Appendix II 



REDUCTION FACTORS F(Mn) AND 1.02 F, AND CORRECTION 



FACTOR ijB. 



Derivation of F (Mn) 



1. As pointed out in paragraph 171, the mean range, Mn, at a tidal 

 station varies shghtly with the inclination, /, of the moon's orbit. 

 The factor 7^(Mn) is applied to reduce a mean range derived from 

 observations extending over a month or year to the true mean value 

 during the 19-year period in which the orbit tilts to and fro as the 

 moon's node makes the chcuit of the ecliptic (par. 35). The values 

 of FQAvl) are derived from the relation between the mean range and 

 the harmonic components of the tide at a station. 



2. Relation of high water to the amplitude of the M2 component. — At 

 most tidal stations the M2 component is so much larger than the 

 others that high water occurs near the time at which the ordinate of 

 this component is a maximum. 



In figiu-e 1, CP is the generating radius of the M2 component at an 

 instant when its ordinate is a maximum, CR is the radius vector of the 

 Y resultant of all of the compo- 



nents at that instant, deter- 

 -;=:-==-i — -^ mined bv drawing successive 

 I lines i3arallel and equal to the 



[ generating radii of the other 



-At-^ components (par. 51), and TH 



^ is the ordinate of the resultant 



on the tide curve. At the high 

 water immediately ensuing (or preceding), the radius vector of the 

 resultant is CR', nearly, if not quite, coinciding with the Y axis, 

 its ordinate on the tide curve is T'H', and CP' is the position of the 

 generating radius of the dominant component. Let At be the time 

 interval in which R moves to R' and P to P'; v, the corresponding 

 angle between CP and CP'; and let T'H'—TH=Ay. 



3. The height of mean high water above sea level is the mean of the 

 successive values of TH plus the mean value of Ay. Since the succes- 

 sive values of TH occm- at intervals equal to the period of the prin- 

 cipal com.ponent, and at the instants at which this component is a 

 maximum, their mean is the amplitude, M2, of this component, 



(260) 



FiGPBE 1. 



