When I hold this box in my hands (Fig. 6), I find that if I move it with a motion of mere translation in any direction, it feels just as it would do {22} if its contents were at rest, but if I try to turn it in my hands I find the most curious great resistance to such a motion. The result is that when you hold this in your hands, its readiness to move so long as it is not turned round, and its great resistance to turning round, and its unexpected tendency to turn in a different way from that in which you try to turn it, give one the most uncanny sensations. It seems almost as if an invisible being had hold of the box and exercised forces capriciously. And {23} indeed there is a spiritual being inside, what the algebraic people call an impossible quantity, what other mathematicians call "an operator." [Illustration: FIG. 6.] Nearly all the experiments, even the tops and other apparatus you have seen or will see to-night, have been arranged and made by my enthusiastic assistant, Mr. Shepherd. The following experiment is not only his in arrangement; even the idea of it is his. He said, you may grin and contort your body with that large gyrostat in your hands, but many of your audience will simply say to {24} themselves that you only _pretend_ to find a difficulty in turning the gyrostat. So he arranged this pivoted table for me to stand upon, and you will observe that when I now try to turn the gyrostat, it will not turn; however I may exert myself, it keeps pointing to that particular corner of the room, and all my efforts only result in turning round my own body and the table, but not the gyrostat. Now you will find that in every case this box only resists having the axis of revolution of its hidden flywheel turned round, and if you are interested in the matter and make a few observations, you will soon see that every spinning body like the fly-wheel inside this case resists more or less the change of direction of its spinning axis. When the fly-wheels of steam-engines and dynamo machines and other quick speed machines are rotating on board ship, you may be quite sure that they offer a greater resistance to the pitching or rolling or turning of the ship, or any other motion which tends to turn their axes in direction, than when they are not rotating. Here is a top lying on a plate, and I throw it up into the air; you will observe that its motion is very difficult to follow, and nobody could predict, before it falls, exactly how it will alight on the plate; it may come down peg-end foremost, or hindmost, or sideways. But when I spin it (Fig. 7), and now throw it up into the air, there is no doubt whatever {25} as to how it will come down. The spinning axis keeps parallel to itself, and I can throw the top up time after time, without disturbing much the spinning motion. [Illustration: FIG. 7.] [Illustration: FIG. 8.]