HAHMOI^IC A^sTALYSIS AND PREDICTION OF TIDES. 91 



(Vq + u) properly refers to the actual time of the beginning of such 

 series. In the usual analysis where the stencils, or similar devices, 

 are used for the summations it is of great convenience to have all 

 series commence at the zero (0) hour of some day. The absolute 

 time of occurrence of this (0) hour will depend upon the kind of time 

 used at the place of observation, which may be either civil or astro- 

 nomical, local or standard. 



In order to provide convenient tables of (Vq + u) which may be 

 easily adapted to any place or kind of time, the Greenwich (^0 + '^) 

 referring to the Greenwich standard time may be used. In this work 

 the reference is to Greenwich mean civil time, but the tables might 

 with equal propriety have been referred to astronomical time had 

 the latter been considered equally convenient. 



The rate of change in the ( V+ u) of any component is the same as 

 the speed of the component. Let.c be its ratio to speed of mean 

 sun. The difference between the Greenwich (V^ + u) and the local 

 (Vq + u), due to the difference in the reference to the Greenwich zero 

 hour and zero hour of the kind of time used for the observations, 

 may therefore be expressed by cS in which S is the longitude of time 

 meridian used for the observations, positive for west longitude, 

 negative for east longitude. Combining the last correction with 

 formula (339), the relation between the local and Greenwich {Vq + u) 

 may be expressed, 



local ( Fo + w) = Greenwich {Va + u)-p L+ c S (340) 



In section 10 attention was called to the distinction between the 

 Vq and the u. The V^ is independent of the length of series and is 

 determined entirely by the beginning of the series. The u, which is 

 treated as constant for the entire length of series, takes its value as 

 of the middle of the series and depends, therefore, both upon the 

 beginning and length of series. In the table of Greenwich (Fo + 'u)'s, 

 the series is taken as one calendar year in length, as the table is 

 designed primarily for preparing constants for the prediction of tides. 

 For the analysis, however, an independent calculation of the local 

 {Vq + u)'s for each series is made in Form 244, Figure 27, which is based 

 upon the formulas of Table 3. Applying these to the f's in accord- 

 ance with formula (338) gives the corrected k's of the components 



The amplitude A as determined from formula (325) must be 

 modified by the argumenting factor, section 27, and Table 20. The 

 resulting amplitude usually designated by R will pertain to the 

 particular time covered by the observations and must be reduced 

 to its mean value H in accordance with section 12. The reduced 

 values of the amplitude H and the epoch k of the component 

 formula 



y^H cos {at +Va + u-K) (341) 



are thus determined, but before final acceptance must be subjected 

 to an elimination process to be discussed in the following sections. 



29. INFERENCE OF CONSTANTS. 



Under the conditions assumed for the equilibrium theory the 

 amplitudes of the components could be computed directly by means 

 of the coefficient formulas without the necessity of securing tidal 



72934— 24t 7 



