them perhaps at every footfall, at the flapping of every coat-tail.
Imagine the following question set in a school examination paper of 2090 A.D.—"Can you account for the crass ignorance of our forefathers in not being able to see from England what their friends were doing in Australia?"[[13]] Or this—"Messages are being received every minute from our friends on the planet Mars, and are now being answered: how do you account for our ancestors being utterly ignorant that these messages were occasionally sent to them?" Or this—"What metal is as strong compared with steel as steel is compared with lead? and explain why the discovery of it was not made in Sheffield."
But there is one question that our descendants will never ask in accents of jocularity, for to their bitter sorrow every man, woman, and child of them will know the answer, and that question is this—"If our ancestors in the matter of coal economy were not quite as ignorant as a baby who takes a penny
as equivalent for a half-crown, why did they waste our coal? Why did they destroy what never can be replaced?"
My friends, let me conclude by impressing upon you the value of knowledge, and the importance of using every opportunity within your reach to increase your own store of it. Many are the glittering things that seem to compete successfully with it, and to exercise a stronger fascination over human hearts. Wealth and rank, fashion and luxury, power and fame—these fire the ambitions of men, and attract myriads of eager worshippers; but, believe it, they are but poor things in comparison with knowledge, and have no such pure satisfactions to give as those which it is able to bestow. There is no evil thing under the sun which knowledge, when wielded by an earnest and rightly directed will, may not help to purge out and destroy; and there is no man or woman born into this world who has not been given the capacity, not merely to gather in knowledge for his own improvement and delight, but even to add something, however little, to that general stock of knowledge which is the world's best wealth.
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].