HAEMONIC ANALYSIS Ai^D PEEDICTIOI^ OF TIDES. 6T 



that day may be rejected and the following day adopted as the first 

 day of series, or the heights for the earlier hours on the original first 

 day may be estimated. The zero solar hour of the first day of the" 

 series is also adopted as the zero component hour of the first com- 

 ponent day for each component. Successive solar hours will fall 

 either earlier or later than the corresponding component hours ac- 

 cording to whether the component day is longer or shorter than the 

 solar day. 



For the construction of the stencils it is necessary to calculate the- 

 component hour that most nearly coincides with each solar hour of 

 the series. 



Let a = speed or rate of change in argument of component sought 

 in degrees per solar hour. 

 2) = number of component periods in component day; 1 for 



diurnal tides, 2 for semidiurnal tides, etc. 

 s^ = number of solar hour reckoned from at beginning of each 



solar day. 

 s^s = number of solar hour reckoned from at beginning of 



series. 

 dos = day of series counting from 1 as the first day. 

 c^ = number of component hour reckoned from O'at beginning 



of each component day. 

 chs = number of component hour reckoned from at beginning 

 of series. 



Then 



1 component period = solar hours. (258)" 



1 component day = solar hours. (259) 



IS© 



1 component hour = — - solar hours. (260) 



1 solar hour =—r- component hours. (261) 



Therefore, 



(cJis) =^{shs) =T^[24{ (dos) - 1} + (sh)] (262) 



lop lop 



The above formula gives the component hour of the series (chs) 

 corresponding to any solar hour of the series (slis). The observed 

 heights of the tide being tabulated for the exact solar hours of the 

 day, the (sJis) with which we are concerned will represent successive 

 integers counting from at the beginning of the series. The (chs) 

 as derived from the formula will generally be a mixed number. As 

 it is desired to obtain the integral component hour corresponding 

 most nearly -with each solar hour, the (cJis) should be taken to the 

 nearest integer by rejecting a fraction less than 0.5, or counting as 

 an extra hour a fraction greater than 0.5, or adopting the usual rule 

 for computations if the fraction is exactly 0.5. The component 



