265 



lative increase in the observed high water, and, similarly a cumulative 

 depression of the observed low water. Equation (16A) establishes, 

 however, a logical basis for determining the corrections to be made 

 for the changing inclination of the moon's orbit to the Equator. 



10. Numerical value of F(M.i\). — The amplitudes of the various 

 lunar tidal components during any particular year (or month) are 

 determined by applying the appropriate factor /=l/i^ to the recorded 

 mean values of these amplitudes (par. 125). For solar components, 

 the value of/ is unity. The expression for the mean tidal range during 

 any particular year is then : 



Mn'-2yxMo{l + )^[(S2S2//M2m2)2+ {m,n,lfM,m2y+ {j'^,\i,im2m,y 



+ (/Qiqi//xM2m2)2]} (17A) 



The factor to be applied to reduce the mean tidal range, as deter- 

 mined from observations during a particular year, to its true mean 

 value is therefore: 



i^(Mn)=Mn/Mn' (18A) 



in which the value of Mn is given by equation (16 A) and the value of 

 Mn' is given by equation (17A). 



11. The computation of the value of F (Mn) for the true ratios of 

 the amplitudes of the actual components of the tide at a tidal station, 

 and for the successive values of the reduction factors / corresponding 

 to the inclination / of the moon's orbit to the equator, would be a 

 very laborious process, not justified by the accuracy of the results 

 secured. A sufficient approximation is afforded by taking for the 

 ratios of the semidiurnal components the ratios of the mean values of 

 the coefficients of the corresponding equilibrium components, set 

 forth in table IV, paragraph 129. The ratios of the amplitudes of 

 the diurnal components to M2 vary widely at different tidal stations, 

 but these amplitudes have a fairly consistent ratio between themselves. 

 The index for the amplitude of the diurnal components is therefore 

 taken as the ratio of Ki + Oi to M2 at the tidal station, the ratio of 

 the diurnal components to Ki+Oi being taken as that of the mean val- 

 ues of the coefficients of the corresponding equilibrium components, 

 as given in the same table. 



12. Equation (16A) may be written: 



Mn=2M2{l + (S2S2/2M2m2)'+ (Non2/2M2mo)-^+ (K2k2/2M2m2)2 



+ [(Ki + O07M2'][(Kiki/2(Ki+O0m.)'+(OiOi/2(Ki+Oi)m2)^ 

 + (PiPi/2(Ki + O0m2)^+(Qiq/2(Ki + O0m2)^]}. 



