69 



The value of N at the middle of the period was found in paragraph 

 119 to be 24°. 17. The corresponding tabular value of /is 28°.22; 

 and for tliis value the tabular value of log F for the M2 component is 

 0.0148. 



Then log i?=0.5353 



log F= .0148 



logiJ= .5501 

 iJ=3.549 



The value of H derived from a year's observation is 3.591 (table V, 

 par. 134). 



Since solar components do not vary with I, no reduction factor is 

 to be applied to them. 



128. Reduction factors for other components. — It has been seen that 

 for the M2 component 



ct>ir)=cos^ %I u=2^—2v 



The corresponding expressions for the M3 component are, from 

 equation (80): 



0(/)=cos*^ yj w=3^— 3^ 



Since cos® /2/= (cos^ ){!) ^''^^ it may be presumed that the reduction 

 factor for the M3 component is 



F= (F of M.y' 



and this relation is established by a detailed analysis. 



Similarly the reduction factor for the lunar overtides are taken as 

 the squares, cubes, etc., of the fundamental tide. These factors are 

 then: 



For M4, F= {F of M2)-; M„ F= (F of M2)^ and so on. 



No reduction factors are to be applied to the solar overtides. 



The factors for compound tides are taken as the products of the 

 factors of the components compounded, the factor for any solar 

 component entering into the compound tide being unity. 



129. "Mean values of coefficients." — An examination of equations 

 (68) and (69) shows that the amplitude of each semidiurnal com- 

 ponent of the equilibrium tide is the product of a coefficient, whose 

 numerical value may be determined from astronomical data, times 

 cos^X; the amplitude of each diurnal component is a coefficient times 

 sin 2X; and the amplitude of each long period component a coefficient 

 times (1/2 — 3/2 sin-X). The mean values of these coefficients there- 

 fore show the relative magnitudes of the mean values of the ampli- 

 tudes of the semidiurnal, diurnal, and long-period equilibrium com- 

 ponents, respectively, at a given station. The "mean values of the 



