148 U. Si: COAST AND GEODETIC SURVEY 
436. The operation of the machine for the prediction of the cur- 
rents is similar to that for the prediction of the tides. The machine 
automatically stops at each maximum flood and ebb velocity and the 
corresponding times and velocities are then recorded, the flood veloci- 
ties being read to the right and the ebb velocities to the left of the 
scale zero. In the prediction of the currents the times of slack water 
are also desired. These are indicated by the zero position of the 
recording hand as well as by the intersections of the curve and medial 
line in the graphic record. The velocity of the current at any inter- 
mediate time can be read directly from the height dial when the 
machine has been turned to the time desired and it may be also scaled 
from the graphic record. 
437. Predictions of hydraulic currents in a strait, based upon the 
difference in the tidal head at the two entrances, may be made by 
means. of harmonic constants derived from the tidal constants for 
the entrances. Differences in tidal range or in the times of the high 
and low waters at the two ends of a strait will cause the water surface 
at one end alternately to rise above and fall below that at the other 
end, thus creating a periodic reversing current in the strait. Theo- 
retically, disregarding friction or inertia, the velocity of the current 
would vary as the square root of the difference in head, being zero 
when the surface is at the same level at both ends and reaching a 
maximum when the difference is greatest. Actually there will gen- 
erally be a lag of some minutes in the response of the current 
movement to the difference in head which must be determined from 
observations. 
438. Let the two ends of the strait be designated by A and B, with 
the flow from A toward B considered as flood or positive and the flow 
in the opposite direction as ebb or negative. With the waterway 
receiving the tide from two sources, the application of the terms 
“flood” and ‘‘ebb” will be somewhat arbitrary, and care must be 
taken to indicate clearly the direction assumed for the flood move- 
ment. In the following discussion tidal constants pertaining to 
entrances A and B will be distinguished by subscripts a and b, respec- 
tively, and those pertaining to the difference in tidal head by the 
subscript d. Since the usual constituent epochs known as ‘“‘kappas”’ 
refer to the local meridian, it will be necessary for the purpose of 
comparison between places on different meridians to use the Green- 
wich epochs ‘‘G”’ (par. 226), these being independent of local time and 
longitude. 
439. For any one constituent let 7 represent time as expressed 
in degrees of the constituent reckoned from the phase zero of its 
Greenwich equilibrium argument. Also let Y, and Y, represent the 
height of the constituent tide for any time 7 as referred to the mean 
level at locations A and B, respectively; and let Y, equal the difference 
(Y,—Y,). Formulas for heights and difference may now be written 
Y,=H, cos (T—G,) for location ‘‘A’’ (467) 
Y,=H, cos (T—G,) for location ‘‘B”’ (468) 
Y.=H, cos (T—G,) —H, cos (T— G;) 
=(H, cos G,—H, cos G,) cos T+ (A, sin G,— Hy sin G,) sin T 
=H, cos (T—G;) (469) 
