HARMONIC* ANALYSIS! AND PREDICTION OF TIDES 51 
148. If hourly heights have not been observed but a record of high 
and low waters is available, an approximate evaluation of the more 
important constituents may be obtained by a special treatment. 
The results, however, are not nearly as satisfactory as those obtained 
from the hourly heights. 
149. Although the hourly interval for the tabulated heights of the 
tide has usually been adopted as most convenient and practicable for 
the purposes of the harmonic analysis, a greater or less interval might. 
be used. A shorter interval would cause a considerable increase in 
the amount of work without materially increasing the accuracy of the 
results for the constituents usually sought. However, if an attempt 
were made to analyze for the short period seiches a closer interval 
would be necessary. An interval greater than one hour would lessen 
the work of the analysis but would not be sufficient for the satisfactory 
development of the overtides. 
150. In selecting the length of series of observations for the purpose 
of the analysis, consideration has been given to the fact that the pro- 
cedure is most effective in separating two constituents from each other 
when the length of series is an exact multiple of the synodic period of 
these constituents. By synodic period is meant the interval between 
two consecutive conjunctions of like phases. Thus, if the speeds of 
the two constituents in degrees per solar hour are represented by a and 
b, the synodic period will equal 360°/ (a~b) hours. If there were only 
two constituents in the tide the best length of series could be easily 
fixed, but in the actual tide there are many constituents and the 
length of series most effective in one case may not be best adapted to: 
another case. It is therefore necessary to adopt a length that is a 
compromise of the synodic periods involved, consideration being 
given to the relative importance of the different constituents. 
151. Fortunately, the exact length of series is not of essential im- 
portance and for convenience all series may be taken to include an 
integral number of days. Theoretically, different lengths of series 
should be used in seeking different constituents, but practically it is 
more convenient to use the same length for all constituents, an excep- 
tion being made in the case of a very short series. The longer the 
series of observations the less important is its exact length. Also the 
greater the number of synodic periods of any two constituents the 
more nearly complete will be their separation from each other. Con- 
stituents like S, and K, which have nearly equal speeds and a synodic 
period of about 6 months will require a series of not less than 6 months 
for a satisfactory separation. On the other hand, two constituents 
differing greatly in speed such as a diurnal and a semidiurnal con- 
stituent may have a synodic period that will not greatly exceed a day, 
and a moderately short series of observations will include a relatively 
large number of synodic periods. For this reason, when selecting the 
length of series no special consideration need be given to the effect of 
a diurnal and a semidiurnal constituent upon each other. 
152. The following lengths of series have been selected as conform- 
ing approximately to multiples of synodic periods involving the more 
important constituents—14, 15, 29, 58, 87, 105, 134, 163, 192, 221, 250, 
279, 297, 326, 355, and 369 days. The 369-day series is considered as 
a standard length to be used for the analysis whenever observations 
covering this period are available. This length conforms very closely 
with multiples of the synodic periods of practically all of the short- 
