266 



Applying the numerical values of the speeds of the various com- 

 ponents and the mean values of the coefficients of the corresponding- 

 equilibrium components, tliis reduces to: 



Mn=2M2{l.0717 + 0.03585(Ki+Oi)7M22}. (19A) 



Designating the reduction factors of the several components as 



/(M2), /(N2), /(K2), etc., and their squares as fiMi), /(K2), etc., 

 and noting that /(M2)=/(N2) and /(Qi)=/(0,) and that 1//(M2)- 

 F(M.2); equation (17A) similarly reduces, after applying the same 

 numerical values to the amplitudes and speeds of the components, to : 



Mn'=2M2/(M2){l.009+F2(M2)[0.0583 + 0.0043/(K2)] 

 +i^'(M2) ((Ki+Oi)/M2)'[0.0025+0.0230/(Ki) 

 + 0.0103/(Oi)]}. (20A) 



Designating for brevity the expressions within the brackets in 

 equations (19A) and (20A) as R and R' respectively: 



F{Mii)=Mn/Mn'=2M2R/2M,f(M2)R' = FiM2)R/R'. (21A) 



The M2 component may be considered the dominant one when it 

 is not less than Ki + Oi. The values of F{Mn) for a given value of 

 the inclination of the moon's orbit, /, and of the ratio (Ki + 0i)/M2, 

 when the latter does not exceed unity, may then be found from 

 equation (21 A) by substituting in this equation and in the expression 

 for R' the values of -F(M2), J(K2), etc., corresponding to the value 

 of /, as given in the tables contained in manuals on the harmonic 

 analysis of the tides. The determination of the values of F{Md.) for 

 values of (Ki+OO/Mo exceeding unity becomes more complicated 

 and need not be here described. The values of i^(Mn) are shown 

 in table VI, paragraph 173. 



Derivation of I.O2F1 



13. The factor I.O2F1 is applied to the low- and high-water in- 

 equalities, DLQ and DHQ, derived from observations during a month 

 or more, to reduce these inequalities, and the consequent elevations 

 of mean lower low and higher high waters, to their astronomical 

 long-term means (par. 189). The diurnal inequalities are due to 

 the diurnal components of the tide at the station. Since the equi- 

 librium components have the same relation to their long-term means 

 as the actual components, the expression for the reduction factor 

 may be derived from the diurnal equilibrium components. For this 

 purpose only the Ki, Oi, and Pi components need be considered; 



