25 



Neglecting the squares and cubes of tlie ratio djP, it is apparent 

 that the variation in the equihbrium tide is three times the variation in 

 the distance to the moon. As the ratio djP usually exceeds 10 per- 

 cent, the amplitudes of the diurnal and semidiurnal lunar equilibrium 

 tides are subject to a variation of 30 percent or more during the 

 anomalistic month. This variation is sometimes called the parallax 

 inequality, since the distance to the moon is measured by its parallax 

 (par. 15). 



The lunar fortnightly component of the tide is so small that its 

 parallax inequality is not taken into consideration. The variation in 

 B, produces, however, a variation in the fixed term: 



)ia{Ma^lEB')l{l-^ sin' X) (l-^sin^ /) 



developed in paragraph 42, giving rise to a small monthly tidal com- 

 ponent with the period of an anomalistic month. 



44. The solar equilibrium tides. — The equilibrium tide due to the 

 sun is similarly made up of a semidurnal part, which goes through 

 two complete cycles in a mean solar day of 24 hours; a diurnal part 

 which goes through one cyle per day; both of which vary with the 

 declination of the sun ; together with a semiannual component of rela- 

 tively small range. Since the eccentricity of the earth's orbit around 

 the sun is much less than the eccentricity of the moon's orbit, the 

 parallax inequalities of the solar equilibrium tides are small m compar- 

 ison with those of the lunar equilibrium tides. 



45. As will be shown in the following chapter, the varying semi- 

 diurnal and diurnal fluctuations of the tide, because of the changing 

 declinations of the sun and the moon, and the varying distances 

 of the earth from these bodies, may be resolved into components of 

 fixed amplitudes with periods not far from 12 hours and 24 hours 

 respectively. 



THE ACTUAL TIDES 



46. The actual fluctuations of the surfaces of the oceans because of 

 the tide-producing forces are somewhat akin to the slopping around 

 of the water in a basin on a moving train. The momentum of the 

 moving masses in the deep seas tends to pile up the water in the 

 shallow depths along the coasts, producing tides whose ranges may 

 greatly exceed the range of the equlibrium tide. The tidal ranges at 

 different points along the shores, and the times of high and low water, 

 depend upon the contour of the ocean beds and the conformation of 

 the coasts and cannot be determined by abstract calculation. The 

 relation of the times of the actual to the equilibrium tides may possibly 

 be more apparent if the varying pull upon the waters of the oceans 

 due to the attraction of the moon and sun be conceived to be replaced 



