24 



% a (MaySE^) (1-3 sin^ X) (1-3 sin^sin^ I). Again substituting for 

 sin^ I its equivalent, ji (1 — cos 21) the term reduces to the two terms: 



% a {Ma'/ER') (1-3 sin^ X) sin^ / cos 2l 

 -\-%a{Ma'/ER') (1-3 sin^ X) (1-3/2 sin^ I) 



The first of these terms evidently goes through two cycles from 

 to 360° while I is making one cycle in the tropical month. It is called 

 the lunar fortnightly component of the tide. 



The last term remains constant as the earth revolves about its 

 axis and the moon changes its declination. It represents therefore a 

 permanent distortion of the ocean surface, so far as these movements 

 are concerned. 



The substitution of the numerical of the constants in the expression 

 for the lunar fortnightly equilibrium tide shows that, at the earth's 

 Equator, its range varies from 0.086 foot when the inclination of the 

 moon's orbit is a minimum, to 0.20 foot when the inclination is a 

 maximum. The range decreases to zero at a latitude of 35°16' north 

 or south of the Equator, increasing again toward the poles. The 

 actual fortnightly tide is correspondingly small. At most tidal sta- 

 tions tliis component produces, however, a fortnightly fluctuation of 

 an inch or more in the daily mean height of the sea. 



43. Effect of eccentricity of the moon's orbit. — As the moon travels its 

 orbit, its distance, R, from the earth varies. The point at which it is 

 nearest the earth is its perigee, and the point at which it is the most 

 distant is its apogee. Because of the disturbing effect of the attraction 

 of the sun, the moon's orbit varies somewhat, but its distance from the 

 earth at apogee ordinarily exceeds by more than 10 percent the dis- 

 tance at perigee. The moon makes the circuit from perigee to perigee 

 in the anomalistic month of 27 days, 13.309 hours. Since the coeffici- 

 ents of the terms in equation (24) each contain the factor l/i?^ the 

 amplitudes of the diurnal and semidiurnal parts of the lunar equilib- 

 rium tides, as derived from these terms, tend to vary from a maximum 

 to a minimum once during the anomalistic month, as well as varying 

 twice during the tropical month because of the changing declination 

 of the moon. A corresponding variation may be expected in the actual 

 tides. 



To gage the amount of the variation in the tides because of the 

 elliptical form of the moon's orbit, let P be the distance of the moon 

 at perigee and ^=P+c^ its distance at apogee. The ratio of the ampli- 

 tude of the equilibrium tides at perigee to those at apogee is then 



{}iMayEP')/(%MayEA')=AyP'={P^dYIP^ 



= 1+3 d/P+d (d/Py+{dJPY (26) 



