You will observe here an instance of the sort of untruth which it is almost imperative to tell in explaining natural phenomena. Hitherto I had spoken only of the sun as producing precession of the earth. This was convenient, because the plane of the ecliptic makes always almost exactly 23½° with the earth's equator, and although on the whole the moon's action is nearly identical with that of the sun, and about twice as great, yet it varies considerably. The superior tilting action of the moon, just like its tide-producing action, is due to its being so much nearer us than the sun, and exists in spite of the very small mass of the moon as compared with that of the sun. As the ecliptic makes an angle of 23½° with the earth's equator, and the moon's orbit makes an angle 5½° with the ecliptic, we see that the moon's orbit sometimes makes an angle of 29° with the earth's equator, and sometimes only 18°, changing from 29° to 18°, and back to 29° again in about nineteen years. This causes what is called "Nutation," or the nodding of the earth, for the tilting action due to the sun is greatly helped and greatly modified by it. The result of the variable nature of the moon's action is then that the earth's axis {87} rotates in an elliptic conical path round what might be called its mean position. We have also to remember that twice in every lunar month the moon's tilting action on the earth is greater, and twice it is zero, and that it continually varies in value. On the whole, then, the moon and sun, and to a small extent the planets, produce the general effect of a precession, which repeats itself in a period of about 25,695 years. It is not perfectly uniform, being performed at a speed which is a maximum in summer and winter; that is, there is a change of speed whose period is half a year; and there is a change of speed whose period is half a lunar month, the precession being quicker to-night than it will be next Saturday, when it will increase for about another week, and diminish the next. Besides this, because of 5½° of angularity of the orbits, we have something like the nodding of our precessing gyrostat, and the inclination of the earth's axis to the ecliptic is not constant at 23½°, but is changing, its periodic time being nineteen years. Regarding the earth's centre as fixed at O we see then, as illustrated in this model and in Fig. 40, the axis of the earth describes almost a perfect circle on the celestial sphere once in 25,866 years, its speed fluctuating every half year and every half month. But it is not a perfect circle, it is really a wavy {88} line, there being a complete wave every nineteen years, and there are smaller ripples in it, corresponding to the half-yearly and fortnightly periods. But the very cause of the nutation, the nineteen-yearly period of retrogression of the moon's nodes, as it is called, is itself really produced as the precession of a gyrostat is produced, that is, by tilting forces acting on a spinning body.