HAEMOISnC ANALYSIS AND PREDICTION OF TIDES, 63 



very satisfactory length but will serve for obtaining tbe approximate 

 constants for the principal components at a place where a longer 

 series of observations is not available. 



The 29-day series conforms approximately in length to the multi- 



?les of the synodic periods of nearly all the principal components, 

 'his may be considered as a standard length for short series, and 

 whenever it is necessary to limit the observations to a short period of 

 time, the minimum requirement should be 29 days. 



The 369-day series may be considered as the standard long series, 

 and whenever there are sufficient observations available it should be 

 used for the analysis. This length conforms very closely with the 

 multiples of the synodic periods of practically all of the short-period 

 components. The length is also well adapted for the elimination 

 of the irregular meteorological effects. If tidal observations have 

 been continued at a place for a number of years, it is desirable to 

 have an independent analysis for each year in order that the results 

 from the different years may be compared, and thus serve as a check 

 on the work. Although not essential, there are certain conveniences 

 in having such series commence on January 1 of each year. If 

 observations for several successive years are analyzed, each may be 

 made to begin on the first day of th^ calendar year without regard to 

 the fact that the last few days of a 369-day series will thus extend 

 into the following year and become the first days of the next series. 

 If the observations are for a period of less than 369 days, the 

 standard length selected will usually be the greatest one that is 

 entirely covered by the observations, extra days of the observations 

 being rejected; but if the period of observations lacks only a few hours 

 of being equal to the next larger standard length, it may be advan- 

 tageous to extrapolate additional hourly heights in order to complete 

 the larger series. 



23. SUMMATIONS. 



The first approximate separation of the components of the ob- 

 served tide is accomplished by a system of sunmiations. For each 

 component of independent speed that is sought a separate summation 

 is required, but the overtides will be combined with their fundamental 

 components, and these will not require a separate smnmation. 

 A single summation mil serve for any group of components with 

 comhiensurate periods. 



Let us assume that the entire series of observations is divided into 

 periods, each equal to the mean period of the component sought, 

 which, for convenience, may be designated as component A. Each 

 such division will include exactly one complete period of this com- 



Eonent, but all the other components with incommensurate periods will 

 e represented in each division by more or less than a whole period. 

 Each division will include also certain irregularities due to meteoro- 

 logical conditions. Starting -with the same phase at the beginning 

 of each division, component A will be exactly reproduced in each 

 successive division throughout the entire series, but the other com- 

 ponents and the meteorological irregularities will occur differently 

 in each division. 



Now, suppose that each of these divisions which corresponds to the 

 period of component A be subdivided into any number of convenient 

 parts, and that the initial instants of the subdivisions of each original 



