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THE SIOON :

18| years. Hence the inclination of the moon’s orbitto the equator is affected by an oscillation of rathermore than five degrees on either side of the mean in-clination, which is the same as that of the ecliptic tothe equator, or about 23| degrees. Thus the inclina-tion passes in the course of rather more than 18|years from about 18^ degrees to about 28^ degrees,and thence to about 18^ degrees again. Obviouslythe lunar action varies accordingly; and, moreover,it is to be remembered that if the lunar action werealone in question, the pole of the equator would circle,not about the pole of the ecliptic, but about the poleof the moon’s orbit-plane; and as this pole is itself Icircling about the pole of the ecliptic in a period of |rather more than 18^ years, it is readily seen thatthere will be a fluctuation in the motion of the pole ofthe heavens, having the same period. This fluctua- ,tion is necessarily small, because in 18^ years the whole jmotion due to precession is small,* and this fluctua- jtion is only a minute portion of the whole motion.

It is found to amount in fact to about 9" - 2, by whichamount the pole of the heavens, and with it the appa-rent position of every star in the heavens, is at amaximum displaced from the mean position estimatedfor a perfectly uniform precessional motion. Now, sincethis displacement (called nutation ) is solely dependent

* The 1360th part of the complete circuit made by the pole ofthe heavens round the pole of the ecliptic (less than 16' of a smallcircle of the heavens having an arc-radius of 23^ degrees), orabout 6.j' of arc.