12. How a gyrostat would enable a person living in subterranean regions to know, _1st, that the earth rotates_; _2nd, the amount of rotation_; _3rd, the direction of true north_; _4th, the latitude_, 101-111. Some men's want of faith, 101; disbelief in the earth's rotation, 102; how a free gyrostat behaves, 103, 104; Foucault's laboratory measurement of the earth's rotation, 105-107; to find the true north, 108; all rotating bodies vainly endeavouring to point to the pole star, 108; to find the latitude, 110; analogies between the gyrostat and the mariner's compass and the dipping needle, 110, 111; dynamical connection between magnetism and gyrostatic phenomena, 111. 13. How the lecturer spun his tops, using electro-motors, 112-114. 14. _Light_, _magnetism_, _and molecular spinning tops_, 115-128. Light takes time to travel, 115; the electro-magnetic {136} theory of light, 116, 117; signalling through fogs and buildings by means of a new kind of radiation, 117; Faraday's rotation of the plane of polarization by magnetism, with illustrations and models, 118-124; chain of gyrostats, 124; gyrostat as a pendulum bob, 126; Thomson's mechanical illustration of Faraday's experiment, 127, 128. 15. _Conclusion_, 129-132. The necessity for cultivating the observation, 129; future discovery, 130; questions to be asked one hundred years hence, 131; knowledge the thing most to be wished for, 132. * * * * * {137} APPENDIX I. THE USE OF GYROSTATS. In 1874 two famous men made a great mistake in endeavouring to prevent or diminish the rolling motion of the saloon of a vessel by using a rapidly rotating wheel. Mr. Macfarlane Gray pointed out their mistake. It is only when the wheel is allowed to _precess_ that it can exercise a steadying effect; the moment which it then exerts is equal to the angular speed of the precession multiplied by the moment of momentum of the spinning wheel. It is astonishing how many engineers who know the laws of motion of mere translation, are ignorant of angular motion, and yet the analogies between the two sets of laws are perfectly simple. I have set out these analogies in my book on _Applied Mechanics_. The last of them between centripetal force on a body moving in a curved path, and torque or moment on a rotating body is the simple key to all gyrostatic or top calculation. When the spin of a top is greatly reduced it is necessary to remember that the total moment of momentum is not about the spinning axis (see my _Applied Mechanics_, page 594); correction for this is, I suppose, what introduces the complexity which scares students from studying the vagaries of tops; but in all cases that are likely to come before an engineer it would be absurd to study {138} such a small correction, and consequently calculation is exceedingly simple.