118 U. S. COAST AND GEODETIC SURVEY 
stituent the logarithms of the resulting products for column (2) may 
be readily obtained. Similarly, for column (4), the ¢’s of B from 
column (6) of form 452 may be copied on a strip of paper and applied 
to the bottom line of the tabular values for each constituent and the 
differences obtained. The natural numbers for column (3) correspond- 
ing to the logarithms in column (2) can usually be obtained most 
expeditiously from table 27, this table giving the critical logarithm for 
each change of 0.001 in the corresponding natural number. If the 
logarithm is less than 6.6990, the natural number will be too small to 
appear in the third decimal place, and the effects of the corresponding 
constituent may be considered as nil. The products for columns (6) 
and (7) may be conveniently obtained from table 30. In column (8) 
the references to (6) and (7) are to the sums of these columns. The 
values of log F(A) and (V)+ 4) for column (8) may be obtained from 
forms 244 and 244a. 
328. In the use of this form it will be noted that the R’s and ¢’s 
referring to constituent B are to be the best known values whether 
derived from the analysis or by inference, but the R’ and ¢’ of con- 
stituent A, entered as items (9) and (19), respectively, must be the 
unmodified values as obtained directly by form 194. 
ANALYSIS OF TIDAL CURRENTS 
329. 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. Constituents 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. 
330. In the reversing type the current flows alternately in opposite 
directions, the velocity inereasing from zero at the time of turning 
to a maximum about 3 hours later and then diminishes to zero again, 
when it begins to flow in the opposite direction. By considering the 
velocities as positive in one direction and negative in the opposite 
direction, such a current may be expressed by a single harmonic 
series, such as 
V=Acos (at+a)+B cos (6t+ 8)+C cos (ct+y)+ete. (450) 
in which V=velocity of the current in the positive direction at any 
time ¢. 
A, B, C, ete.=maximum velocities of current constituents. 
a, 6, c, ete.=speeds of constituents. 
a, B, y, etc.=initial phases of constituents. 
331. In the rotary type the direction of the current changes through 
all pomts 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 
