~~— » I Toward the Moon or Sun (' 



Figure 9. Tide-producing forces. The arrows represent the magnitude and 

 direction of the horizontal component of tlie tide-producing 

 force on the Earth's surface: A— when the Moon is in the plane 

 of tlie Equator, the forces are equal in magnitude at the two 

 points on the same parallel of latitude and 180° apart in 

 longitude; B— when the Moon is at north (or soutli) declination, 

 the forces are unequal at such points and tend to cause an 

 inequality in the two high waters and the two low waters of a 

 day (Bowditch, 1958). 



It is not so widely known that the plane of the lunar orbit is inclined to the plane of the 

 terrestrial orbit by an angle of 5° 8'. Thus, the Moon may appear to be as much as 5° 8' north 

 or soutli of the Sun. If the Moon appears to be 5°8' north of tlie Sun near the summer 

 solstice when the Sun appears to be 23° 27' north of tlie Equator, the Moon wUl appear to be 

 23° 27' + 5° 8' or 28° 35' north of the Equator. This would correspond to a time of 

 maximum inequaHty between the two daily semidiurnal tides. If the Moon appears to be 

 5° 8' south of the Sun when the Sun is 23° 27' north of the Equator, the Moon wiU be only 

 18° 19' north of the Equator. Altliough this corresponds to the maximum diurnal equalitj' 

 of the fortnight, the inequahty will be less than for the case when both Sun and Moon are 

 near the most nortliern part of their orbits. The Moon, Uke the Sun, appears to be over the 

 Equator twice within each north-south cycle, wliicli for the Moon consists of 27.212220 

 solar days. Tliis period is called an anomalistic month. When tlie Moon is above the Equator, 

 the two tidal bulges each day due to the Moon are nearly equal in each hemisphere. The 

 maximum inequaUties in the tides occur on or near tlie days on which the Moon is at the 

 nortliern or soutliern extremes of its orbit. The complete lunar orbit of the Earth, measured 

 with respect to the vernal equinox requires tlie slightly longer tropical montli of 27.321582 

 solar days. The two nearly equal tidal bulges which occur when the Sun is over the Equator 

 are called equatorial tides. The unequal bulges which coincide with tlie northern and 

 southern limits of the lunar orbit are called tropical tides. 



The functions of z, required by equation (15), can be expanded as a polynomial of 

 trignometric functions depending on the periods discussed above. These polynomials can be 

 converted into simple sums of trignometric functions by the repetitive use of trignometric 

 identities or the binomial theorem. 



These expansions yield two sets of trignometric functions, one depending on the Moon 

 and the other on the Sun. A few terms are common to both series. 



