52 U. S. COAST AND GEODETIC SURVEY 
period constituents and is well adapted for the elimination of seasonal 
meteorological effects. When observations at any station are avail- 
able for a number of years, it is desirable to have separate analyses 
made for different years in order that the results may be compared 
and serve as a check on each other. Although not essential, there are 
certain conveniences in having each such series commence on January 
1 of the year, regardless of the fact that series of consecutive years 
may overlap by several days because the length of series is a little 
longer than the calendar year. 
153. If the available observations cover a period less than 369 days, 
the next longest series listed above which is fully covered by the 
observations will usually be taken, any extra days of observations 
being rejected. However, if the observations lack only a few hours 
of being equal to the next greater length, it may be advantageous to 
extrapolate additional hourly heights to complete the larger series. 
The 29-day series is usually considered as a minimum standard for 
short series of observations. This is a little shorter than the synodical 
month and a little longer than the nodical, tropical, and anomalistic 
months. It is the minimum length for a satisfactory development of 
the more important constituents. 
154. For observations of less than 29 days, but more than 14 days, 
provisions are made for an analysis of a 14-day series for the diurnal 
constituents and a 15-day series for the semidiurnal constituents, the 
first conforming to the synodic period of constituents K, and O,, 
and the latter to the synodic period of Mz, and S;. Through special 
treatment involving a comparison with another station, it is possible 
to utilize even shorter series of observations. This treatment is 
rarely required in case of tide observations but is useful in connection 
with tidal currents where observations may be limited to only a few 
days. 
SUMMATIONS FOR ANALYSIS 
155. The first approximate separation of the constituents of the 
observed tide is accomplished by a system of summations, separate 
summations being made for all constituents with incommensurable 
periods. Designating the constituent sought by A, assume that the 
entire series of observations is divided into periods equal to the period 
of A and each period is subdivided into a convenient number of equal 
parts, the subdivisions of each period being numbered consecutively 
beginning with zero at the initial mstant of each period. All subdivi- 
sions of like numbers will then include the same phase of constituent 
A but different phases for all other constituents with incommensurable 
speeds. The subdivisions will also include irregular variations arising 
from meteorological causes. By summing and averaging separately 
all heights corresponding to each of the numbered subdivisions over a 
sufficient length of time, the effects of constituents with incommensur- 
able periods as well as the meteorological variations will be averaged 
out leaving intact constituent A with its overtides. 
156. The principle just described for separating constituent A 
from the rest of the tide is applicable if the original periods into which 
the series of observations is divided are taken as some multiple of 
constituent A period. In general practice, that multiple of the 
constituent period which is most nearly equal to the solar day is taken 
as the unit. This is the constituent day and includes one or more 
