23 



declination of the moon is zero, as the moon crosses the ascending 

 intersection of the moon's orbit with the celestial Equator. The 

 amplitude then decreases to a minimum when, a week later, the moon 

 has its maximum north declination; again increases to a maximum 

 when, in another week, the moon is at its descending intersection; 

 and decreases to a second minimum when the moon reaches its maxi- 

 mum south declination. The amplitude of the fluctuations of the 

 semidiurnal part of the lunar equilibrium tide therefore varies between 

 a maximum and a minimum twice during a tropical month. 



The amplitude of the fluctuations of the diurnal part of the lunar 

 equilibrium tide at any tidal station (except those on the earth's 

 Equator) varies with sin 2 8. It therefore increases twice during the 

 tropical month from zero, when the moon has a zero declination, to a 

 maximum when the moon has its maximum declination north or south 

 of the Equator. 



The amount of the variation in the amplitudes of the fluctuations 

 both of the semidiurnal and the diurnal parts of the lunar equilibrium 

 tide slowly changes with the inclination of the moon's orbit to the 

 Equator (par. 35) and hence with the longitude of the moon's node 

 (par. 36). 



41. Variations in the range of the actual tide with themooii's declina- 

 tion. — Since the equilibrium tides are a measure of the astronomical 

 causes of the actual tides, it may be expected that the part of the actual 

 tide due to the moon is made up of diurnal and semidiurnal elements, 

 each varying with the declination of the moon in the same manner 

 maimer as the equilibrium tides; the amount of the variation slowly 

 changing with the longitude of the moon's node. It does not follow 

 however that the diurnal and semidiurnal parts of the actual tides 

 change with the latitude in the same manner as the parts of the 

 equilibrium tide; for the latter, while affording a measure of the 

 astronomical causes of the variation in the tide at a particular station, 

 afford no indication of the relationship between 

 the tides at two different stations. 



42. Lunar jortnightly tide. — In figure 14, IMi 

 is the celestial Equator, IM the celestial circle 

 of the moon's orbit, / the intersection, M the 

 position of the moon at any time, NMMi the 

 hour circle through M. MiM is then the moon's 

 declination, 8. Let IM, the angular distance of 

 the moon from the intersection, be represented 

 hjl. Then in the right spherical triangle IMiM: 



sin 5 = sin I sin / (25) 



where / is the inclination of the moon's orbit to the Equator. 



Substituting this expression for sin 8 in the last term of equation 



(24), % a (Ma^/ER^) (1-3' sin^ X) (1-3 sin^ 5), this becomes 



