The precession of the earth is then of the same nature as that of a gyrostat suspended above its centre of gravity, of a body which would be stable and not top-heavy if it were not spinning. In fact the precession of the earth is of the same nature as that of this large gyrostat (Fig. 22), which is suspended in gymbals, so that it has a vibration like a pendulum when not spinning. I will now spin it, so that looked at from above it goes against the hands of a watch, and you observe that it precesses with the hands of a watch. Here again is a hemispherical wooden ship, in which there is a gyrostat with its axis vertical. It is in stable
equilibrium. When the gyrostat is not spinning, the ship vibrates slowly when put out of equilibrium; when the gyrostat is spinning the ship gets a motion of precession which is opposite in direction to that of the spinning. Astronomers, beginning with Hipparchus, have made observations of the earth's motion for us, and we have observed the motions of gyrostats, and we naturally seek for an explanation of the precessional motion of the earth. The equator of the earth makes an angle of 23½° with the ecliptic, which is the plane of the earth's orbit. Or the spinning axis of the earth is always at angle of 23½° with a perpendicular to the ecliptic, and makes a complete revolution in 26,000 years. The surface of the water on which this wooden ship is floating represents the ecliptic. The axis
of spinning of the gyrostat is about 23½° to the vertical; the precession is in two minutes instead of 26,000 years; and only that this ship does not revolve in a great circular path, we should have in its precession a pretty exact illustration of the earth's precession.
The precessional motion of the ship, or of the gyrostat (Fig. 22), is explainable, and in the same way the earth's precession is at once explained if we find that there are forces from external bodies tending to put its spinning axis at right angles to the ecliptic. The earth is a nearly spherical body. If it were exactly spherical and homogeneous, the resultant force of attraction upon it, of a distant body, would be in a line through its centre. And again, if it were spherical and non-homogeneous, but if its mass were arranged in uniformly dense, spherical layers, like the coats of an onion. But the earth is not spherical, and to find what is the nature of the attraction of a distant body, it has been necessary to make pendulum observations all over the earth. You know that if a pendulum does not alter in length as we take it about to various places, its time of vibration at each place enables the force of gravity at each place to be determined; and Mr. Green proved that if we know the force of gravity at all places on the surface of the earth, although we may know nothing about the
state of the inside of the earth, we can calculate with absolute accuracy the force exerted by the earth on matter placed anywhere outside the earth; for instance, at any part of the moon's orbit, or at the sun. And hence we know the equal and opposite force with which such matter will act on the earth. Now pendulum observations have been made at a great many places on the earth, and we know, although of course not with absolute accuracy, the attraction on the earth, of matter outside the earth. For instance, we know that the resultant attraction of the sun on the earth is a force which does not pass through the centre of the earth's mass. You may comprehend the result better if I refer to this diagram of the earth at midwinter (Fig. 39), and use a popular method of description. A and B may roughly be called the protuberant parts of the earth—that protuberant belt of matter which makes the
earth orange-shaped instead of spherical. On the spherical portion inside, assumed roughly to be homogeneous, the resultant attraction is a force through the centre.
I will now consider the attraction on the protuberant equatorial belt indicated by A and B. The sun attracts a pound of matter at B more than it attracts a pound of matter at A, because B is nearer than A, and hence the total resultant force is in the direction M N rather than O O, through the centre of the earth's mass. But we know that a force in the direction M N is equivalent to a force O O parallel to M N, together with a tilting couple of forces tending to turn the equator edge on to the sun. You will get the true result as to the tilting tendency by imagining the earth to be motionless, and the sun's mass to be distributed as a circular ring of matter 184 millions of miles in diameter, inclined to the equator at 23½°. Under the influence of the attraction of this ring the earth would heave like a great ship on a calm sea, rolling very slowly; in fact, making one complete swing in about three years. But the earth is spinning, and the tilting couple or torque acts upon it just like the forces which are always tending to cause this ship-model to stand upright, and hence it has a precessional motion whose complete period is 26,000 years. When there is no spin in the ship, its complete oscillation takes place in three seconds, and
when I spin the gyrostat on board the ship, the complete period of its precession is two minutes. In both cases the effect of the spin is to convert what would be an oscillation into a very much slower precession.