35 



SPEEDS OF THE TIDAL COMPONENTS 



64. Semidiurnal lunar components.— It has been shown m para- 

 graphs 40 and 41 that the amphtude of the semidiurnal part of the 

 lunar tide increases and decreases twice during the tropical month 

 because of the changing declination of the moon, and in paragraph 43 

 that it increases and decreases once during the anomalistic month 

 because of its changing distance. Since the effect of one of these 

 variations on the other is small, these variations may be reproduced 

 by a combination of a major component and two pairs of minor com- 

 ponents in the form indicated in paragraph 57; i. e., 



y=M.2 cos (m2^+Q:i)+K2 cos [(m2+6)^+Q!2]+K2 cos[(m2— 6)^+q!3] 

 +L2 cos [(m2 + c)i+«4] + N2 cos [{m.2—c)t+a^] (38) 



In equation (38), M2 is the amplitude of the major component. 

 Its speed m2 is the mean speed of the semidiurnal component of the 

 tide, and is therefore twice the speed of a lunar day, or 28. °984, 104,2 

 per mean solar hour (par. 55) . 



Either or both of the next two terms will produce a variation in 

 the amplitude of the resultant, of the same period as the varia- 

 tion in the amplitude of the actual tide due to the changing decli- 

 nation of the moon, if 360°/6 is made equal to that period (par. 54). 

 Since the period of these fluctuations is one half of a tropical month, 

 h is twice the "speed" of the tropical month, or l.°098, 033,0 per 

 mean solar hour. The relative amplitudes of this pair of minor 

 components should produce a variation in the speed of the resultant 

 conforming to the variation in the speed of the semidiurnal tide, and 

 hence in the true speed of the hour angle of the moon, due to the 

 changing declination of the moon. Since, when the effect of the vary- 

 ing declination is alone considered, the hour angle reaches its maxi- 

 mum speed when the declination is zero (par. 60) and the ampli- 

 tude of the semidiurnal part of the lunar equilibrium tide is then 

 a maximum (par. 40), the component with the greater speed, 

 K2 cos [{m.2-^ h)t + ao] must be the dominant one of the pair (par. 57). 

 A mathematical derivation of the tidal components, later outlined, 

 shows that this component correcth^ reproduces the entire variation 

 in the amplitude of the semidiurnal part of the lunar equilibrium tide, 

 and hence of the actual tide as well, because of the changing declina- 

 tion of the moon. The third term in equation (38) therefore dis- 

 appears. 



Similarly either or both of the fourth and fifth terms of equation 

 (38) will produce a variation in the amplitude of the resultant of the 

 same period as that of the actual tide due to the changing distance 

 of the moon if 360°/c is made equal to the anomalistic month, or if c 

 is the speed of the anomalistic month, 0.°544,374,7 per mean solar hour. 



