138 U. S. COAST AND GEODETIC SURVEY. 



in contact with each other. The time and height may then be read 

 directly from the dials on the face of the machine. The movement 

 of the height pointer before the stopping of the machine and also 

 the tide curve will clearly indicate whether the tide is a high or low 

 water. After the tide has been recorded an inward pressm:e on the 

 crank handle will release the brake and the machine can be turned 

 forward to the next tide, the process being repeated until all the 

 tides of the year have been predicted and recorded. 



35. TIDAL CURRENTS. 



Tidal currents are the periodic horizontal movements of the waters 

 of the earth's surface. As they are caused by the same periodic 

 forces that produce the vertical rise and fall of the tide, it is possible 

 to represent these currents by harmonic expressions similar to those 

 used for the tides. Components with the same periods as those con- 

 tained in the tides are involved, but the current velocities take the 

 place of the tidal heights. There are two general types of tidal cur- 

 rents, known as the reversing type and the rotary type. 



In the reversing type the current flows alternately in opposite 

 directions, the velocity increasing from zero at the time of turning 

 to a maximum about tliree hours later and then diminishes to zero 

 again, when it begins to flow in the opposite direction. By consid- 

 ering the velocities as positive in one direction and negative in the 

 opposite direction, such a current may be expressed by a single har- 

 monic series, such as 



V=A cos (at + a) +B cos (at + ^) + C cos (c^ + t) +etc. (475) 



in which F= velocity of the current in the positive direction at any 

 time t. 



A, B, C, etc. = maximum velocities of current components. 



a, i, e, etc. = speeds of components. 



a, /3, y, etc. = initial phases of components. 



In the rotary type the direction of the current changes through 

 all points of the compass, and the velocity, although varying in 

 strength, seldom becomes zero. In the analysis of this type of cur- 

 rent it is necessary to resolve the observed velocities in two directions 

 at right angles to each other. For convenience the north and east 

 directions are selected for this purpose, velocities toward the south 

 and west being considered as negatives of these. For the harmonic 

 representation of such currents it is therefore necessary to have two 

 series — one for the north and the other for the east component. 



For the analysis of either type of current the original hourly veloci- 

 ties or the resolved hourly velocities are tabulated in the same form 

 used for the hourly heights of the tide. To avoid the inconvenience 

 of negative readings in this tabulation, a constant, such as 3 knots, 

 is added to all velocities. 



These hourly velocities are then summed with the same stencils 

 that are used for the tides, and the hourly mean velocities are analyzed 

 in the same manner as the hourly heights of the tide. The same 

 forms are used for the currents, with the necessary modifications 

 in the headings. The rotary currents will be represented by a double 



