HAEM0:N'IC AISTALYSIS AND PEEDIGTION OF TIDES. 13 



be noted. The angle between the ecHptic and the celestial equator 

 CO is known as the obliquit}" of the ecliptic. Its value is about 23^° 

 at the present time, but it is subject to a very slow secular change 

 (see Tables 1 and 2). The angle i, measuring the inclination of the 

 moon's orbit to the ecliptic, has a consta,nt value of a little more 

 than 5°. The angle /, measuring the inclination of the moon's 

 orbit to the plane of the earth's equator, varies in value from oo — i 

 to aj + -i; that is, from about 18| to 28^°. The complete cycle of 

 this variation is approximately 19 years, so that if the angle is 18^° 

 in any year it will gradually increase for about 9-| years until it 

 reaches its maximum value and then diminish for about 9^ years 

 until it returns to its minimum value. 



The vernal equinox T although subject to a very slow westward 

 motion, known as the procession of the equinoxes, which amounts 

 to only about 50 inches per year, is frequently taken as a fixed point 



Fig. 6. 



of reference for the motion of the other parts of the solar system. 

 The moon's node Q, has a vs^estward motion of about 19° a year, 

 which is sufficient to carry it entirely around a great circle in approxi- 

 mately 19 j'^ears. It is upon this motion that the variations in the 

 value of the angle / depend, and it is of considerable importance in 

 its effects upon the tides. 



In the celestial sphere the terms "'latitude" and ''longitude" 

 apply especially to measurements referred to the ecliptic and vernal 

 equinox, but the terms may with propriety also be applied to meas- 

 urements referred to other great circles and origins, provided they 

 are sufficiently well defined to prevent any ambiguity. For example, 

 we ma}'' say "longitude in the moon's orbit measured from the 

 moon's node. " Celestial longitude is always understood to be 

 measured toward the east entirely around the circle. Longitude in 

 the celestial equator reckoned from the vernal equinox is called 

 right ascension, and the angular distance north or south of the 

 celestial equator is called declination. The true longitude of any 

 point referred to any great circle in the celestial sphere may be 



