HAEMONIC ANALYSIS AND PREDICTION OF TIDES. 47 



F for terms {A)^^ to {A)^^, including component lunar (Kg), 



sin^ (o [1-3/2 sin2 i] 0.1565 ,,^^, 

 ^mTT ==^mrr (1^^) 



F for terms (^)26 to (-4)33, including components O^, Qj, 2Q, and p^, 



_ sin (jd cos^ I CD cos* ^ i _ 0.3800 nfi?^ 



sin / cos^ ^ I sin / cos^ ^ I 



F for term (^) 34 for component 00 



_ sin (o sill' ^ CD cos* i '^ _ 0-0164 nR8^ 



sin / sin^ 1 / sin / sin^ 1 / ^^^^'' 



Ffor terms {A)^2 to (^)48, including components lunar (KJ and J^, 



sm 2 CD [1 - 3/2 sin2 -^J 0.7214 „^^, 



= imTT = Sr27 (1^^) 



Ffor terms (^)5i to (-4)55, including component Mf, 



_ sin^ CO cos* i ^ _ 0.1578 



sin^ / ~ sin^ / ^^^^^ 



FioT terms (^)5o to (A)^^, including component Mm, 



^ (1 - 3/2 sin^ oj) (1 - 3/2 sin^ i) ^ 0.7532 



1-3/2 sin^/ 1-3/2 sin^/ ^^'^^ 



The last is also the factor of reduction for the equilibrium com- 

 ponent MSf; but as there is also a compound component having the 

 same argument and generally a greater amplitude, which unites with 

 the equilibrium component, the factor of reduction is usually deter- 

 mined from the compound part, which will be discussed in a later 

 section. The factor of reduction for a number of other special cases 

 will be treated separately in the text. 



The factor / may, of course, be readily obtained by taking the 

 reciprocals of the above expressions for the factor F. 



Table 12 gives the logarithm of the factor F for the principal 

 components corresponding to every tenth of a degree of /, and Table 

 14 gives the natural factor / for the principal components for the 

 middle of each year from 1850 to 1999. 



13. THE L2 TIDE. 



The separation of the components from each other by the processes 

 of the analysis depends upon the differences in the speeds of the 

 components. If two components have speeds that are very nearly 

 equal, the analysis of a series of observations, unless of a very long 

 period, will not separate such components from each other but will 

 give a single component that is a resultant of the two. Referring to 

 equation (100), we note that the speeds of the terms (^)3 and (4.), 9 

 are very nearly equal, the difference being twice the rate of change 

 in p, the longitude of the .moon's perigee, and this changes only 

 about 41° in an entire year. 



