44 



ponent is not affected by overtides of any substantial amplitude. 

 A complete analysis for a year confirms this fact. This symmetry 

 shows also that a summation for even this short period nearly elimi- 

 nates the other components. 



82. The computation of the S2 component in paragraph 80 is ar- 

 ranged to illustrate the process most directly. In the conventional 

 form of computation, the observed hourly heights, numbered from 

 to 23 each day, are entered in daily vertical columns on standard 

 sheets. The S group of components is computed by summing the 

 observed heights horizontally, the aggregates of these sums being 

 checked against the aggregate of the sums of the daily columns. 

 The amplitude and the initial phase of each component of the S 

 group are then computed from the average hourly heights of the whole 

 set of observations by a method to be explained later. 



83. Separation oj other components. — The observed tidal heights at 

 each mean lunar hour similarly could be taken off and tabulated by 

 lunar days, and the M group of components segregated by averaging 

 the tidal heights at each hour of the lunar day. In like manner all 

 of the components could be determined by averaging the tidal heights 

 at their component hours, tabulated by component days. The process 

 of taldng off new observed tidal heights for each of the several com- 

 ponents would be a laborious one. Instead, the height at each lunar 

 or other component hour is taken as the observed height at the nearest 

 mean solar hour. These heights are sometimes a little greater and 

 sometimes a little less than the true heights at the component hour, 

 but their average over a sufficient number of days closely approximates 

 the average at the given component hour. The same process of averag- 

 ing which separates the component sought from the others, reduces 

 the observed heights as taken at the nearest mean solar hour to the 

 heights at the component hour. The correction for a small systematic 

 error resulting from the process is developed in paragraph 97. 



84. Component days and hours. — To select the observed mean solar 

 hourly heights which are to be taken as the component hourly heights, 

 a tabulation is prepared showing the component hour nearest to each 

 solar hour on each successive calendar day. For diurnal components, 

 the component day is the period of the component, and the component 

 hour, one twenty-fourth part of that period. For semidiurnal com- 

 ponents, the component day is twice the period of the component, 

 and the component hour is one-twelfth of the period. For components 

 of shorter periods, the component day is that multiple of the period 

 nearest to a mean solar day. It will be observed that the com- 

 ponents Ml, M2, M3, M4, Me, and Mg aU have the same component 

 hour; and that the components Ki and K2 similarly have the same 



