267 



since, as shown in table IV, paragraph 129, the amplitudes of the 

 other diurnal equilibrium components are relatively small. 



14. The resultant of the diurnal components may be termed the 

 diurnal wave, and its varying amplitude designated Z>i. The diurnal 

 wave increases one of the two daily high waters of tides of the semi- 

 diurnal and mixed types, and decreases the other. Since the diurnal 

 wave keeps in general step with the semidiurnal tidal fluctuations, 

 the consequent diurnal inequalities durmg any period is taken as 

 proportional to the mean value of Z>i during that period. 



15. Long-term mean value of Dx. — As Ki is the largest diurnal 

 equilibrium component, the approximate long-term mean value of 

 Di is, from equation (14A): 



L>m=Ki[l + (OiOi/2KjM)^+(PiPi/2Kik:)2]. 



The corresponding long-term mean value of the resultant of the 

 Ki and Oi components only is: 



i?m=Ki[l + (OiOi/2Ki^i)2]. 

 Whence : 



VmjRm^l + (Pipi/2Kiki)7[l + {0,o,l2K,hY]. 



By substituting the speeds and the mean values of the coefficients 

 of the components, the long-term mean value of Z>i is found to be 

 approximately 1.02 times the mean value of the resultant of the Ki 

 and Oi components only. 



The amplitude of the resultant of the Ki and Oi components 

 fluctuates between Ki+d, and Kj— Oi during the period of one-half 

 a tropical month. Its mean value may be written: 



Em=C(Ki+Oi). 



In which C is a constant which need not here be determined. 

 The long-term mean value of Di is then: 



Z)7/i=1.02(7(Ki+Oi). (22A) 



16. Monthly mean value ojDi. — During a month in which the moon's 

 declination is /, the amplitudes of the Ki and Oi equilibrium com- 

 ponents are Ki/(Ki) and Oi/(Oi) respectively, /(KO and/(Oi) being 

 the reduction factors for this value of 7. Since Pi is a solar com- 

 ponent, its amplitude remains constant. It combines with the Ki 

 component into a resultant whose amplitude fluctuates between a 

 maximum and a minimum in a period of the half tropical year. The 

 angle between this resultant and the Ki component changes but 



192750—40 18 



