REDUCTION OF CURRENT RECORDS 73 
The computations for all higher harmonies of even subscripts may be carried out in the 
same form using the spaces originally designed for the harmonics with subscripts one- 
half as great. In this adaptation, of the form no provision is made for the computation 
of a harmonic of odd subscript which is here of relatively little importance. Other forms 
which are used in connection with the analysis will not be affected by the use of the 
special stencils for the half-hourly velocities. 
177. Observations on the half-hour may also be analyzed separately from those on 
exact hour, using the standard stencils for the summation. In this case the stencils 
are moved to the right one column and dropped one line, thus covering the hourly 
values and exposing those occurring on the half-hour. Allowance must be made 
for the difference of a half-hour in the begmning of the series when computing 
the (Vo-+w)’s in Form 244. This may be conveniently done by assuming a time 
meridian a half-hour or 74° westerly from the actual time meridian used so that the 
first half-hourly observation will correspond to the 0 hour of the assumed time meridian. 
The difference of 15 minutes for the middle of the series has a negligible effect in the 
computations and may be disregarded. {n other respects the analysis is carried on in 
same manner as the analysis for the hourly observations, and the results obtained afford 
a useful check on the latter. 
178. Current constituent ellipse.—It has already been shown (par. 22) that an 
observed rotary current can be represented graphically by a crude ellipse in which 
the velocity and direction of the current are indicated by the length and direction of 
the radius vector for different hours of the tidal cycle. From the harmonic constants 
for the north and east components of any current constituent a smooth ellipse may be 
constructed to represent that constituent. During the constituent cycle there will 
be two maximum velocities of equal strength in opposite directions. These will be 
represented in the ellipse by the two semimajor axes. There will also be two minimum 
velocities represented by the two semiminor axes of the ellipse. The construction of 
the current constituent ellipse from the harmonic constants and the computations for 
the times, velocities, and directions of the current for the maximum and minimum 
velocities are explained in the following paragraphs. 
179. Let H,, and K; represent respectively the amplitude and epoch of the north 
component, and H, and K, the amplitude and epoch of the east component of the particu- 
lar constituent for which the ellipse is to be constructed. Let 7 represent time as ex- 
pressed in degrees of the equilibrium argument for this constituent. It is therefore 
reckoned from the same origin as the epochs of the constituent. Let V, and V, respec- 
tively represent velocities for the north and east components, and V and A respectively 
the velocity and azimuth of the resultant current for any time 7. The equations for the 
north and east component velocities of the constituent may then be written— 
V,=H, cos (T—K,) for north component_______________----__-_- (1) 
V.=H, cos (T—K,) for east component____________-__________- (2) 
Replacing the symbols for the harmonic constants by their actual values and substitut- 
ing successive values for 7’ we obtain the corresponding values for the component veloci- 
ties. Plotting the north component velocities as ordinates with the corresponding east 
component velocities as abscissas, a series of points will be obtained which when con- 
nected will form the current constituent ellipse. 
*As a matter of convenience in the formulas that follow, the capital letter (K) is adopted as a symbol for local constituent epochs 
in place of the Greek letter kappa (x) which is generally used for this purpose. 
