°). If the ratio H,/H, exceeds unity use 
formulas (473) and (475) and take argument r=H,/H, and argument 
z=(G,—G,+180°). The tabular values will give the ratios and 
angular differences represented in the first terms of the formulas. 
Therefore, in order to obtain the amplitude H,, the tabular value 
from table 41 must be multiplied by H, if the ratio H,/H, does not 
exceed unity, or by H, if this ratio does exceed unity. Also to obtain 
the epoch Gj, the tabular value from table 42 must be increased by G, 
if the ratio does not exceed unity or by (G,+180°) if the ratio is greater 
than unity. 
441. By the formulas given above separate computations are made 
for each of the tidal constituents. The values obtained for H, and Gz 
are the corresponding amplitudes and Greenwich epochs in an har- 
monic expression for the continually changing difference in elevation 
of the water surface at the two entrances to the strait. When only a 
single time zone is involved, the small g’s or modified kappas («’) per- 
taining to that zone may be substituted for the Greenwich epochs (G) 
in the formulas. For the prediction of the current, further modifica- 
tions are necessary in the amplitudes to reduce to velocity units and in 
the epochs to allow for the lag in the response of the current to the 
changing difference in water level at the two entrances to the strait. 
442. Since the velocity of an hydraulic current is theoretically 
proportional to the square root of the difference in head, we may write 
Tan (Ga— Gy te 180°) — (475) 
(Velocity)?=constant (C) Xheight difference (476) 
If we now let V equal the average velocity of the current at time of 
strength as determined from actual observations and assume that the 
corresponding difference in water level is 1.02 times the difference 
resulting from the principal constituent M>, we may obtain an approxi- 
mate value for the constant (C) by the formula 
C=V?/(1.02Mp) (477) 
in which M,j is the amplitude of the constituent M, in the harmonic 
expression for the difference in head. The application of the factor 
(C) to all the constituent amplitudes in this expression has the effect 
of changing the height units into units representing the square of the 
velocity of the resulting current. 
443. The lag in the current is usually determined by a comparison 
of the times of strengths and slacks from actual observations with 
preliminary predictions of the corresponding phases based upon the 
harmonic constants derived by the method just described. This lag 
expressed in hours is multiplied successively by the speed of each 
constituent and the result applied to the preliminary epoch for that 
constituent. 
444. In order that the magnitude of the constituent amplitudes may 
be adapted for use with the predicting machine, a scale factor (S) is 
