19 



angular distance of the moon from the equator. This angle is the 

 declination of the moon. The solar equilibrium tides vary similarly 

 with the declination of the sun. It may be noted that the solar 

 equilibrium tides are equal when the days and nights have the same 

 length, and that the inequality of the two daily tides when the moon 

 or sun are off the equator is for a cause analogous to that of the 

 inequality of the days and nights. 



35. Periodic variations in the declinations of the sun and moon. — The 

 changes in the form and range of the equilibrium tide at a given station 

 produced by the changing declinations of the moon and sun, and the 

 corresponding changes in the actual tides, obviously run through 

 cycles whose respective periods are the periods of the declinations. 

 It will be recalled that as the sun moves along the ecliptic, its apparent 

 path on the celestial sphere, it crosses the celestial circle of the earth's 

 equator, and has therefore a zero declination, at the vernal equinox, 

 passing this point yearly in the latter part of March. It then ascends 

 north of the equator and its declination reaches a maximum angle of 

 23°. 452 at the summer solstice, late in June. Tliis angle is the in- 

 clination of ecliptic to the equator, and may be considered as constant 

 so far as tidal computations are concerned. At the summer solstice 

 the sun is directly overhead at noon on the tropic which separates the 

 torrid from the temperate zone in the northern hemisphere. The sun 

 again crosses the equator at the autumnal equinox in late September, 

 and reaches its maximum negative (south) declination of — 23°.452 at 

 the winter solstice in late December. The period of its travel from 

 vernal equinox to vernal equinox is the tropical year of 365 days^ 

 5.813 hours. 



The moon, in its movement along the celestial circle marking its 

 orbit, similarly crosses the earth's celestial equator monthly at the 

 ascending intersection, reaches a maximum north (positive) declination 

 in about a week, again crosses the equator at the descending intersec- 

 tion in another week, to reach its maximum south (negative) declina- 

 tion . The period of its travel, from ascending intersection to ascend- 

 ing intersection, is the tropical month of 27 days, 7.718 hours. 



The points at which the moon's celestial orbit crosses the ecliptic 

 are called its ascending and descending nodes, respectively. The plane 

 of the moon's orbit has a constant inclination of 5°. 145 to the plane 

 of the ecliptic, but because of a slow retrograde movement of the 

 moon's nodes along the ecliptic, the inclination of the moon's orbit to 

 the equator, and hence the maximum montlily declination of the 

 moon, slowly varies. The moon's node makes the circuit of the eclip- 

 tic in approximately 19 years. 



