Very good illustrations of change of direction are obtained in playing _bowls_. You know that a bowl, if it had no _bias_, that is, if it had no little weight inside it tending to tilt it, would roll along the level bowling-green in a straight path, its speed getting less and less till it stopped. As a matter of fact, however, you know that at the beginning, when it is moving fast, its path is pretty straight, but because it always has bias the path is never quite straight, and it bends more and more rapidly as the speed diminishes. In all our examples the slower the spin the quicker is the precession produced by given tilting forces. Now close observation will give you a simple rule about the behaviour of a gyrostat. As a matter of fact, all that has been incomprehensible or curious disappears at once, if instead of speaking of this gyrostat as moving up or down, or to the right or left, I speak of its motions about its various axes. It offers no resistance to mere motion of translation. But when I spoke of its moving {40} horizontally, I ought to have said that it moved about the vertical axis A B (Fig. 13). Again, what I referred to as up and down motion of F is really motion in a vertical plane about the horizontal axis C D. In future, when I speak of trying to give motion to F, think only of the axis about which I try to turn it, and then a little observation will clear the ground. [Illustration: FIG. 17.] [Illustration: FIG. 18.] Here is a gyrostat (Fig. 17), suspended in gymbals so carefully that neither gravity nor any frictional forces at the pivots constrain it; nothing that I can do to this frame which I hold in my hand will affect the direction of the axis E F of the gyrostat. Observe that I whirl round on my toes like a ballet-dancer while this is in my hand. I move it about in all sorts of ways, but if it was pointing to the pole star at the beginning it remains pointing to the pole star; if it pointed towards the moon at the beginning it still points {41} towards the moon. The fact is, that as there is almost no frictional constraint at the pivots there are almost no forces tending to turn the axis of rotation of the gyrostat, and I can only give it motions of translation. But now I will clamp this vertical spindle by means of a screw and repeat my ballet-dance whirl; you will note that I need not whirl round, a very small portion of a whirl is enough to cause this gyrostat (Fig. 18) to set its spinning axis vertical, to set its axis parallel to the vertical axis of rotation which I give it. Now I whirl in the opposite direction, the gyrostat at once turns a somersault, turns completely round and remains again with its axis vertical, and if you were to carefully note the direction of the spinning of the {42} gyrostat, you would find the following rule to be generally true:--Pay no attention to mere translational motion, think only of rotation about axes, and just