42 



same solar hour each succeeding day. The progressive variation of 

 the M2 component, whose period is 12.420 hours, is illustrated for 

 example, in figure 23, in which Pi P2, and P3, etc., show the relative 

 values of the component at 3 a. m. on 3 successive days; the amphtude 

 and initial phase of the component being taken at random. In this 



Figure 23.— Variation in M2 component at given solar hour. 



progressive variation, these components run through their entire 

 range of values, both positive and negative. 



While, therefore, the sum of the successive values of the S group of 

 components at a given hour over a period of days increases directly 

 with the number of days in the period, the average value remaining 

 constant, the sum of all other components at that hour does not so 

 increase. On the contrary, at the intervals at which the positive 

 and negative values of a component offset each other, the sum of the 

 values of that component nearly disappears. If the number of days 

 in the period is suitably chosen, the average value of the resultant of 

 all of the components at a given hour reduces therefore to nearly the 

 value of the S group at that hour. 



79. The observed hourly tidal heights are ordinarily scaled from 

 the record of a recording tide gage, and give these heights above an 

 arbitrarily chosen datum, usually set low enough to make all of the 

 readings positive. Each of the recorded heights is then the algebraic 

 sum of the height of mean sea level above datum, plus the resultant 

 of all the tidal components at the hour, plus the accidental variations 

 due to meteorological disturbances, as well as to inaccuracies of 

 observation. The average of the heights at a given hour of the day 

 over a suitably chosen number of days, then closely approximates 

 the height of the resultant of the S group of components at that hour 

 above the datum plane, the other components, together with the 

 accidental variations, being averaged out by the process. 



80. Example. — The period of the diurnal component Ki is so close to 

 that of the Si component that 6 months of observations are necessary to 

 segregate the S group of components as a whole. The principal 

 solar component, S2 (with the overtides) may however be approxi- 

 mately determined from a set of observations extending over 15 days. 



