ARGUMENT.
1. Introduction, pages [9]-[14], showing the importance of the study of spinning-top behaviour.
2. Quasi-rigidity induced even in flexible and fluid bodies by rapid motion, [14]-[21].
Illustrations: Top, [14]; belt or rope, [14]; disc of thin paper, [14]; ring of chain, [15]; soft hat, [16]; drunken man, [16]; rotating water, [16]; smoke rings, [17]; Thomson's Molecular Theory, [19]; swimmer caught in an eddy, [20]; mining water jet, [20]; cased gyrostat, [21].
3. The nature of this quasi-rigidity in spinning bodies is a resistance to change of direction of the axis of spinning, [21]-[30].
Illustrations: Cased gyrostat, [21]-[24]; tops, biscuits, hats, thrown into the air, [24]-[26]; quoits, hoops, projectiles from guns, [27]; jugglers at the Victoria Music Hall, [26]-[30]; child trundling hoop, man on bicycle, ballet-dancer, the earth pointing to pole star, boy's top, [30].
4. Study of the crab-like behaviour of a spinning body, [30]-[49].
Illustrations: Spinning top, [31]; cased gyrostat, [32]; balanced gyrostat, [33]-[36]; windage of projectiles from rifled guns, [36]-[38]; tilting a hoop or bicycle, turning quickly on horseback, [38]; bowls, [39]; how to simplify one's observations, [39], [40]; the illustration which gives us our simple universal rule, [40]-[42]; testing the rule, [42]-[44]; explanation of precession of gyrostat, [44], [45]; precession of common top, [46]; precession of overhung top, [46]; list of our results given in a wall sheet, [48], [49].
5. Proof or explanation of our simple universal rule, [50]-[54].
Giving two independent rotations to a body, [50], [51]; composition of rotations, [52], [53].
6. Warning that the rule is not, after all, so simple, [54]-[66].
Two independent spins given to the earth, [54]; centrifugal force, [55]; balancing of quick speed machinery, [56], [57]; the possible wobbling of the earth, [58]; the three principal axes of a body, [59]; the free spinning of discs, cones, rods, rings of chain, [60]; nodding motion of a gyrostat, [62]; of a top, [63]; parenthesis about inaccuracy of statement and Rankine's rhyme, [63], [64]; further complications in gyrostatic behaviour, [64]; strange elastic, jelly-like behaviour, [65]; gyrostat on stilts, [66].
7. Why a gyrostat falls, [66], [67].
8. Why a top rises, [67]-[74].
General ignorance, [67]; Thomson preparing for the mathematical tripos, [68]; behaviour of a water-worn stone when spun on a table, [68], [69]; parenthesis on technical education, [70]; simple explanation of why a top rises, [70]-[73]; behaviour of heterogeneous sphere when spun, [74].
9. Precessional motion of the earth, [74]-[91].
Its nature and effects on climate, [75]-[80]; resemblance of the precessing earth to certain models, [80]-[82]; tilting forces exerted by the sun and moon on the earth, [82]-[84]; how the earth's precessional motion is always altering, [85]-[88]; the retrogression of the moon's nodes is itself another example, [88], [89]; an exact statement made and a sort of apology for making it, [90], [91].
10. Influence of possible internal fluidity of the earth on its precessional motion, [91]-[98].
Effect of fluids and sand in tumblers, [91]-[93]; three tests of the internal rigidity of an egg, that is, of its being a boiled egg, [93], [94]; quasi-rigidity of fluids due to rapid motion, forgotten in original argument, [95]; beautiful behaviour of hollow top filled with water, [95]; striking contrasts in the behaviour of two tops which are very much alike, [97], [98]; fourth test of a boiled egg, [98].
11. Apology for dwelling further upon astronomical matters, and impertinent remarks about astronomers, [99]-[101].
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 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].
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].