64 MANUAL OF CURRENT OBSERVATIONS 
162. In order to find the velocity and direction of the resultant current from its 
north and east component velocities, the latter must first be freed from the arbitrary 
constant previously introduced to avoid negative values. The components will then 
be expressed in their true velocities with positive or negative signs to indicate the 
actual directions. The velocity of the resultant current will equal the square root of 
the sum of the squares of the component velocities and its direction will be expressed 
by the angle whose tangent is the quotient obtained by dividing the east component 
velocity by the north component velocity. The quadrant for the angle will be de- 
termined by the signs of the east and north components which will correspond respec- 
tively to those of the sine and cosine of the angle. 
163. Table 7 provides a means of readily determining the resultant current from 
its north and east component velocities. The table contains values representing the 
velocity and direction of current corresponding to north- and east-component velocities 
for each hundredth of a knot from 0.01 to 0.60 knot. There is a line for each north- 
component velocity and a column for each east-component velocity. Of each group 
of four figures in the body of the table the first two represent the velocity in hundredths 
of a knot and the last two the direction in degrees measured from north (0° or 360°) 
or south (180°) according to the following rule which takes into account the signs of 
the component velocities. If these are both positive the direction will be the same 
as in the table; if the east component alone is negative, the tabular direction must be 
subtracted from 360°; if the north component alone is negative, the tabular direction 
is to be subtracted from 180°; and if both components are negative, the tabular direc- 
tion is to be added to 180°. 
Example: To find the resultant velocity and direction corresponding to a 
north component velocity of —0.42 knot and an east component velocity of 
+0.13 knot, Table 7 is entered at the line marked ‘‘.42”. On this line in the 
column headed ‘0.13” it is found that the resultant velocity is 0.44 knot and 
the tabular direction 17 degrees. Applying the rule just stated for the case 
where the north component alone is negative we find the actual direction of 
the resultant current to be 180°—17°=163°. So the current represented 
by north and east components, —0.42 and -+-0.13 respectively, has a velocity 
of 0.44 knot and a direction of 163°. 
Specially prepared charts were formerly used both for resolving the observed current 
velocities and for obtaming the resultant currents. These charts and their use are 
described in detail on pages 51 and 52 of the first (1938) edition of this manual. 
164. Tabulation of rotary currents.—Korm 768 is used for this tabulation, which 
consists of grouping hourly or half-hourly current observations according to the high 
and low water phases at a reference station. If the observed velocities have not been 
resolved, the actual velocities and corresponding azimuths are entered in the double 
columns provided in the form, but if the observations have been resolved, the north 
and east component velocities are tabulated, a constant being included to avoid nega- 
tive readings. On the Atlantic coast where the diurnal inequality in the tides is rela- 
tively small, the groups are usually reckoned from 3 hours before high water to 3 hours 
after high water and from 3 hours before low water to 3 hours after low water. On the 
Pacific coast where the diurnal inequality is of considerable importance, separate 
references are made to the higher high, lower high, higher low, and lower low water. 
If the current is largely diurnal, references are mace to the higher high and lower low 
waters only. As the type of current varies somewhat in different localities, a special 
grouping may sometimes be required to meet existing conditions. Sometimes it may 
