62 U. S. COAST AND GEODETIC SURVEY. 



An interval greater or less than the solar hour might be used for 

 the record of tabulated heights. A shorter interval would cause a 

 considerable increase in, the work of the reduction without materially 

 increasing the accuracy of the results for the components usually 

 sought. However, if an attempt were made to analyze 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 over- 

 tides. The hour interval appears to be the most convenient and 

 practicable for the usual analysis. 



The summations are most effective in separating a disturbing 

 component from the component sought when the length of the series 

 of observations is an exact multiple of the synodic period of those 

 components. The synodic period of two components is the time 

 required for the difference in their phases to complete a cycle of 360°. 

 If the speeds of two components in degrees per solar hour be repre- 

 sented by a and h the synodic period will be 360°/ (a ~ h) hours. If there 

 were only two components in the tide, the best length of series would 

 be easHy fixed; but in the actual tide there are many components and 

 a length of series most effective in the elimination of one disturbing 

 component may not be best adapted to the ehmination of another. 

 It is therefore necessary to adopt a length that is a compromise of the 

 synodic periods involved, weight being given according to the 

 theoretical relative magnitudes of the components. 



Fortunately, the exact length of series to be used is not of essential 

 importance, and for convenience all series may be taken to include 

 an integral number of solar days. Theoretically, different lengths 

 should be used for the different components sought, but practically 

 it is more convenient to use the same length for aU of the components. 

 An exception to this is found desirable for the very short series which 

 is taken as 14 days for components chiefly diurnal and 15 days for 

 components chiefly semidiurnal. The longer the series the less 

 important is the exact length, and the greater the number of synodic 

 periods of two components included the more nearly complete will be 

 the separation of those two components from each other. Two 

 components hke Sj and K.^, which have a very small difference in 

 speed and a synodic period of about six months, can not be satis- 

 factorily separated by the summation of a series of less than six 

 months. On the other hand, two components with a large difference 

 in speeds like a diurnal and a semidiurnal component may have a 

 sjmodic period that wiU not greatly exceed a day, and a moderately 

 short series of observations ^vill include a relatively large number of 

 synodic periods. For this reason, in selecting the length of series, 

 no special consideration need be given to the effect of a diurnal and 

 a semidiurnal component upon each, other. The length of series 

 adop|ed for the harmonic analysis of the tides in the office of 

 the iK, S. Coast and Geodetic Survey are as foUows: 14-15, 29, 58, /* 

 S7,{0S;-134:, 163, 192, 221, 250, 279, 297, 326, 355, and 369 days. 



ror the 14-15-day series — 14 for diurnal and 15 for semidiurnal 

 cyfo.ponents — the length conforms to the synodic periods of the 

 mncipal diurnal components Kj and O^, and the principal semidiurnal 

 components Mj and S2, and also to the synodic periods involving a 

 few of the less important components. This is the shortest series for 

 which the harmonic analysis is made. It can not be considered as a 



