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 MAGNETISM, LIGHT, AND MOLECULAR SPINNING TOPS. 
 
 Page 122. 
 
THE ROMANCE OF SCIENCE. ,9/6 
 
 SPINNING TOPS. 
 
 THE "OPERATIVES' LECTURE' 1 
 OF THE BRITISH ASSOCIATION MEETING AT LEEDS 
 
 BY 
 
 PROFESSOR JOHN PERRY, 
 ME., D.Sc, LL.D., F.R.S. 
 
 titij %xcmmix% llhtsiraticws. 
 
 REPRINT OF NEW AND REVISED EDITION, 
 
 With Illustrated Appendices on the Use of Gyrostats 
 and the Gyro- Compass. 
 
 SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE, 
 
 LONDON: NORTHUMBERLAND AVENUE, W.C.; 
 
 BRIGHTON: 129, North Street. 
 
 1916. 
 
[Dale of last impression, January igio\ 
 
^hi* ftepm-t oi ait (Experimental lecture 
 
 WAS INSCRIBED TO 
 THE LATE 
 
 LORD KELVIN, 
 
 BY HIS AFFECTIONATE PUPIL, THE LECTURER, WHO 
 
 HEREBY TOOK A CONVENIENT METHOD OF 
 
 ACKNOWLEDGING THE REAL AUTHOR OF 
 
 WHATEVER IS WORTH PUBLICATION 
 
 IN THE FOLLOWING 
 
 PAGES. 
 
Digitized by the Internet Archive 
 
 in 2011 with funding from 
 
 University of North Carolina at Chapel Hill 
 
 http://www.archive.org/details/spinningtopsoperOOperr 
 
PREFACE. 
 
 This is not the lecture as it was delivered. 
 Instead of two pages of letterpress and a wood- 
 cut, the reader may imagine that for half a minute 
 the lecturer played with a spinning top or gyrostat, 
 and occasionally ejaculated words of warning, 
 admonition, and explanation towards his audience. 
 A verbatim report would make rather uninterest- 
 ing reading, and I have taken the liberty of trying, 
 by greater fullness of explanation, to make up to 
 the reader for his not having seen the moving 
 apparatus. It has also been necessary in a treatise 
 intended for general readers to simplify the 
 reasoning, the lecture having been delivered to 
 persons whose life experiences peculiarly fitted 
 them for understanding scientific things. An 
 " argument " has been added at the end to make 
 the steps of the reasoning clearer. 
 
 JOHN PERRY. 
 
SPINNING TOPS. 
 
 At a Leeds Board School last week, the master 
 said to his class, " There is to be a meeting of the 
 British Association in Leeds. What is it all about ? 
 Who are the members of the British Association ? 
 What do they do ? " There was a long pause. 
 At length it was broken by an intelligent shy boy : 
 " Please, sir, I know — they spin tops ! " 1 
 
 Now I am sorry to say that this answer was 
 wrong. The members of the British Association 
 and the Operatives of Leeds have neglected top- 
 spinning since they were ten years of age. If more 
 attention were paid to the intelligent examination 
 of the behaviour of tops, there would be greater 
 advances in mechanical engineering and a great 
 many industries. There would be a better general 
 knowledge of astronomy. Geologists would not 
 make mistakes by millions of years, and our know- 
 ledge of Light, and Radiant Heat, and other 
 
 1 The Operative^ Lecture is always well advertised in the 
 streets beforehand by large posters. 
 
IO SPINNING TOPS. 
 
 Electro-magnetic Phenomena would extend much 
 more rapidly than it does. 
 
 I shall try to show you towards the end of the 
 lecture that the fact of our earth's being a spinning 
 body is one which would make itself known to us 
 even if we lived in subterranean regions like the 
 coming race of an ingenious novelist. 1 It is the 
 greatest and most persistent cause of many of the 
 phenomena which occur around us and beneath us, 
 and it is probable that even Terrestrial Magnetism 
 is almost altogether due to it. Indeed there is 
 only one possible explanation of the Vril-ya ignor- 
 ance about the earth's rotation. Their knowledge of 
 mechanics and dynamics was immense ; no member 
 attending the meeting of the British Association 
 can approach them in their knowledge of, I will 
 not say, Vril, but even of quite vulgar electricity 
 and magnetism ; and yet this great race which 
 expresses so strongly its contempt for Anglo- 
 Saxon Koom-PosJiery was actually ignorant of the 
 fact that it had existed for untold generations 
 inside an object that spins about an axis. 
 
 Can we imagine for one instant that the children 
 of that race had never spun a top or trundled a 
 hoop, and so had had no chance of being led to the 
 greatest study of nature ? No ; the only possible 
 explanation lies in the great novelist's never 
 1 Bulwer Lytton's Coming Race. 
 
SPINNING TOPS. I I 
 
 having done these things himself. He had pro- 
 bably as a child a contempt for the study of nature, 
 he was a baby Pelham, and as a man he was con- 
 demned to remain in ignorance even of the powers 
 of the new race that he had created. 
 
 The Vril-ya ignorance of the behaviour of spin- 
 ning bodies existing as it does side by side with 
 their deep knowledge of magnetism, becomes 
 even more remarkable when it comes home to 
 us that the phenomena of magnetism and of light 
 are certainly closely connected with the behaviour 
 of spinning bodies, and indeed that a familiar 
 knowledge of the behaviour of such bodies is 
 absolutely necessary for a proper comprehension 
 of most of the phenomena occurring in nature. 
 The instinctive craving to investigate these phe- 
 nomena seems to manifest itself soon after we 
 are able to talk, and who knows how much of 
 the intellectual inferiority of woman is due to 
 . her neglect of the study of spinning tops ; but 
 alas, even for boys in the pursuit of top-spinning, 
 the youthful mind and muscle are left with no 
 other guidance ,than that which is supplied by 
 the experience of young and not very scientific 
 companions. I remember distinctly that there 
 were many puzzling problems presented to me 
 every day. There were tops which nobody 
 seemed able to spin, and there were others, well 
 
12 SPINNING TOPS. 
 
 prized objects, often studied in their behaviour and 
 coveted as supremely valuable, that behaved well 
 under the most unscientific treatment. And yet 
 nobody, even the makers, seemed to know why one 
 behaved badly and the other well. 
 
 I do not disguise from myself the fact that it is 
 rather a difficult task to talk of spinning tops to 
 men who have long lost that skill which they 
 wonder at in their children ; that knowingness of 
 touch and handling which gave them once so much 
 power over what I fear to call inanimate nature. 
 A problem which the child gives up as hopeless of 
 solution, is seldom attacked again in maturer years ; 
 he drives his desire for knowledge into the obscure 
 lumber-closets of his mind, and there it lies, with 
 the accumulating dust of his life, a neglected and 
 almost forgotten instinct. Some of you may think 
 that this instinct only remains with those minds so 
 many of which are childish even to the limit of 
 life's span ; and probably none of you have had 
 the opportunity of seeing how the old dust rubs 
 off from the life of the ordinary man, and the 
 old desire comes back to him to understand the 
 mysteries that surround him. 
 
 But I have not only felt this desire myself, I 
 have seen it in the excited eyes of the crowd of 
 people who stand by the hour under the dropping 
 cherry-blossoms beside the red-pillared temple of 
 
SPINNING TOPS. 13 
 
 Asakusa in the Eastern capital of Japan, watching 
 the tedzu-maslii directing the evolutions of his heavily 
 rimmed Koina. First he throws away from him 
 his great top obliquely into the air and catches it 
 spinning on the end of a stick, or the point of a 
 sword, or any other convenient implement ; he now 
 sends it about quite carelessly, catching it as it 
 comes back to him from all sorts of directions ; he 
 makes it run up the hand-rail of a staircase into a 
 house by the door and out again by the window ; 
 he makes it travel up a great corkscrew. Now he 
 seizes it in his hands, and with a few dexterous 
 twists gives it a new stock of spinning energy. 
 He makes it travel along a stretched string or the 
 edge of a sword ; he does all sorts of other curious 
 things with his tops, and suddenly sinks from his 
 masterful position to beg for a few coppers at the 
 end of his performance. 
 
 How tame all this must seem to you who more 
 than half forget your childish initiation into the 
 mysteries of nature ; but trust me, if I could only 
 make that old top-spinner perform those magical 
 operations of his on this platform, the delight 
 of the enjoyment of beautiful motion would come 
 back. Perhaps it is only in Japan that such an 
 exhibition is possible ; the land where the waving 
 bamboo, and the circling hawk, and the undulating 
 summer sea, and every beautiful motion of nature 
 
14 SPINNING TOPS. 
 
 are looked upon with tenderness ; and perhaps it is 
 from Japan that we shall learn the development of 
 our childish enthusiasm. 
 
 The devotees of the new emotional art of beau- 
 tiful motion and changing colour are still in the 
 main beggars like Homer, and they live in garrets 
 like Johnson and Savage ; but the dawn of a new 
 era is heralded, or rather the dawn has already come, 
 for Sir William Thomson's achievements in the 
 study of spinning tops rank already as by no 
 means the meanest of his great career. 
 
 If you will only think of it, the behaviour of the 
 commonest spinning top is very wonderful. When 
 not spinning you see that it falls down at once, 
 I find it impossible to balance it on its peg ; but 
 what a very different object it is when spinning ; 
 you see that it not only does not fall down, it offers 
 a strange resistance when I strike it, and actually 
 lifts itself more and more to an upright position. 
 Once started on scientific observation, nature gives 
 us facts of an analogous kind in great plenty. 
 
 Those of you who have observed a rapidly 
 moving heavy belt or rope, know that rapid motion 
 gives a peculiar quasi-rigidity to flexible and even 
 to fluid things. 
 
 Here, for example, is a disc of quite thin paper 
 (Fig. i), and when I set it in rapid rotation you 
 observe that it resists the force exerted by my 
 
SPINNING TOPS. 
 
 15 
 
 hand, the blow of my fist, as if it were a disc of 
 steel. Hear how it resounds when I strike it with 
 a stick. Where has its flexibility gone ? 
 
 Fig. 
 
 Here again is a ring of chain which is quite 
 flexible. It seems ridiculous to imagine that this 
 
i6 
 
 SPINNING TOPS. 
 
 could be made to stand up like a stiff hoop, and yet 
 you observe that when I give it a rapid rotation on 
 this mandril and let it slide off upon the table, it 
 runs over the table just as if it were a rigid ring, 
 and when it drops on the floor it rebounds like a 
 boy's hoop (Fig. 2). 
 
 Fig. 2. 
 
 Here again is a very soft hat, specially made for 
 this sort of experiment. You will note that it 
 collapses to the table in a shapeless mass when I 
 lay it down, and seems quite incapable of resisting 
 forces which tend to alter its shape. ~ In fact, there 
 is almost a complete absence of rigidity ; but 
 when this is spun on the end of a stick, first note 
 
SPINNING TOPS. 17 
 
 how it has taken a very easily defined shape ; 
 secondly, note how it runs along the table as if it 
 were made of steel ; thirdly, note how all at once it 
 collapses again into a shapeless heap of soft material 
 when its rapid motion has ceased. Even so you 
 will see that when a drunken man is not leaning 
 against a wall or lamp-post, he feels that his only 
 chance of escape from ignominious collapse is to get 
 up a decent rate of speed, to obtain a quasi-sobriety 
 of demeanour by rapidity of motion. 
 
 The water inside this glass vessel (Fig. 3) is in 
 a state of rapid motion, revolving with the vessel 
 itself. Now observe the piece of paraffin wax A 
 immersed in the water, and you will see when I 
 push at it with a rod that it vibrates just as if it 
 were surrounded with a thick jelly. Let us now 
 apply Prof. Fitzgerald's improvement on this 
 experiment of Sir William Thomson's. Here is 
 a disc B stuck on the end of the rod ; observe 
 that when I introduce it, although it does not touch 
 A, A is repelled from the disc. Now observe that 
 when I twirl the disc it seems to attract A. 
 
 At the round hole in front of this box a rapid 
 motion is given to a small quantity of air which is 
 mixed with smoke that you may see it. That 
 smoke-ring moves through the air almost like a 
 solid body for a considerable distance unchanged, 
 and I am not sure that it may not be possible yet 
 
SPINNING TOPS. 
 
 to send as a projectile a huge poisoned smoke- 
 ring, so that it may destroy or stupefy an army 
 miles away. Remember that it is really the same 
 
 Fig. 3. 1 
 
 air all the time. You will observe that two smoke- 
 rings sent from two boxes have curious actions 
 
 1 The glass vessel ought to be broader in comparison with 
 its height. 
 
SPINNING TOPS. 
 
 19 
 
 upon one another, and the study of these actions 
 
 has given rise 
 
 to Thomson's 
 
 smoke-ring or 
 
 vortex theory of 
 
 the constitution 
 
 of matter (Fig. 
 
 4). 
 ItwasRankine, 
 
 the great guide 
 of all engineers, 
 who first sug- 
 gested the idea 
 of molecular vor- 
 tices in his ex- 
 planations of 
 heat phenomena 
 and the phe- 
 nomena of elas- 
 ticity — the idea 
 that every par- 
 ticle of matter is 
 like a little spin- 
 ning top ; but I 
 am now speaking 
 of Thomson's 
 theory. To 
 imagine that an 
 
 Fig. 4. 
 
 atom of matter is merely a 
 
20 SPINNING TOPS. 
 
 curiously shaped smoke-ring formed miraculously 
 in a perfect fluid, and which can never undergo 
 permanent alteration, looks to be a very curious 
 and far-fetched hypothesis. But in spite of cer- 
 tain difficulties, it is the foundation of the theory 
 which will best explain most of the molecular phe- 
 nomena observed by philosophers. Whatever be 
 the value of the theory, you see from these experi- 
 ments that motion does give to small quantities 
 of fluid curious properties of elasticity, attraction 
 and repulsion ; that each of these entities refuses 
 to be cut in two ; that you cannot bring a knife 
 even near the smoke-ring ; and that what may be 
 called a collision between two of them is not very 
 different in any way from the collision between 
 two rings of india-rubber. 
 
 Another example of the rigidity given to a fluid 
 by rapid motion, is the feeling of utter helplessness 
 which even the strongest swimmers sometimes 
 experience when they get caught in an eddy 
 underneath the water. 
 
 I could, if I liked, multiply these instances of the 
 quasi-rigidity which mere motion gives to flexible 
 or fluid bodies. In Nevada a jet of water like the 
 jet from a fireman's hose, except J:hat it is much 
 more rapid, which is nearly as easily projected in 
 different directions, is used in mining, and huge 
 masses of earth and rock are rapidly disintegrated 
 
SPINNING TOPS. 2 1 
 
 by the running water, which seems to be rather like 
 a bar of steel than a jet of water in its rigidity. 
 
 It is, however, probable that you will take more 
 interest in this box of brass which I hold in my 
 hands. You see nothing moving, but really, inside 
 this case there is a fly-wheel revolving rapidly. 
 Observe that I rest this case on the table on its 
 sharp edge, a sort of skate, and it does not tumble 
 down as an ordinary box would do, or as this box 
 will do after a while, when its contents come to 
 rest. Observe that I can strike it violent blows, 
 and it does not seem to budge from its vertical 
 position ; it turns itself just a little round, but does 
 not get tilted, however hard I strike it. Observe 
 that if I do get it tilted a little it does not fall 
 down, but slowly turns with what is called a 
 precessional motion (Fig. 5). 
 
 You will, 1 hope, allow me, all through this 
 lecture, to use the term precessional for any motion 
 of this kind. Probably you will object more 
 strongly to the great liberty I shall take presently, 
 of saying that the case precesses when it has this 
 kind of motion ; but I really have almost no option 
 in the matter, as I must use some verb, and I have 
 no time to invent a less barbarous one. 
 
 When I hold this box in my hands (Fig. 6), I 
 find that if I move it with a motion of mere trans- 
 lation in any direction, it feels just as it would do 
 
22 
 
 SPINNING TOPS. 
 
 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 
 
 Fig. 5. 
 
 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 
 
SPINNING TOPS. 
 
 23 
 
 indeed there is a spiritual being inside, what 
 the algebraic people call an impossible quantity, 
 what other mathematicians call " an operator." 
 
 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 
 
 Fiu. 6. 
 
 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 them- 
 
24 SriNNING TOPS. 
 
 selves 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 fly- 
 wheel 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 re- 
 sistance 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 
 
SPINNING TOrS. 
 
 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 spin- 
 ning motion. 
 
 I f I pitch up this biscuit, you will observe that I 
 
 Fig. 7. Fig. 8. 
 
 can have no certainty as to how it will come down, 
 but if I give it a spin before it leaves my hand 
 there is no doubt whatever (Fig. 8). Here is a hat. 
 I throw it up, and I cannot be sure as to how it 
 will move, but if I give it a spin, you see that, as 
 
26 
 
 SPINNING TOPS. 
 
 
 ,: Zrl-~_---J;? 
 
 with the top and the biscuit, the axis about which 
 the spinning takes place keeps parallel to itself, 
 and we have perfect certainty as to the hat's alight- 
 ing on the ground brim downwards (Fig. 9). 
 
 I need not again bring before you the very soft 
 hat to which we gave a quasi-rigidity a few minutes 
 ago ; but you 
 will remember /■- j 
 
 that my assist- 
 ant sent that 
 off like a pro- 
 jectile through 
 the air when it 
 was spinning, 
 and that it kept 
 its spinning 
 axis parallel to 
 itself just like 
 this more rigid 
 hat and the 
 biscuit. 
 
 I once show- 
 ed some exper- 
 iments on spin- 
 ning tops to a coffee- drinking, tobacco-smoking audi- 
 ence in that most excellent institution, the Victoria 
 Music Hall in London. In that music hall, things are 
 not very different from what they are at any other 
 
 Fig. 9. 
 
SPINNING TOPS. 27 
 
 music hall except in beer, wine, and spirits being 
 unobtainable, and in short scientific addresses being 
 occasionally given. Now, I impressed my audience 
 as strongly as I could with the above fact, that if 
 one wants to throw a quoit with certainty as to 
 how it will alight, one gives it a spin ; if one wants 
 to throw a hoop or a hat to somebody to catch 
 upon a stick, one gives the hoop or hat a spin ; the 
 disinclination of a spinning body to let its axis get 
 altered in direction can always be depended upon. 
 I told them that this was why smooth-bore guns 
 cannot be depended upon for accuracy; 1 that the 
 spin which an ordinary bullet took depended 
 greatly on how it chanced to touch the muzzle as 
 it just left the gun, whereas barrels are now rifled, 
 that is, spiral grooves are now cut inside the barrel 
 of a gun, and excrescences from the bullet or pro- 
 jectile fit into these grooves, so that as it is forced 
 along the barrel of the gun by the explosive force 
 of the powder, it must also spin about its axis. 
 Hence it leaves the gun with a perfectly well- 
 known spinning motion about which there can be 
 no doubt, and we know too that Fig. 10 shows the 
 
 1 In 1746 Benjamin Robins taught the principles of rifling 
 as we know them now. He showed that the spin of the round 
 bullet was the most important thing to consider. He showed 
 that even the bent barrel of a gun did not deflect the bullet 
 to anything like the extent that the spin of the bullet made 
 it deflect in the opposite direction. 
 
28 SPINNING TOPS. 
 
 kind of motion which it has 
 afterwards, for, just like the 
 hat or the biscuit, its spin- 
 ning axis keeps nearly 
 parallel to itself. Well, this 
 was all I could do, for I am 
 not skilful in throwing hats 
 or quoits. But after my 
 address was finished, and 
 after a young lady in a 
 spangled dress had sung a 
 comic song, two jugglers 
 came upon the stage, and I 
 could not have had better 
 illustrations of the above 
 principle than were given 
 in almost every trick per- 
 formed by this lady and 
 gentleman. They sent hats, 
 and hoops, and plates, and 
 umbrellas spinning from 
 one to the other. One of 
 them threw a stream of 
 knives into the air, catching 
 them and throwing them up 
 again with perfect precision 
 and my now educated audi- 
 ence shouted with delight, 
 and showed in other unmis- 
 
 /9 
 
SPINNING TOPS. 
 
 2 9 
 
 takable ways that they observed the spin which 
 that juggler gave to every knife as it left his hand, 
 
 Fig. 11. 
 
 so that he might have a perfect knowledge as to 
 how it would come back to him again (Fig. n). 
 
30 SPINNING TOPS. 
 
 It struck me with astonishment at the time that, 
 almost without exception, every juggling trick per- 
 formed that evening was an illustration of the above 
 principle. And now, if you doubt my statement, just 
 ask a child whether its hoop is more likely to tumble 
 down when it is rapidly rolling along, or when it is 
 going very slowly ; ask a man on a bicycle to go 
 more and more slowly to see if he keeps his balance 
 better ; ask a ballet-dancer how long she could stand 
 
 Fig. t2. 
 
 on one toe without balancing herself with her arms 
 or a pole, if she were not spinning ; ask astronomers 
 how many months would elapse before the earth 
 would point ever so far away from the pole star if it 
 were not spinning ; and above all, ask a boy whether 
 his top is as likely to stand upright upon its peg 
 when it is not spinning as when it is~spinning. 
 
 We will now examine more carefully the beha- 
 viour of this common top (Fig. 12). It is not spin- 
 
SPINNING TOPS. 31 
 
 ning, and you observe that it tumbles down at once ; 
 it is quite unstable if I leave it resting upright on 
 its peg. But now note that when it is spinning, 
 it not only will remain upright resting on its peg, 
 but if I give it a blow and so disturb its state, 
 it goes circling round with a precessional motion 
 which grows gradually less and less as time goes 
 on, and the top lifts itself to the upright posi- 
 tion again. I hope you do not think that time 
 spent in careful observation of a phenomenon 
 of this kind is wasted. Educated observation of 
 the commonest phenomena occurring in our every- 
 day life is never wasted, and I often feel that if 
 workmen, who are the persons most familiar with 
 inorganic nature, could only observe and apply 
 simple scientific laws to their observations, instead 
 of a great discovery every century we should have 
 a great discovery every year. Well, to return to 
 our top ; there are two very curious observations 
 to make. Please neglect for a short time the 
 slight wobbling motions that occur. One observation 
 we make is, that the top does not at first bow 
 down in the direction of the blow. If I strike 
 towards the south, the top bows towards the west ; 
 if I strike towards the west, the top bows down 
 towards the north. Now the reason of this is 
 known to all scientific men, and the principle 
 underlying the top's behaviour is of very great 
 
32 
 
 SPINNING TOPS. 
 
 importance in many ways, and I hope to make it 
 clear to you. The second fact, that the top gradu- 
 ally reaches its upright position again, is one known 
 to everybody, but the reason for it is not by any 
 
 Fig. 13. 
 
 means well known, although 1 think that you will 
 have no great difficulty in understanding it. 
 
 The first phenomenon will be observed in this case 
 which I have already shown you. This case (Fig. 5), 
 
spinning Tors. 33 
 
 with the fly-wheel inside it, is called a gyrostat. 
 When I push the case it does not bow down, but 
 slowly turns round. This gyrostat will not exhibit 
 the second phenomenon ; it will not rise up again 
 if I manage to get it out of its upright position, 
 but, on the contrary, will go precessing in wider 
 and wider circles, getting further and further away 
 from its upright position. 
 
 The first phenomenon is most easily studied in 
 this balanced gyrostat (Fig. 13). You here see the 
 fly-wheel G in a strong brass frame F, which is 
 supported so that it is free to move about the 
 vertical axis A B, or about the horizontal axis C D. 
 The gyrostat is balanced by a weight W. Observe 
 that I can increase the leverage of W or diminish 
 it by shifting the position of the sleeve at A 
 so that it will tend to either lift or lower the 
 gyrostat, or exactly balance it as it does now. 
 You must observe exactly what it is that we wish 
 to study. If I endeavour to push F downwards, with 
 the end of this stick (Fig. 14), it really moves 
 horizontally to the right ; now I push it to the right 
 (Fig. 15), and it only rises ; now push it up, and 
 you see that it goes to the left ; - push it to the 
 left, and it only goes downwards. You will notice 
 that if I clamp the instrument so that it cannot 
 move vertically, it moves at once horizontally ; if I 
 prevent mere horizontal motion it readily moves 
 vertically when I push it. Leaving it free as 
 
 C 
 
34 
 
 SPINNING TOPS. 
 
 before, I will now shift the position of the weight 
 W, so that it tends continually to lift the 
 gyrostat, and of course the instrument does not 
 lift, it moves horizontally with a slow precessional 
 
 Fig. 14. 
 
 motion. I now again shift the weight W, so that the 
 gyrostat would fall if it were not spinning (Fig. 16), 
 and it now moves horizontally with a slow preces- 
 sional motion which is in a direction opposed to the 
 last. These phenomena are easily explained, but, 
 
SPINNING TOPS. 35 
 
 as I said before, it is necessary first to observe them 
 carefully. You all know now, vaguely, the funda- 
 mental fact. It is that if I try to make a very 
 quickly spinning body change the direction of its 
 
 Fig. 15. 
 
 axis, the direction of the axis will change, but 
 not in the way I intended. It is even more curious 
 than my countryman's pig, for when he wanted 
 the pig to go to Cork, he had to pretend that he 
 was driving the pig home. His rule was a very 
 
36 
 
 SPINNING TOPS. 
 
 simple one, and we must find a rule for our spinning 
 body, which is rather like a crab, that will only 
 go along the road when you push it sidewise. 
 As an illustration of this, consider the spinning 
 
 Fig. 16. 1 
 
 projectile of Fig. 10. The spin tends to keep its 
 axis always in the same direction. But there is a 
 defect in the arrangement, which you are now in a 
 
 1 Note. — In Fig. 16 the axis is shown inclined, but, only that 
 it would have been more troublesome to illustrate, I should 
 have preferred to show the precession occurring when the 
 axis keeps horizontal. 
 
SPINNING TOPS. 
 
 37 
 
 position to understand. You 
 see that at A the air must 
 be pressing upon the under- 
 surface A A, and I have to 
 explain that this pressure 
 tends to make the projectile 
 turn itself broadside on to 
 the air. A boat in a current 
 not allowed to move as a 
 whole, but tied at its middle, 
 sets itself broadside on to 
 the current. Observe this 
 disc of cardboard which I 
 drop through the air edge- 
 wise, and note how quickly 
 it sets itself broadside on 
 and falls more slowly ; and 
 some of you may have 
 thrown over into the water 
 at Aden small pieces of 
 silver for the diving boys, 
 and you are aware that if it 
 were not for this slow falling 
 of the coins with a wobbling 
 motion broadside on, it 
 would be nearly impossible 
 for any diving boy to get 
 possession of them. Now all 
 this is a parenthesis. The 
 
 \ 
 
 * 
 
3S SPINNING TOPS. 
 
 pressure of the air tends to make the projectile 
 turn broadside on, but as the projectile is spinning 
 it does not tilt up, no more than this gyrostat does 
 when I try to tilt it up, it really tilts out of the 
 plane of the diagram, out of the plane of its flight ; 
 and only that artillerymen know exactly what it 
 will do, this kind of windage of the projectile 
 would give them great trouble. 
 
 You will notice that an experienced child when 
 it wants to change the direction of a hoop, just 
 exerts a tilting pressure with its hoop-stick. A 
 man on a bicycle changes his direction by leaning 
 over so as to be out of balance. It is well to 
 remind you, however, that the motion of a bicycle 
 and its rider is not all rotational, so that it is not 
 altogether the analogue of a top or gyrostat. The 
 explanation of the swerving from a straight path 
 when the rider tilts his body, ultimately comes to the 
 same simple principle, Newton's second law of motion, 
 but it is arrived at more readily. It is for the same 
 reason — put briefly, the exercise of a centripetal 
 force — that when one is riding he can materially 
 assist his horse to turn a corner quickly, if he. does 
 not mind appearances, by inclining his body towards 
 the side to which he wants to turn ; and the more 
 slowly the horse is going the greater is the tendency 
 to turn for a given amount of tilting of one's body. 
 Circus-riders, when galloping in a circle, assist their 
 horses greatly by the position of their bodies ; it is 
 
SPINNING TOPS. 39 
 
 not to save themselves from falling by centrifugal 
 force that they take a position on a horse's back 
 which no riding-master would allow his pupil to 
 imitate ; and the respectable riders of this country 
 would not scorn to help their horses in this way to 
 quick turning movements, if the)' had to chase and 
 collect cattle like American cowboys. 
 
 Very good illustrations of change of direction 
 are obtained in playing bozvls. 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 pro- 
 duced 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 
 
 SPINNING TOPS. 
 
 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 observ- 
 ation will clear the 
 ground. 
 
 Here is a gyrostat 
 (Fig. 17), suspended 
 in gymbals so care- 
 fully 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 gyro- 
 stat. 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, hut if it was 
 pointing to the pole star at the beginning it re- 
 mains pointing to the pole star ; if it pointed 
 towards the moon at the beginning it still points 
 
 Fig. 17. 
 
SPINNING TOPS. 
 
 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 spin- 
 dle by means of a 
 screw and repeat 
 my ballet -dance 
 whirl ; you will 
 note that I need 
 not whirl round, 
 a very small por- 
 tion of a whirl is 
 enough to cause 
 this gyrostat 
 (Fig. 18) to set its 
 spinning axis ver- 
 tical, 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 
 
 Fig. 18. 
 
42 
 
 SPINNING TOPS. 
 
 gyrostat, you would find the following rule to be 
 generally true : — Pay no attention to mere trans- 
 lational motion, think only of rotation about axes, 
 and just remember that when you constrain the axis 
 of a spinning body to rotate, it will endeavour to 
 set its own axis parallel to 
 the new axis about which 
 you rotate it ; and not only 
 is this the case, but it will 
 endeavour to have the direc- 
 tion of its own spin the 
 same as the direction of 
 the new rotation. I again 
 twirl on my toes, holding 
 this frame, and now I know 
 that to a person looking 
 down upon the gyrostat and 
 me from the ceiling, as I 
 revolved in the direction 
 of the hands of a clock, 
 the gyrostat is spinning in 
 the direction of the hands 
 of a clock ; but if I revolve 
 against the clock direction (Fig. 19) the gyrostat 
 tumbles over so as again to be revolving in the 
 same direction as that in which I revolve. 
 
 This then is the simple rule which will enable 
 you to tell beforehand how a gyrostat will move 
 
 Fig. 19. 
 
SPINNING TOPS. 43 
 
 when you try to turn it in any particular direction. 
 You have only to remember that if you continued 
 your effort long enough, the spinning axis would 
 become parallel to your new axis of motion, and 
 the direction of spinning would be the same as the 
 direction of your new turning motion. 
 
 Now let me apply my rule to this balanced 
 gyrostat. I shove it, or give it an impulse down- 
 wards, but observe that this really means a rotation 
 about the horizontal axis C D (Fig. 13), and hence 
 the gyrostat turns its axis as if it wanted to become 
 parallel to C D. Thus, looking down from above 
 (as shown by Fig. 20), O E was the direction of the 
 spinning axis, O D was the axis about which I en- 
 deavoured to move it, and the instantaneous effect 
 was that O E altered to the position O G. A greater 
 impulse of the same kind would have caused the 
 spinning axis instantly to go to O H or O J, whereas 
 an upward opposite impulse would have instantly 
 made the spinning axis point in the direction O K, 
 O L. or O M, depending on how great the impulse was 
 and the rate of spinning. When one observes these 
 phenomena for the first time, one says, " I shoved 
 it down, and it moved to the right ; I shoved it up, 
 and it moved to the left ; " but if the direction of 
 the spin were opposite to what it is, one would say, 
 " I shoved it down, and it moved to the left ; I 
 shoved it up, and it moved to the right." The simple 
 
44 
 
 SPINNING TOPS. 
 
 statement in all cases ought to be, " I wanted to 
 rotate it about a new axis, and the effect was to 
 send its spinning axis towards the direction of the 
 new axis." And now if you play with this balanced 
 
 -7^0 
 
 M 
 
 Fig. 20. 
 
 gyrostat as I am doing, shoving it about in all 
 sorts of ways, you will find the rule to be a correct 
 one, and there is no difficulty in predicting what 
 will happen. 
 
SPINNING TOPS. 45 
 
 If this rule is right, \vc see at once why precession 
 takes place. I put this gyrostat (Fig. 13) out of 
 balance, and if it were not rotating it would fall 
 downwards ; but a force acting downwards really 
 causes the gyrostat to move to the right, and so you 
 see that it is continually moving in this way, for the 
 force is always acting downwards, and the spinning 
 axis is continually chasing the new axes about which 
 gravity tends continually to make it revolve. We 
 see also why it is that if the want of balance is 
 the other way, if gravity tends to lift the gyrostat, 
 the precession is in the opposite direction. And in 
 playing with this gyrostat as I do now, giving it all 
 sorts of pushes, one makes other observations and 
 sees that the above rule simplifies them all ; that is, 
 it enables us to remember them. For example, if 
 I use this stick to hurry on the precession, the 
 gyrostat moves in opposition to the force which 
 causes the precession. I am particularly anxious 
 that you should remember this. At present the 
 balance-weight is so placed that the gyrostat 
 would fall if it were not spinning. But it is 
 spinning, and so it precesses. If gravity were 
 greater it would precess faster, and it comes home 
 to Us that it is this precession which enables the 
 force of gravity to be inoperative in mere down- 
 ward motion. You see that if the precession is 
 hurried, it is more than sufficient to balance gravity, 
 
46 SPINNING TOPS. 
 
 and the gyrostat rises. If I retard the precession, it 
 is unable to balance gravity, and the gyrostat falls. 
 If I clamp this vertical axis so that precession is 
 impossible, you will notice that the gyrostat falls 
 just as if it were not spinning. If I clamp the 
 instrument so that it cannot move vertically, you 
 notice how readily I can make it move horizontally ; 
 I can set it rotating horizontally like any ordinary 
 body. 
 
 In applying our rule to this top, observe that 
 the axis of spinning is the axis E F of the top 
 (Fig. 12). As seen in the figure, gravity is tending to 
 make the top rotate about the axis F D, and the 
 spinning axis in its chase of the axis F D describes 
 a cone in space as it precesses. This gyrostat, 
 which is top-heavy, rotates and precesses in much 
 the same way as the top ; that is, if you apply 
 our rule, or use your observation, you will find that 
 to an observer above the table the spinning and 
 precession occur in the same direction, that is, 
 either both with the hands of a watch, or both 
 against the hands of a watch. Whereas, a top like 
 this before you (Fig. 21), supported above its centre 
 of gravity, or the gyrostat here (Fig. 22), which is 
 also supported above its centre of gravity, or the 
 gyrostat shown in Fig. 56, or any other gyrostat 
 supported in such a way that it would be in stable 
 equilibrium if it were not spinning ; in all these 
 
SPINNING TOPS. 47 
 
 cases, to an observer placed above the table, the 
 
 Fig. 21. 
 
 Fig. 22. 
 
 precession is in a direction opposite to that of the 
 spinning. 
 
48 SPINNING TOPS. 
 
 If an impulse be given to a top or gyrostat 
 in the direction of the precession, it will rise in 
 opposition to the force of gravity, and should at 
 any instant the precessional velocity be greater 
 than what it ought to be for the balance of the 
 force of gravity, the top or gyrostat will rise, its 
 precessional velocity diminishing. If the preces- 
 sional velocity is too small, the top will fall, and as 
 it falls the precessional velocity increases. 
 
 Now I say that all these facts, which are mere 
 facts of observation, agree with our rule. I wish I 
 dare ask you to remember them all. You will 
 observe that in this wall sheet I have made a 
 list of them. I speak of gravity as causing the 
 precession, but the forces may be any others than 
 such as are due to gravity. 
 
 Wall Sheet. 
 
 I. Rule. When forces act upon a spinning body, 
 tending to cause rotation about any other axis than 
 the spinning axis, the spinning axis sets itself in 
 better agreement with the new axis of rotation. 
 Perfect agreement would mean perfect parallelism, 
 the directions of rotation being the same. 
 
 II. Hurry on the precession, and the body rises 
 in opposition to gravity. 
 
SPINNING TOPS. 49 
 
 III. Delay the precession and the body falls, as 
 gravity would make it do if it were not spinning. 
 
 IV. A common top precesscs in the same 
 direction as that in which it spins. 
 
 V. A top supported above its centre of gravity, 
 or a body which would be in stable equilibrium if 
 not spinning, precesses in the opposite direction to 
 that of its spinning. 
 
 VI. The last two statements come to this : — 
 When the forces acting on a spinning body tend to 
 make the angle of precession greater, the precession 
 is in the same direction as the spinning, and vice 
 versa. 
 
 Having by observation obtained a rule, every 
 natural philosopher tries to make his rule a rational 
 one ; tries to explain it. I hope you know what we 
 mean when we say that we explain a phenomenon ; 
 we really mean that we show the phenomenon to 
 be consistent with other better known phenomena. 
 Thus when you unmask a spiritualist and show 
 that the phenomena exhibited by him are due to 
 mere sleight-of-hand and trickery, you explain the 
 phenomena. When you show that they are all 
 consistent with well-observed and established 
 mesmeric influences, you are also said to explain 
 the phenomena. When you show that they can be 
 effected by means of telegraphic messages, or by 
 reflection of light from mirrors, you explain the 
 
 D 
 
5o 
 
 SPINNING TOPS. 
 
 phenomena, although in all these cases you do not 
 really know the nature of mesmerism, electricity, 
 light, or moral obliquity. 
 
 The meanest kind of criticism is that of the man 
 who cheapens a scientific explanation by saying 
 that the very simplest facts 
 of nature are unexplain- 
 able. Such a man prefers 
 the chaotic and indiscrim- 
 inate wonder of the savage 
 to the reverence of a Sir 
 Isaac Newton. 
 
 The explanation of our 
 rule is easy. Here is a 
 gyrostat (Fig. 23) some- 
 thing like the earth in 
 shape, and it is at rest. I 
 am sorry to say that I am 
 compelled to support this 
 globe in a very visible 
 manner by gymbal rings. 
 If this globe were just float- 
 ing in the air, if it had no tendency to fall, my 
 explanation would be easier to understand, and 
 I could illustrate it better experimentally. Observe 
 the point P. If I move the globe slightly about 
 the axis A, the point P moves to Q. But suppose 
 instead of this that the globe and inner gymbal 
 
 Fro. 23. 
 
SPINNING TOPS. 51 
 
 ring had been moved about the axis B ; the point 
 P would have moved to R. Well, suppose both 
 those rotations took place simultaneously. You 
 all know that the point P would move neither to 
 Q nor to R, but it would move to S ; PS being 
 the diagonal of the little parallelogram. The re- 
 sultant motion then is neither about the axis O A 
 in space, nor about the axis O B, but it is about 
 some such axis as O C. 
 
 To this globe I have given two rotations simul- 
 taneously. Suppose a little being to exist on this 
 globe which could not see the gymbals, but was 
 able to observe other objects in the room. It 
 would say that the direction of rotation is neither 
 about O A nor about O B, but that the real 
 axis of its earth is some line intermediate, O C 
 in fact. 
 
 If then a ball is suddenly struck in two different 
 directions at the same instant, to understand how 
 it will spin we must first find how much spin each 
 blow would produce if it acted alone, and about 
 what axis. A spin of three turns per second about 
 the axis O A (Fig. 24). and a spin of two turns 
 per second about the axis O B, really mean that 
 the ball will spin about the axis O C with a spin 
 of three and a half turns per second. To arrive 
 at this result, I made O A, 3 feet long (any other 
 scale of representation would have been right) 
 
.52 
 
 SPINNING TOPS. 
 
 and O B, 2 feet long, and I found the diagonal O C 
 of the parallelogram shown on the figure to be 
 3 1 feet long. 
 
 Observe that if the rotation about the axis O A 
 is with the hands of a watch looking from O to A, 
 the rotation about the axis O B looking from O to 
 B, must also be with the 
 hands of a watch, and the 
 resultant rotation about vl^ 
 the axis O C is also in a 
 direction with the hands 
 of a watch looking from 
 O to C. Fig. 25 shows 
 in two diagrams how 
 necessary it is that on 
 looking from O along 
 either O A or O B, the 
 rotation should be in the 
 same direction as regards 
 the hands of a watch. 
 These constructions are 
 well known to all who have studied elementary 
 mechanical principles. Obviously if the. rotation 
 about O A is very much greater than the rotation 
 about O B, then the position of the new axis O C 
 must be much nearer O A than O B. 
 
 We see then that if a body is spinning about 
 an axis O A, and we apply forces to it which 
 
 Fig. 24. 
 
SPINNING TOPS. 
 
 53 
 
 would, if it were at rest, turn it about the axis 
 O B ; the effect is to cause the spinning axis to be 
 altered to O C ; that is, the spinning axis sets 
 itself in better agreement with the new axis of 
 rotation. This is the first statement on our wall 
 sheet, the rule from which all our other statements 
 
 Fig. 25. 
 
 are derived, assuming that they were not really 
 derived from observation. Now I do not say that 
 I have here given a complete proof for all cases, 
 for the fly-wheels in these gyrostats are running in 
 bearings, and the bearings constrain the axes to 
 take the new positions, whereas there is no such 
 
54 SPINNING TOPS. 
 
 constraint in this top ; but in the limited time of 
 a popular lecture like this it is not possible, even 
 if it were desirable, to give an exhaustive proof of 
 such a universal rule as ours is. That I have not 
 exhausted all that might be said on this subject 
 will be evident from what follows. 
 
 If we have a spinning ball and we give to it a 
 new kind of rotation, what will happen ? Suppose, 
 for example, that the earth were a homogeneous 
 sphere, and that there were suddenly impressed 
 upon it a new rotatory motion tending to send 
 Africa southwards ; the axis of this new spin 
 would have its pole at Java, and this spin combined 
 with the old one would cause the earth to have its 
 true pole somewhere between the present pole and 
 Java. It would no longer rotate about its present 
 axis. In fact the axis of rotation would be altered, 
 and there would be no tendency for anything 
 further to occur, because a homogeneous sphere 
 will as readily rotate about one axis as another. 
 But if such a thing were to happen to this earth of 
 ours, which is not a sphere but a flattened spheroid 
 like an orange, its polar diameter being the one- 
 third of one per cent, shorter than the equatorial 
 diameter ; then as soon as the new axis was estab- 
 lished, the axis of symmetry would resent the 
 change and would try to become again the axis of 
 rotation, and a great wobbling motion would ensue. 
 
SPINNING TOPS. 55 
 
 I put the matter in popular language when I speak 
 of the resentment of an axis ; perhaps it is better 
 to explain more exactly what I mean. I am going 
 to use the expression Centrifugal Force. Now there 
 are captious critics who object to this term, but all 
 engineers use it, and I like to use it, and our 
 captious critics submit to all sorts of ignominious 
 involution of language in evading the use of it. 
 It means the force with which any body acts upon 
 its constraints when it is constrained to move in a 
 curved path. The force is always directed away 
 from the centre of the curve. When a ball is 
 whirled round in a curve at the end of a string its 
 centrifugal force tends to break the string. When 
 any body keyed to a shaft is revolving with the 
 shaft, it may be that the centrifugal forces of all 
 the parts just balance one another ; but sometimes 
 they do not, and then we say that the shaft is 
 out of balance. Here, for example, is a disc of 
 wood rotating. It is in balance. But I stop 
 its motion and fix this piece of lead, A, to it, 
 and you observe when it rotates that it is so 
 much out of balance that the bearings of the 
 shaft and the frame that holds them, and even 
 the lecture-table, are shaking. Now I will put 
 things in balance again by placing another piece 
 of lead, B, on the side of the spindle remote from 
 A, and when I again rotate the disc (Fig. 26) there 
 
$6 SPINNING TOPS. 
 
 is no longer any shaking of the framework. When 
 the crank-shaft of a locomotive has not been put in 
 balance by means of weights suitably placed on 
 the driving-wheels, there is nobody in the train 
 who does not feel the effects. Yes, and the coal- 
 bill shows the effects, for an unbalanced engine 
 tugs the train spasmodically instead of exerting an 
 efficient steady pull. My friend Professor Milne, 
 of Japan, places earthquake measuring instruments 
 
 Fig. 2b. 
 
 on engines and in trains for measuring this and 
 other wants of balance, and he has shown unmis- 
 takably that two engines of nearly the same 
 general design, one balanced properly and the 
 other not, consume very different amounts of 
 coal in making the same journey at the same 
 speed. 
 
 If a rotating body is in balance, not only does 
 the axis of rotation pass through the centre of 
 gravity (or rather centre of mass) of the body, but 
 
SPINNING TOPS. 
 
 57 
 
 the axis of rotation must be one of the three prin- 
 cipal axes through the centre of mass of the body. 
 Here, for example, is an ellipsoid of wood ; A A, 
 B B, and C C (Fig. 27) are its 
 three principal axes, and it 
 would be in balance if it rotated 
 about any one of these three 
 axes, and it would not be in 
 balance if it rotated about any 
 other axis, unless, indeed, it were 
 like a homogeneous sphere, every 
 diameter of which is a principal 
 axis. 
 
 Every body has three such 
 principal axes through its centre 
 of mass, and this body (Fig. 27) 
 has them ; but I have here constrained it to rotate 
 about the axis D D, and you all observe the effect 
 of the unbalanced centrifugal forces, which is nearly 
 great enough to tear the framework in pieces. The 
 higher the speed the more important this want of 
 balance is. If the speed is doubled, the centri- 
 fugal forces become four times as great ; and 
 modern mechanical engineers with their quick 
 speed engines, some of which revolve, like the fan- 
 engines of torpedo-boats, at 1700 revolutions per 
 minute, require to pay great attention to this sub- 
 ject, which the older engineers never troubled their 
 
 Fig. 27. 
 
58 SPINNING TOPS. 
 
 heads about. You must remember that even when 
 want of balance does not actually fracture the 
 framework of an engine, it will shake everything, 
 so that nuts and keys and other fastenings are 
 pretty sure to get loose. 
 
 I have seen, on a badly-balanced machine, a 
 securely-fastened pair of nuts, one supposed to be 
 locking the other, quietly revolving on their bolt 
 at the same time, and gently lifting themselves at 
 a regular but fairly rapid rate, until they both 
 tumbled from the end of the bolt into my hand. 
 If my hand had not been there, the bolts would 
 have tumbled into a receptacle in which they 
 would have produced interesting but most de- 
 structive phenomena. You would have somebody 
 else lecturing to you to-night if that event had 
 come off. 
 
 Suppose, then, that our earth were spinning 
 about any other axis than its present axis, the axis 
 of figure. If spun about any diameter of the equator 
 for example, centrifugal forces would just keep 
 things in a state of unstable equilibrium, and no 
 great change might be produced until some acci- 
 dental cause effected a slight alteration in the spin- 
 ning axis, and after that the earth would wobble 
 very greatly. How long and how violently it v/ould 
 wobble, would depend on a number of circumstances 
 about which I will not now venture to guess. If you 
 
SPINNING TOPS. 59 
 
 tell me that on the whole, in spite of the violence 
 of the wobbling, it would not get shaken into a new 
 form altogether, then I know that in consequence 
 of tidal and other friction it would eventually 
 come to a quiet state of spinning about its present 
 axis. 
 
 You see, then, that although every body has 
 three axes about which it will rotate in a balanced 
 fashion without any tendency to wobble, this 
 balance of the centrifugal forces is really an unstable 
 balance in two out of the three cases, and there is 
 only one axis about which a perfectly stable 
 balanced kind of rotation will take place, and a 
 spinning body generally comes to rotate about this 
 axis in the long run if left to itself, and if there is 
 friction to still the wobbling. 
 
 To illustrate this, I have here a method of 
 spinning bodies which enables them to choose as 
 their spinning axis that one principal axis about 
 which their rotation is most stable. The various 
 bodies can be hung at the end of this string, and I 
 cause the pulley from which the string hangs to 
 rotate. Observe that at first the disc (Fig. 28 a) 
 rotates soberly about the axis A A, but you note 
 the small beginning of the wobble ; now it gets 
 quite violent, and now the disc is stably and 
 smoothly rotating about the axis B B, which is the 
 most important of its principal axes. 
 
60 SPINNING TOTS. 
 
 Again, this cone (Fig. 28 b) rotates smoothly at 
 first about the axis A A, but the wobble begins 
 and gets very great, and eventually the cone rotates 
 smoothly about the axis B B, which is the most 
 important of its principal axes. Here again is a 
 rod hung from one end (Fig. 28 d). 
 
 See also this anchor ring. But you may be more 
 interested in this limp ring of chain (Fig. 28 c). See 
 how at first it hangs from the cord vertically, and 
 how the wobbles and vibrations end in its be- 
 coming a perfectly circular ring lying all in a 
 horizontal plane. This experiment illustrates also 
 the quasi-rigidity given to a flexible body by rapid 
 motion. 
 
 To return to this balanced gyrostat of ours 
 (Fig. 13). It is not precessing, so you know that 
 the weight W just balances the gyrostat F. Now 
 if I leave the instrument to itself after I give a 
 downward impulse to F, not exerting merely a 
 steady pressure, you will notice that F swings to 
 the right for the reason already given ; but it swings 
 too fast and too far, just like any other swinging 
 body, and it is easy from what I have already 
 said, to see that this wobbling motion (Fig. 29) 
 should be the result, and that it should continue 
 until friction stills it, and F takes its permanent 
 new position only after some time elapses. 
 
 You see that I can impose this wobble or nodding 
 
SPINNING TOPS. 
 
 61 
 
 IP** 
 I 
 
 ^ 
 
62 SPINNING TOPS. 
 
 motion upon the gyrostat whether it has a motion 
 of precession or not. It is now nodding as it pre- 
 cesses round and round — that is, it is rising and 
 falling as it precesses. 
 
 Fig. 29. 
 
 Perhaps I had better put the matter a little more 
 clearly. You see the same phenomenon in this 
 top. If the top is p recessing too fast for the force 
 of gravity the top rises, and the precession diminishes 
 in consequence ; the precession being now too slow 
 to balance gravity, the top falls a little and the 
 
SPINNING TOPS. 63 
 
 precession increases again, and this sort of vibration 
 about a mean position goes on just as the vibration 
 of a pendulum goes on till friction destroys it, and 
 the top precesses more regularly in the mean posi- 
 tion. This nodding is more evident in the nearly 
 horizontal balanced gyrostat than in a top, because 
 in a top the turning effect of gravity is less in the 
 higher positions. 
 
 When scientific men try to popularize their dis- 
 coveries, for the sake of making some fact very 
 plain they will often tell slight untruths, making 
 statements which become rather misleading when 
 their students reach the higher levels. Thus 
 astronomers tell the public that the earth goes 
 round the sun in an elliptic path, whereas the 
 attractions of the planets cause the path to be only 
 approximately elliptic ; and electricians tell the 
 public that electric energy is conveyed through 
 wires, whereas it is really conveyed by all other 
 space than that occupied by the wires. In this 
 lecture I have to some small extent taken advantage 
 of you in this way ; for example, at first you will 
 remember, I neglected the nodding or wobbling 
 produced when an impulse is given to a top or 
 gyrostat, and, all through, I neglect the fact that 
 the instantaneous axis of rotation is only nearly 
 coincident with the axis of figure of a precessing 
 gyrostat or top. And indeed you may generally 
 
64 SPINNING TOPS. 
 
 take it that if all one's statements were absolutely 
 accurate, it would be necessary to use hundreds 
 of technical terms and involved sentences with 
 explanatory, police-like parentheses ; and to listen 
 to many such statements would be absolutely im- 
 possible, even for a scientific man. You would 
 hardly expect, however, that so great a scientific 
 man as the late Professor Rankine, when he was 
 seized with the poetic fervour, would err even more 
 than the popular lecturer in making his accuracy 
 of statement subservient to the exigencies of the 
 rhyme as well as to the necessity for simplicity of 
 statement. He in his poem, The Mathematician in 
 Love, has the following lines — 
 
 " The lady loved dancing ; — he therefore applied 
 To the polka and waltz, an equation ; 
 But when to rotate on his axis he tried, 
 His centre of gravity swayed to one side, 
 And he fell by the earth's gravitation." 
 
 Now I have no doubt that this is as good "drop- 
 ping into poetry" as can be expected in a scientific 
 man, and 's science is as good as can be ex- 
 pected in a man who calls himself a poet ; but in 
 both cases we have illustrations of the incompati- 
 bility of science and rhyming. 
 
 The motion of this gyrostat can be made even 
 more complicated than it was when we had nuta- 
 
SPINNING TOPS. 
 
 65 
 
 tion and precession, but there is really nothing in 
 it which is not readily explainable by the simple 
 principles I have put before you. Look, for 
 example, at this well-balanced gyrostat (Fig. if). 
 When I strike this inner gymbal ring in any way 
 you see that it wriggles quickly just as if it were 
 
 Fig. 17. 
 
 a lump of jelly, its rapid vibrations dying away 
 just like the rapid vibrations of any yielding 
 elastic body. This strange elasticity is of very 
 great interest whsn we consider it in relation to 
 the molecular properties of matter. Here again 
 (Fig. 30) we have an example which is even 
 more interesting. I have supported the cased 
 
 E 
 
66 
 
 SPINNING TOPS. 
 
 gyrostat of Figs. 5 and 6 upon a pair of stilts, 
 and you will observe that it is moving about 
 a perfectly stable position with a very curious 
 staggering kind of vibratory motion ; but there 
 is nothing in these motions, however curious, 
 that you cannot easily explain if you have followed 
 me so far. 
 
 Fig. 30. 
 
 Some of you who are more observant than the 
 others, will have remarked that all these precessing 
 gyrostats gradually fall lower and lower, just as 
 they would do, only more quickly, if they were not 
 spinning. And if you cast your eye upon the 
 third statement of our wall sheet-(p. 49) you will 
 readily understand why it is so. 
 
 " Delay the precession and the body falls, as 
 gravity would make it do if it were not spinning." 
 
SPINNING TOPS. 67 
 
 Well, the precession of every one of these is 
 resisted by friction, and so they fall lower and 
 lower. 
 
 I wonder if any of you have followed me so 
 well as to know already why a spinning top rises. 
 Perhaps you have not yet had time to think it out, 
 but I have accentuated several times the particular 
 fact which explains this phenomenon. Friction 
 makes the gyrostats fall, what is it that causes a 
 top to rise ? Rapid rising to the upright position 
 is the invariable sign of rapid rotation in a top, 
 and I recollect that when quite vertical we used 
 to say, " She sleeps ! " Such was the endearing 
 way in which the youthful experimenter thought 
 of the beautiful object of his tender regard. 
 
 All so well known as this rising tendency of a 
 top has been ever since tops were first spun, I 
 question if any person in this hall knows the 
 explanation, and I question its being known to 
 more than a few persons anywhere. Any great 
 mathematician will tell you that the explanation 
 is surely to be found published in Routh, or that 
 at all events he knows men at Cambridge who 
 surely know it, and he thinks that he himself must 
 have known it, although he has now forgotten 
 those elaborate mathematical demonstrations which 
 he once exercised his mind upon. I believe that 
 all such statements are made in error, but I cannot 
 
68 SPINNING TOPS. 
 
 be sure. 1 A partial theory of the phenomenon was 
 given by Mr. Archibald Smith in the Cambridge 
 Mathematical Journal many years ago, but the 
 problem was solved by Sir William Thomson and 
 Professor Blackburn when they stayed together one 
 year at the seaside, reading for the great Cambridge 
 mathematical examination. It must have alarmed 
 a person interested in Thomson's success to notice 
 that the seaside holiday was really spent by him 
 and his friend in spinning all sorts of rounded 
 stones which they picked up on the beach. 
 
 And I will now show you the curious phenomenon 
 that puzzled him that year. This ellipsoid (Fig. 31) 
 will represent a waterworn stone. It is lying in 
 its most stable state on the table, and I give it a 
 spin. You see that for a second or two it was 
 inclned to go on spinning about the axis A A, but 
 it began to wobble violently, and after a while, 
 when these wobbles stilled, you saw that it was 
 spinning nicely with its axis B B vertical ; but then 
 a new series of wobblings began and became more 
 violent, and when they ceased you saw that the 
 object had at length reached a settled state of 
 
 1 When this lecture containing the above statement was 
 in the hands of the printers, I was directed by Prof. Fitzgerald 
 to the late Prof. Jellet's Treatise on the Theory of Friction, 
 published in 1872, and there at page 18 I found the mathe- 
 matical explanation of the rising of a top. 
 
SPINNING TOPS. 
 
 6 9 
 
 spinning, standing upright upon its longest axis. 
 This is an extraordinary phenomenon to any 
 person who knows about the great inclination of 
 this body to spin in the very way in which I first 
 started it spinning. You will find that nearly 
 any rounded stone when spun will get up in 
 this way upon its longest axis, if the spin is 
 only vigorous enough, and in the very same way 
 
 Fig. 31. 
 
 this spinning top tends to get more and more 
 upright. 
 
 I believe that there are very few mathematical 
 explanations of phenomena which may not be 
 given in quite ordinary language to people who 
 have an ordinary amount of experience. In most 
 cases the symbolical algebraic explanation must 
 be given first by somebody, and then comes the 
 time for its translation into ordinary language. 
 This is the foundation of the new thing called 
 Technical Education, which assumes that a work- 
 
70 SPINNING TOPS. 
 
 man may be taught the principles underlying the 
 operations which go on in his trade, if we base 
 our explanations on the experience which the 
 man has acquired already, without tiring him 
 with a four yearn' course of study in elementary 
 things such as is most suitable for inexperienced 
 children and youths at public schools and the 
 universities. 
 
 With your present experience the explanation 
 of the rising of the top becomes ridiculously simple. 
 If you look at statement two on this wall sheet (p. 48) 
 and reflect a little, some of you will be able, with- 
 out any elaborate mathematics, to give the simple 
 reason for this that Thomson gave me sixteen 
 years ago. " Hurry on the precession, and the 
 body rises in opposition to gravity." Well, as I 
 am not touching the top, and as the body does 
 rise, we look at once for something that is hurrying 
 on the precession, and we naturally look to the 
 way in which its peg is rubbing on the table, for, 
 with the exception of the atmosphere this top 
 is touching nothing else than the table. Observe 
 carefully how any of these objects precesses. Fig. 32 
 shows the way in which a top spins. Looked at 
 from above, if the top is spinning in-the direction 
 of the hands of a watch, we know from the fourth 
 statement of our wall sheet, or by mere observation, 
 that it also precesses in the direction of the hands 
 
SPINNING TOPS. 
 
 71 
 
 of a watch ; that is, its precession is such as to 
 make the peg roll at B into the paper. For you 
 will observe that the peg is rolling round a circular 
 
 path on the table, G being nearly motionless, and 
 the axis A G A describing nearly a cone in space 
 whose vertex is G, above the table. Fig. 33 
 
7 2 SPINNING TOPS. 
 
 shows the peg enlarged, and it is evident that the 
 point B touching the table is really like the bottom 
 of a wheel B B', and as this wheel is rotating, 
 the rotation causes it to roll into the paper, away 
 from us. But observe that its mere precession 
 
 A 
 
 Fig. 33. 
 
 is making it roll into the paper, and that the spin 
 if great enough wants to roll the top faster than 
 the precession lets it roll, so that it Hurries on the 
 precession, and therefore the top rises. That is 
 the simple explanation ; the spin, so long as it is 
 
SPINNING TOPS. 
 
 73 
 
 great enough, is always hurrying on the precession, 
 and if you will cast your recollection back to the 
 days of your youth, when a top was supported on 
 your hand as this is now on mine (Fig 34), and the 
 spin had grown to be quite 
 small, and was unable to 
 keep the top upright, you 
 will remember that you 
 dexterously helped the pre- 
 cession by giving your hand 
 a circling motion so as to 
 get from your top the ad- 
 vantages as to uprightness 
 of a slightly longer spin. 
 
 I must ask you now by 
 observation, and the application of exactly the 
 same argument, to explain the struggle for up- 
 rightness on its longer axis of any rounded stone 
 when it spins on a table. I may tell you that 
 some of these large rounded-looking objects which 
 I now spin before you in illustration, are made 
 hollow, and they are either of wood or zinc, 
 because I have not the skill necessary to spin 
 large solid objects, and yet I wanted to have 
 objects which you would be able to see. This 
 small one (Fig. 31) is the largest solid one to which 
 my fingers are able to give sufficient spin. Here 
 is a very interesting object (Fig. 35), spherical 
 
 Fig. 34. 
 
74 SPINNING TOPS. 
 
 in shape, but its centre of gravity is not exactly 
 at its centre of figure, so when I lay it on the 
 table it always gets to its position of stable 
 equilibrium, the white spot touching the table 
 as at A. Some of you know that if this sphere 
 is thrown into the air it seems to have very 
 curious motions, because one is so apt to forget 
 that it is the motion of its centre of gravity 
 which follows a simple path, and the boundary is 
 eccentric to the centre of gravity. Its motions 
 
 when set to roll upon a carpet are also extremely 
 curious. 
 
 Now for the very reasons that I have already 
 given, when this sphere is made to spin on the 
 table, it always endeavours to get its white spot 
 uppermost, as in C, Fig. 35 ; to get into the posi- 
 tion in which when not spinning it would be 
 unstable. 
 
 The precession of a top or gyrostat leads us at 
 once to think of the precession of the great spinning 
 body on which we live. You know that the earth 
 
SPINNING TOPS. 75 
 
 spins on its axis a little more than once every twenty- 
 four hours, as this orange is revolving, and that it 
 goes round the sun once in a year, as this orange is 
 now going round a model sun, or as is shown in the 
 diagram (Fig. 36). Its spinning axis points in the 
 direction shown, very nearly to the star which is 
 called the pole star, almost infinitely far away. In 
 the figure and model I have greatly exaggerated 
 the elliptic nature of the earth's path, as is quite 
 usual, although it may be a little misleading, because 
 the earth's path is much more nearly circular than 
 many people imagine. As a matter of fact the 
 earth is about three million miles nearer the sun in 
 winter than it is in summer. This seems at first 
 paradoxical, but we get to understand it when we 
 reflect that, because of the slope of the earth's axis 
 to the ecliptic, we people who live in the northern 
 hemisphere have the sun less vertically above us, 
 and have a shorter day in the winter, and hence 
 each square foot of our part of the earth's surface 
 receives much less heat every day, and so we feel 
 colder. Now in about 13,000 years the earth will 
 have precessed just half a revolution {see Fig. 38) ; 
 the axis will then be sloped towards the sun when 
 it is nearest, instead of away from it as it is now ; 
 consequently we shall be much v/armer in summer 
 and colder in winter than we are now. Indeed we 
 shall then be much worse off than the southern 
 
76 
 
 SPINNING TOPS. 
 
 GO 
 
 / 
 
 / 
 
SPINNING TOPS. 77 
 
 hemisphere people are now, for they have plenty 
 of oceanic water to temper their climate. It is 
 easy to see the nature of the change from figures 
 36, 37, and 38, or from the model as I carry the 
 orange and its symbolic knitting-needle round the 
 model sun. Let us imagine an observer placed 
 above this model, far above the north pole of the 
 earth. He sees the earth rotating against the 
 direction of the hands of a watch, and he finds that 
 it precesses with the hands of a watch, so that spin 
 and precession are in opposite directions. Indeed 
 it is because of this that we have the word " pre- 
 cession," which we now apply to the motion of a 
 top, although the precession of a top is in the 
 same direction as that of the spin. 
 
 The practical astronomer, in explaining the luni- 
 solar precession of the equinoxes to you, will not 
 probably refer to tops or gyrostats. He will tell 
 you that the longitude and right ascension of a 
 star seem to alter ; in fact that the point on the 
 ecliptic from which he makes his measurements, 
 namely, the spring equinox, is slowly travelling 
 round the ecliptic in a direction opposite to that 
 of the earth in its orbit, or to the apparent path 
 of the sun. The spring equinox is to him for 
 heavenly measurements what the longitude of 
 Greenwich is to the navigator. He will tell you 
 that aberration of light, and parallax of the stars, 
 
78 
 
 SPINNING TOPS. 
 
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SPINNING TOPS. 
 
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80 SPINNING TOPS. 
 
 but more than both, this precession of the equinoxes, 
 are the three most important things which prevent 
 us from seeing in an observatory by transit observ- 
 ations of the stars, that the earth is revolving with 
 perfect uniformity. But his way of describing the 
 precession must not disguise for you the physical 
 fact that his phenomenon and ours are identical, and 
 that to us who are acquainted with spinning tops, 
 the slow conical motion of a spinning axis is more 
 readily understood than those details of his measure- 
 ments in which an astronomer's mind is bound up, 
 and which so often condemn a man of great in- 
 tellectual power to the life of drudgery which we 
 generally associate with the idea of the pound-a- 
 week cheap clerk. 
 
 The precession of the earth is then of the same 
 nature as that of a gyrostat suspended above its 
 centre of gravity, of a body which would be stable 
 and not top-heavy if it were not spinning. In fact 
 the precession of the earth is of the same nature 
 as that of this large gyrostat (Fig. 22), which is 
 suspended in gymbals, so that it has a vibration 
 like a pendulum when not spinning. I will now 
 spin it, so that looked at from above it goes against 
 the hands of a watch, and you observe that it pre- 
 cesses with the hands of a watch. Here again 
 is a hemispherical wooden ship, in which there is 
 a gyrostat with its axis vertical. It is in stable 
 
SPINNING TOPS. 
 
 81 
 
 equilibrium. When the gyrostat is not spinning, 
 the ship vibrates slowly when put out of equili- 
 brium ; when the gyrostat is spinning the ship gets a 
 motion of precession which is opposite in direction to 
 that of the spinning. Astronomers, beginning with 
 Hipparchus, have made observations of the earth's 
 motion for us, and we have observed the motions 
 of gyrostats, and we naturally seek for an explana- 
 
 FlG. 22. 
 
 tion of the precess : onal motion of the earth. The 
 equator of the earth makes an angle of 231° with 
 the ecliptic, which is the plane of the earth's orbit. 
 Or the spinning axis of the earth is always at 
 angle of 231° with a perpendicular to the ecliptic, 
 and makes a complete revolution in 26,000 years. 
 The surface of the water on which this wooden 
 ship is floating represents the ecliptic. The axis 
 
 F 
 
82 SPINNING TOPS. 
 
 of spinning of the gyrostat is about 23^° to the 
 vertical ; the precession is in two minutes instead 
 of 26,000 years ; and only that this ship does not 
 revolve in a great circular path, we should have in 
 its precession a pretty exact illustration of the 
 earth's precession. 
 
 The precessional motion of the ship, or of the 
 gyrostat (Fig. 22), is explainable, and in the same 
 way the earth's precession is at once explained if 
 we find that there are forces from external bodies 
 tending to put its spinning axis at right angles to 
 the ecliptic. The earth is a nearly spherical body. 
 If it were exactly spherical and homogeneous, the 
 resultant force of attraction upon it, of a distant 
 body, would be in a line through its centre. And 
 again, if it were spherical and non homogeneous, 
 but if its mass were arranged in uniformly dense, 
 spherical layers, like the coats of an onion. But 
 the earth is not spherical, and to find what is the 
 nature of the attraction of a distant body, it has 
 been necessary to make pendulum observations all 
 over the earth. You know that if a pendulum does 
 not alter in length as we take it about to various 
 places, its time of vibration at each place enables 
 the force of gravity at each place to be determined ; 
 and Mr. Green proved that if we know the force 
 of gravity at all places on the surface of the 
 earth, although we may know nothing about the 
 
SPINNING TOPS. 
 
 state of the inside of the earth, we 
 can calculate with absolute accuracy 
 the force exerted by the earth on 
 matter placed anywhere outside the 
 earth ; for instance, at any part of the 
 moon's orbit, or at the sun. And 
 hence we know the equal and oppo- 
 site force with which such matter will 
 act on the earth. Now pendulum 
 observations have been made at a 
 great many places on the earth, and 
 we know, although of course not 
 with absolute accuracy, the attrac- 
 tion on the earth, of matter outside 
 the earth. For instance, we know 
 that the resultant attraction of A 
 the sun on the earth is a force 
 which does not pass through 
 the centre of the earth's mass. 
 You may comprehend the 
 result better if I refer to 
 this diagram of the 
 earth at midwinter 
 (Fig. 39), and use a 
 popular method of de- 
 scription. A and B may 
 roughly be called the protuberant 
 parts of the earth — that protuberant 
 belt of matter which makes the 
 
 zO 
 
 83 
 
84 SPINNING TOPS. 
 
 earth orange-shaped instead of spherical. On the 
 spherical portion inside, assumed roughly to be 
 homogeneous, the resultant attraction is a force 
 through the centre. 
 
 I will now consider the attraction on the pro- 
 tuberant equatorial belt indicated by A and B. 
 The sun attracts a pound of matter at B more 
 than it attracts a pound of matter at A, because 
 B is nearer than A, and hence the total resultant 
 force is in the direction M N rather than O O, 
 through the centre of the earth's mass. But we 
 know that a force in the direction M N is equiva- 
 lent to a force O O parallel to M N, together with a 
 tilting couple of forces tending to turn the equator 
 edge on to the sun. You will get the true result as 
 to the tilting tendency by imagining the earth to 
 be motionless, and the sun's mass to be distributed 
 as a circular ring of matter 184 millions of miles in 
 diameter, inclined to the equator at 23J . Under 
 the influence of the attraction of this ring the earth 
 would heave like a great ship on a calm sea, rolling 
 very slowly ; in fact, making one complete swing in 
 about three years. But the earth is spinning, and the 
 tilting couple or torque acts upon it just like the 
 forces which are always tending to cause this ship- 
 model to stand upright, and hence it has^a preces- 
 sional motion whose complete period is 26,000 
 years. When there is no spin in the ship, its com- 
 plete oscillation takes place in three seconds, and 
 
SPINNING TOPS. 85 
 
 when I spin the gyrostat on board the ship, the 
 complete period of its precession is two minutes. 
 In both cases the effect of the spin is to convert 
 what would be an oscillation into a very much 
 slower precession. 
 
 There is, however, a great difference between the 
 earth and the gyrostat. The forces acting on the 
 top are always the same, but the forces acting on 
 the earth are continually altering. At midwinter 
 and midsummer the tilting forces are greatest, and 
 at the equinoxes in spring and autumn there are 
 no such forces. So that the precessional motion 
 changes its rate every quarter year from a maxi- 
 mum to nothing, or from nothing to a maximum. 
 It is, however, always in the same direction — the 
 direction opposed to the earth's spin. When we 
 speak then of the precessional motion of the earth, 
 we usually think of the mean or average motion, 
 since the motion gets quicker and slower every 
 quarter year. 
 
 Further, the moon is like the sun in its action. 
 It tries to tilt the equatorial part of the earth into 
 the plane of the moon's orbit. The plane of the 
 moon's orbit is nearly the same as that of the 
 ecliptic, and hence the average precession of the 
 earth is of much the same kind as if only one of 
 the two, the moon or the sun, alone acted. That 
 is, the general phenomenon of precession of the 
 
86 SPINNING TOPS. 
 
 earth's axis in a conical path in 26,000 years is the 
 effect of the combined tilting actions of the sun 
 and moon. 
 
 You will observe here an instance of the sort of 
 untruth which it is almost imperative to tell in 
 explaining natural phenomena. Hitherto I had 
 spoken only of the sun as producing precession of 
 the earth. This was convenient, because the plane 
 of the ecliptic makes always almost exactly 23!° 
 with the earth's equator, and although on the whole 
 the moon's action is nearly identical with that of 
 the sun, and about twice as great, yet it varies 
 considerably. The superior tilting action of the 
 moon, just like its tide-producing action, is due to 
 its being so much nearer us than the sun, and 
 exists in spite of the very small mass of the moon 
 as compared with that of the sun. 
 
 As the ecliptic makes an angle of 23^° with the 
 earth's equator, and the moon's orbit makes an 
 angle 5^° with the ecliptic, we see that the moon's 
 orbit sometimes makes an angle of 29 with the 
 earth's equator, and sometimes only 18 , changing 
 from 29 to 1 8°, and back to 29 again in about 
 nineteen years. This causes what is called " Nuta- 
 tion," or the nodding of the earth, for the tilting 
 action due to the sun is greatly helped and greatly 
 modified by it. The result of the variable nature 
 of the moon's action is then that the earth's axis 
 
SPINMING TOPS. 87 
 
 rotates in an elliptic conical path round what might 
 be called its mean position. We have also to 
 remember that twice in every lunar month the 
 moon's tilting action on the earth is greater, and 
 twice it is zero, and that it continually varies in 
 value. 
 
 On the whole, then, the moon and sun, and to a 
 small extent the planets, produce the general effect 
 of a precession, which repeats itself in a period of 
 about 25,695 years. It is not perfectly uniform, 
 being performed at a speed which is a maximum 
 in summer and winter ; that is, there is a change of 
 speed whose period is half a year ; and there is a 
 change of speed whose period is half a lunar month, 
 the precession being quicker to-night than it will 
 be next Saturday, when it will increase for about 
 another week, and diminish the next. Besides this, 
 because of Si° of angularity of the orbits, we have 
 something like the nodding of our precessing 
 gyrostat, and the inclination of the earth's axis to 
 the ecliptic is not constant at 23 J°, but is changing, 
 its periodic time being nineteen years. Regarding 
 the earth's centre as fixed at o we see then, as 
 illustrated in this model and in Fig. 40, the axis of 
 the earth describes almost a perfect circle on the 
 celestial sphere once in 25,866 years, its speed 
 fluctuating every half year and every half month. 
 But it is not a perfect circle, it is really a wavy 
 
88 
 
 SPINNING TOPS. 
 
 line, there being a complete wave every nineteen 
 years, and there are smaller ripples in it, corre- 
 sponding to the half-yearly and fortnightly periods. 
 
 N 65! 
 
 YEA 
 
 Now \ 
 
 00 
 RS 
 
 IN I3'000 
 YE/ARS 
 
 Fig. 4a 
 
 But the very cause of the nutation, the nineteen- 
 yearly period of retrogression of the moon's nodes, 
 as it is called, is itself really produced as the 
 precession of a gyrostat is produced, that is, by 
 tilting forces acting on a spinning body. 
 
 Imagine the earth to be stationary, and the sun 
 and moon revolving round it. It was Gauss who 
 found that the present action is the same as if the 
 masses of the moon and sun were distributed all 
 
SPINNING TOPS. 89 
 
 round their orbits. For instance, imagine the moon's 
 mass distributed over her orbit in the form of a 
 rigid ring of 480,000 miles diameter, and imagine 
 less of it to exist where the present speed is greater, 
 so that the ring would be thicker at the moon's 
 apogee, and thinner at the perigee. Such a ring 
 round the earth would be similar to Saturn's rings, 
 which have also a precession of nodes, only Saturn's 
 rings are not rigid, else there would be no equili- 
 brium. Now if we leave out of account the earth 
 and imagine this ring to exist by itself, and that 
 its centre simply had a motion round the sun in a 
 year, since it makes an angle of 5^° with the 
 ecliptic it would vibrate into the ecliptic till it 
 made the same angle on the other side and back 
 again. But it revolves once about its centre in 
 twenty-seven solar days, eight hours, and it will no 
 longer swing like a ship in a ground-swell, but will 
 get a motion of precession opposed in direction to 
 its own revolution. As the ring's motion is against 
 the hands of a watch, looking from the north down 
 on the ecliptic, this retrogression of the moon's 
 nodes is in the direction of the hands of a watch. 
 It is exactly the same sort of phenomenon as the 
 precession of the equinoxes, only with a much 
 shorter period of 6798 days instead of 25,866 years. 
 I told you how, if we knew the moon's mass or 
 the sun's, we could tell the amount of the forces, or 
 
90 SPINNING TOPS. 
 
 the torque as it is more properly called, with which 
 it tries to tilt the earth. We know the rate at 
 which the earth is spinning, and we have observed 
 the precessional motion. Now when we follow up 
 the method which I have sketched already, we find 
 that the precessional velocity of a spinning body 
 ought to be equal to the torque divided by the 
 spinning velocity and by the moment of inertia 1 
 of the body about the polar axis. Hence the 
 greater the tilting forces, and the less the spin and 
 the less the moment of inertia, the greater is the 
 precessional speed. Given all of these elements 
 except one, it is easy to calculate that unknown 
 element. Usually what we aim at in such a calcula- 
 tion is the determination of the moon's mass, as this 
 phenomenon of precession and the action of the tides 
 are the only two natural phenomena which have 
 as yet enabled the moon's mass to be calculated. 
 
 I do not mean to apologize to you for the 
 introduction of such terms as Moment of Inertia, 
 nor do I mean to explain them. In this lecture 
 I have avoided, as much as I could, the intro- 
 duction of mathematical expressions and the use 
 of technical terms. But I want you to under- 
 
 1 Roughly, the Inertia or Mass of a body expresses its 
 resistance to change of mere translational velocity, whereas, 
 the Moment of Inertia of a body expresses its resistance to 
 change of rotational velocity. 
 
SPINNING TOPS. 91 
 
 stand that I am not afraid to introduce technical 
 terms when giving a popular lecture. If there is 
 any offence in such a practice, it must, in my 
 opinion, be greatly aggravated by the addition 
 of explanations of the precise meanings of such 
 terms. The use of a correct technical term serves 
 several useful purposes. First, it gives some satis- 
 faction to the lecturer, as it enables him to state, 
 very concisely, something which satisfies his own 
 weak inclination to have his reasoning complete, 
 but which he luckily has not time to trouble his 
 audience with. Second, it corrects the universal 
 belief of all popular audiences that they know 
 everything now that can be said on the subject. 
 Third, it teaches everybody, including the lecturer, 
 that there is nothing lost and often a great deal 
 gained by the adoption of a casual method of 
 skipping when one is working up a new subject. 
 Some years ago it was argued that if the earth 
 were a shell filled with liquid, if this liquid were 
 quite frictionless, then the moment of inertia of the 
 shell is all that that we should have to take into 
 account in considering precession, and that if it 
 were viscous the precession would very soon dis- 
 appear altogether. To illustrate the effect of the 
 moment of inertia, I have hung up here a number 
 of glasses — one a filled with sand, another b with 
 treacle, a third c with oil, the fourth d with water, 
 
9 2 
 
 SPINNING TOPS. 
 
 1 
 
 II 
 
 II 
 
 bu 
 
 ^ 
 
SPINNING TOPS. 93 
 
 and the fifth e is empty (Fig. 41). You see that if 
 I twist these suspending wires and release them, 
 a vibratory motion is set up, just like that of the 
 balance of a watch. Observe that the glass with 
 water vibrates quickly, its effective moment of 
 inertia being merely that of the glass itself, and 
 you see that the time of swing is pretty much 
 the same as that of the empty glass ; that is, the 
 water does not seem to move with the glass. 
 Observe that the vibration goes on for a fairly 
 long time. 
 
 The glass with sand vibrates slowly ; here theie 
 is great moment of inertia, as the sand and glass 
 behave like one rigid body, and again the vibration 
 goes on for a long time. 
 
 In the oil and treacle, however, there are longer 
 periods of vibration than in the case of the water 
 or empty glass, and less than would be the case if 
 the vibrating bodies were all rigid, but the vibrations 
 are stilled more rapidly because of friction. 
 
 Boiled (/) and unboiled (g) eggs suspended from 
 wires in the same way will exhibit the same differ- 
 ences in the behaviour of bodies, one of which is 
 rigid and the other liquid inside ; you see how 
 much slower an oscillation the boiled has than 
 the unboiled. 
 
 Even on the table here it is easy to show the 
 difference between boiled and unboiled eggs. 
 
94 SPINNING TOPS. 
 
 Roll them both ; you see that one of them stops 
 much sooner than the other ; it is the unboiled 
 one that stops sooner, because of its internal 
 friction. 
 
 I must ask you to observe carefully the following 
 very distinctive test of whether an egg is boiled or 
 not. I roll the egg or spin it, and then place my 
 finger on it just for an instant ; long enough to stop 
 the motion of the shell. You see that the boiled 
 egg had quite finished its motion, but the unboiled 
 egg's shell alone was stopped ; the liquid inside goes 
 on moving, and now renews the motion of the 
 shell when I take my finger away. 
 
 It was argued that if the earth were fluid inside, 
 the effective moment of inertia of the shell being 
 comparatively small, and having, as we see in these 
 examples, nothing whatever to do with the moment 
 of inertia of the liquid, the precessional motion 
 of the earth ought to be enormously quicker than 
 it is. This was used as an argument against the 
 idea of the earth's being fluid inside. 
 
 We know that the observed half-yearly and half- 
 monthly changes of the precession of the earth 
 would be much greater than they are if the earth 
 were a rigid shell containing much liquid, and if 
 the shell were not nearly infinitely rigid"" the phe- 
 nomena of the tides would not occur, but in regard 
 to the general precession of the earth there is now 
 
SPINNING TOPS. 95 
 
 no doubt that the old line of argument was wrong. 
 Even if the earth were liquid inside, it spins so 
 rapidly that it would behave like a rigid body in 
 regard to such a slow phenomenon as precession of 
 the equinoxes. In fact, in the older line of argu- 
 ment the important fact was lost sight of, that rapid 
 rotation can give to even liquids a quasi-rigid ity. 
 Now here (Fig. 42 a) is a hollow brass top rilled 
 with water. The frame is light, and the water 
 
 Fig. 42. 
 
 inside has much more mass than the outside frame, 
 and if you test this carefully you will find that the 
 top spins in almost exactly the same way as if the 
 water were quite rigid ; in fact, as if the whole top 
 were rigid. Here you see it spinning and pre- 
 cessing just like any rigid top. This top, I know, 
 is not filled with water, it is only partially filled ; 
 but whether partially or wholly filled it spins very 
 much like a rigid top. 
 
96 SPINNING TOPS. 
 
 This is not the case with a long hollow brass 
 top with water inside. I told you that all bodies 
 have one axis about which they prefer to rotate. 
 The outside metal part of a top behaves in a way 
 that is now well known to you ; the friction of its 
 peg on the table compels it to get up on its longer 
 axis. But the fluid inside a top is not constrained 
 to spin on its longer axis of figure, and as it prefers 
 its shorter axis like all these bodies I showed you, 
 
 Fig. 43. 
 
 it spins in its own way, and by friction and pressure 
 against the case constrains the case to spin about 
 the shorter axis, annulling completely the tendency 
 of the outside part to rise or keep up on its long 
 axis. Hence it is found to be simply impossible to 
 spin a long hollow top when filled with water. 
 
 Here, for example, is one (Fig. 42 b) that only 
 differs from the last in being longer. It is filled, or 
 partially filled, with water, and you observe that if 
 
SPINNING TOrS. 
 
 97 
 
 I slowly get up a great spin when it is mounted in 
 this frame, and I let it out on the table as I did the 
 other one, this one lies down at once and refuses to 
 spin on its peg. This difference of behaviour is most 
 remarkable in the two hollow tops you see before 
 you (Fig. 43). They are both nearly spherical, both 
 
 Fig. 44. 
 
 filled with water. They look so nearly alike that 
 few persons among the audience are able to detect 
 any difference in their shape. But one of them (a) is 
 really slightly oblate like an orange, and the other (b) 
 is slightly prolate like a lemon. I will give them 
 both a gradually increasing rotation in this frame 
 
 G 
 
9 8 
 
 SPINNING TOPS. 
 
 (Fig- 44) for a time sufficient to insure the rota- 
 tion of the water inside. When just about to be 
 set free to move like ordinary tops on the table, 
 water and brass are moving like the parts of a 
 rigid top. You see that the orange-shaped one 
 continues to spin and precess, and gets itself up- 
 right when disturbed, like an ordinary rigid top ; 
 indeed I have seldom seen a better behaved top ; 
 whereas the lemon-shaped one lies down on its 
 
 Fig. 45. 
 
 side at once, and quickly ceases to move in any 
 way. 
 
 And now you will be able to appreciate a fourth 
 test of a boiled egg, which is much more easily 
 seen by a large audience than the last. Here 
 is the unboiled one (Fig. 45 b). I try my best 
 to spin it as it lies on the table, but you see 
 that I cannct give it much spin, and so there is 
 nothing of any importance to look at. But you 
 observe that it is quite easy to spin the boiled 
 
SPINNING TOPS. 99 
 
 egg, and that for reasons now well known to you 
 it behaves like the stones that Thomson spun on 
 the sea-beach; it gets up on its longer axis, a 
 very pretty object for our educated eyes to look 
 at (Fig. 45 a). You are all aware, from the beha- 
 viour of the lemon-shaped top, that even if, by 
 the use of a whirling table suddenly stopped, or 
 by any other contrivance, I could get up a spin 
 in this unboiled egg, it would never make the 
 slightest effort to rise on its end and spin about 
 its longer axis. 
 
 I hope you don't think that I have been speaking 
 too long about astronomical matters, for there is 
 one other important thing connected with astronomy 
 that I must speak of. You see, I have had almost 
 nothing practically to do with astronomy, and 
 hence I have a strong interest in the subject. It 
 is very curious, but quite true, that men practically 
 engaged in any pursuit are almost unable to see 
 the romance of it. This is what the imaginative 
 outsider sees. But the overworked astronomer has 
 a different point of view. As soon as it becomes 
 one's duty to do a thing, and it is part of one's 
 every-day work, the thing loses a great deal of its 
 interest. We have been told by a great American 
 philosopher that the only coachmen who ever 
 saw the romance of coach-driving are those titled 
 individuals who pay nowadays so largely for the 
 
IOO SPINNING TOPS. 
 
 privilege. In almost any branch of engineering 
 you will find that if any invention is made it is 
 made by an outsider ; by some one who comes to 
 the study of the subject with a fresh mind. Who 
 ever heard of an old inhabitant of Japan or Peru 
 writing an interesting book about those countries ? 
 At the end of two years' residence he sees only the 
 most familiar things when he takes his walks 
 abroad, and he feels unmitigated contempt for the 
 ingenuous globe-trotter who writes a book about 
 the country after a month's travel over the most 
 beaten tracks in it. Now the experienced astro- 
 nomer has forgotten the difficulties of his pre- 
 decessors and the doubts of outsiders. It is a long 
 time since he felt that awe in gazing at a starry 
 sky that we outsiders feel when we learn of the 
 sizes and distances apart of the hosts of heaven. 
 He speaks quite coolly of millions of years, and is 
 nearly as callous when he refers to the ancient 
 history of humanity on our planet as a weather- 
 beaten geologist. The reason is obvious. Most 
 of you know that the Nautical Almanac is as a 
 literary production one of the most uninterest- 
 ing works of reference in existence. It is even 
 more disconnected than a dictionary, and I should 
 think that preparing census-tables must b6 ever so 
 much more romantic as an occupation than prepar- 
 ing the tables of the Nautical Almanac. And yet 
 
SPINNING TOPS. IOI 
 
 a particular figure, one of millions set down by an 
 overworked calculator, may have all the tragic im- 
 portance of life or death to the crew and passengers 
 of a ship, when it is heading for safety or heading 
 for the rocks under the mandate of that single 
 printed character. 
 
 But this may not be a fair sort of criticism. I 
 so seldom deal with astronomical matters, I know 
 so little of the Avear and tear and monotony of 
 the every-day life of the astronomer, that I do not 
 even know that the above facts are specially true 
 about astronomers. I only know that they are very 
 likely to be true because they are true of other 
 professional men. 
 
 I am happy to say that I come in contact with 
 all sorts and conditions of men, and among others, 
 with some men who deny many of the things 
 taught in our earliest school-books. For example, 
 that the earth is round, or that the earth revolves, 
 or that Frenchmen speak a language different from 
 ours. Now no man who has been to sea will deny 
 the roundness of the earth, however greatly he may 
 wonder at it ; and no man who has been to France 
 will deny that the French language is different 
 from ours ; but many men who learnt about the 
 rotation of the earth in their school-days, and have 
 had a plentiful opportunity of observing the 
 heavenly bodies, deny the rotation of the earth. 
 
102 SPINNING TOPS. 
 
 They tell you that the stars and moon are revolving 
 about the earth, for they see them revolving night 
 after night, and the sun revolves about the earth, 
 for they see it do so every day. And really if you 
 think of it, it is not so easy to prove the revolution 
 of the earth. By the help of good telescopes and 
 the electric telegraph or good chronometers, it is 
 easy to show from the want of parallax in stars 
 that they must be very far away ; but after all, we 
 only know that either the earth revolves or else the 
 sky revolves. 1 Of course, it seems infinitely more 
 likely that the small earth should revolve than that 
 the whole heavenly host should turn about the 
 earth as a centre, and infinite likelihood is really 
 absolute proof. Yet there is nobody who does not 
 welcome an independent kind of proof. The phe- 
 nomena of the tides, and nearly every new astro- 
 nomical fact, may be said to be an addition to the 
 proof. Still there is the absence of perfect certainty, 
 and when we arc told that these spinning-top 
 phenomena give us a real proof of the rotation of 
 the earth without our leaving the room, we welcome 
 
 1 It is a very unlikely, and certainly absurd -looking', 
 hypothesis, but it seems that it is not contradicted by any 
 fact in spectrum analysis, or even by any probable "theory of 
 the constitution of the interstel'ar ether, that the stars are 
 merely images of our own sun, formed by reflection at the 
 boundaries of the ether. 
 
SPINNING TOPS. 
 
 103 
 
 it, even although we may sneer at it as unnecessary 
 after we have obtained it. 
 
 You know that a gyrostat suspended with perfect 
 freedom about axes, which all pass through its 
 centre of gravity, maintains a constant direction in 
 space however its support may be carried. Its 
 
 Fig. 
 
 17. 
 
 axis is not forced to alter its direction in any way. 
 Now this gyrostat (Fig. 17) has not the perfect 
 absence of friction at its axes of which I speak, and 
 even the slightest friction will produce some con- 
 straint which is injurious to the experiment I am 
 about to describe. It must be remembered, that if 
 there were absolutely no constraint, then, even if the 
 
104 SPINNING TOPS. 
 
 gyrostat were not spinning, its axis would keep a 
 constant direction in space. But the spinning 
 gyrostat shows its superiority in this, that any 
 constraint due to friction is less powerful in alter- 
 ing the axis. The greater the spin, then, the better 
 able are we to disregard effects due to friction. 
 You have seen for yourselves the effect of carrying 
 this gyrostat about in all sorts of ways — first, 
 when it is not spinning and friction causes quite a 
 large departure from constancy of direction of the 
 axis ; second, when it is spinning, and you see that 
 although there is now the same friction as before, 
 and I try to disturb the instrument more than 
 before, the axis remains sensibly parallel to itself 
 all the time. Now when this instrument is sup- 
 ported by the table it is really being carried round 
 by the earth in its daily rotation. If the axis kept 
 its direction perfectly, and it were now pointing 
 horizontally due east, six hours after this it will 
 point towards the north, but inclining downwards, 
 six hours afterwards it will point due west horizon- 
 tally, and after one revolution of the earth it will 
 again point as it does now. Suppose I try the 
 experiment, and I see that it points due east now 
 in this room, and after a time it points due west, 
 and yet I know that the gyrostat is constantly 
 pointing in the same direction in space all the 
 time, surely it is obvious that the room must 
 
SPINNING TOPS. IOS 
 
 be turning round in space. Suppose it points 
 to the pole star now, in six hours, or twelve, or 
 eighteen, or twenty-four, it will still point to the 
 pole star. 
 
 Now it is not easy to obtain so frictionless a 
 gyrostat that it will maintain a good spin for such 
 a length of time as will enable the rotation of the 
 room to be made visible to an audience. But I 
 will describe to you how forty years ago it was 
 proved in a laboratory that the earth turns on its 
 axis. This experiment is usually connected with 
 the name of Foucault, the same philosopher who 
 with Fizeau showed how in a laboratory we can 
 measure the velocity of light, and therefore measure 
 the distance of the sun. It was suggested by Mr. 
 Lang of Edinburgh in 1836, although only carried 
 out in 1852 by Foucault. By these experiments, 
 if you were placed on a body from which you 
 could see no stars or other outside objects, say 
 that you were living in underground regions, you 
 could discover — first, whether there is a motion 
 of rotation, and the amount of it ; second, the 
 meridian line or the direction of the true north ; 
 third, your latitude. Obtain a gyrostat like this 
 (Fig. 46) but much larger, and far more friction- 
 lcssly suspended, so that it is free to move verti- 
 cally or horizontally. For the vertical motion 
 your gymbal pivots ought to be hard steel knife- 
 
io6 
 
 SPINNING TOPS. 
 
 edges. As for the horizontal freedom, Foucault 
 used a fine steel wire. Let there be a fine scale 
 engraved crosswise on the outer gymbal rincj, 
 
 Frc 46. 
 
 and try to discover if it moves horizontally by 
 means of a microscope with cross wires. When 
 this is carefully done we find that there is a motion, 
 
SPINNING TOPS. IO7 
 
 but this is not the motion of the gyrostat, it is the 
 motion of the microscope. In fact, the microscope 
 and all other objects in the room are going round 
 the gyrostat frame. 
 
 Now let us consider what occurs. The room 
 is rotating about the earth's axis, and we know 
 the rate of rotation ; but we only want to know 
 for our present purpose how much of the total 
 rotation is about a vertical line in the room. If 
 the room were at the North Pole, the whole rotation 
 would be about the vertical line. If the room 
 were at the equator, none of its rotation would be 
 about a vertical line. In our latitude now, the 
 horizontal rate of rotation about a vertical axis 
 is about four-fifths of the whole rate of rotation 
 of the earth on its axis, and this is the amount 
 that would be measured by our microscope. This 
 experiment would give no result at a place on the 
 equator, but in our latitude you would have a labora- 
 tory proof of the rotation of the earth. Foucault 
 made the measurements with great accuracy. 
 
 If you now clamp the frame, and allow the 
 spinning axis to have no motion except in a 
 horizontal plane, the motion which the earth tends 
 to give it about a vertical axis cannot now affect 
 the gyrostat, but the earth constrains it to move 
 about an axis due north and south, and conse- 
 quently the spinning axis tries to put itself parallel 
 
io8 
 
 SPINNING TOPS. 
 
 to the north and south direction (Fig. 47). Hence 
 with such an instrument it is easy to find the true 
 north. If there were absolutely no friction the 
 instrument would vibrate about the true north 
 
 Fig. 47. 
 
 position like the compass needle (Fig. 50), although 
 with an exceedingly slow swing. 
 
 It is with a curious mixture of feelings that one 
 first recognizes the fact that all rotating bodies, 
 fly-wheels of steam-engines and the like, are always 
 tending to turn themselves tOAvards the pole star ; 
 gently and vainly tugging at their foundations 
 
SPINNING TOPS. 
 
 109 
 
 to get round towards the object of their adoration 
 all the time they are in motion. 
 
 Now we have found the meridian as in Fig. 47, 
 
 NS 
 
 Fig. 48. 
 
 we can begin a third experiment. Prevent motion 
 horizontally, that is, about a vertical axis, but give 
 the instrument freedom to move vertically in the 
 meridian, like a transit instrument in an observatory 
 
no 
 
 SPINNING TOPS. 
 
 about its horizontal axis. Its revolution with the 
 earth will tend to make it change its angular posi- 
 tion, and therefore it places itself parallel to the 
 earth's axis ; when in this position the daily rotation 
 no longer causes any change in its direction in 
 space, so it continues to point to the pole star 
 (Fig. 48). It would be an interesting experiment 
 to measure with a delicate chemical balance the 
 force with which the axis raises itself, and in this 
 way weigh the rotational motion of the earth. 1 
 
 Now let us turn the frame 
 of the instrument G B round 
 a right angle, so that the spin- 
 ning axis can only move in a 
 plane at right angles to the 
 meridian ; obviously it is con- 
 strained by the vertical com- 
 ponent of the earth's rotation, 
 and points vertically down- 
 wards. 
 
 This last as well as the 
 other phenomena of which I 
 have spoken is very sugges- 
 tive. Here is a magnetic 
 needle (Fig. 49), sometimes 
 called a dipping needle from 
 the way in which it is suspended. If I turn its 
 1 Sir William Thomson has performed this. 
 
 Fig. 49. 
 
SPINNING TOPS. 
 
 Ill 
 
 frame so that it can only move at right angles 
 to the meridian, you see that it points vertically. 
 You may reflect upon the analogous properties of 
 this magnetic needle 
 (Fig. 50) and of the 
 gyrostat (Fig. 47); they 
 both, when only cap- 
 able of moving hori- 
 zontally, point to the 
 north ; and you see 
 that a very frictionless 
 gyrostat might be used 
 as a compass, or at all 
 events as a corrector of 
 compasses. 1 I have just put before you another 
 analogy, and I want you to understand that, 
 although these are only analogies, they are not 
 mere chance analogies, for there is undoubtedly a 
 dynamical connection between the magnetic and 
 the gyrostatic phenomena. Magnetism depends on 
 rotatory motion. The molecules of matter are in 
 actual rotation, and a certain allineation of the axes 
 of the rotations produces what we call magnetism. 
 In a steel bar not magnetized the little axes of 
 rotation are all in different directions. The process 
 
 Fig. 50. 
 
 1 It must be remembered that in one case I speak of the 
 true north, and in the other of the magnetic north. 
 
112 
 
 SPINNING TOPS. 
 
 of magnetization is simply bringing these rotations 
 to be more or less round parallel axes, an allineation 
 of the axes. A honey-combed mass with a spinning 
 gyrostat in every cell, with all the spinning axes 
 parallel, and the spins in the same direction, would 
 — I was about to say, would be a magnet, but it 
 would not be a magnet in 
 all its properties, and yet it 
 would resemble a magnet 
 in many ways. 1 
 
 Some of you, seeing elec- 
 tromotors and other electric 
 contrivances near this table, 
 may think that they have to 
 do with our theories and ex- 
 planations of magnetic phe- 
 nomena. But I must explain 
 that this electromotor which 
 I hold in my hand (Fig. 51) 
 is used by me merely as the 
 
 Fig. si. 
 
 1 Rotating a large mass of iron rapidly in one direction 
 and then in the other in the neighbourhood of a delicately- 
 suspended magnetic needle, well protected from air currents, 
 ought, I think, to give rise to magnetic phenomena of very 
 great interest in the theory of magnetism. I have hitherto 
 failed to obtain any trace of magnetic action, but I attribute 
 my failure to the comparatively slow speed^of rotation 
 which I have employed, and to the want of delicacy of my 
 magnetometer. 
 
SPINNING TOPS. 113 
 
 most convenient means I could find for the spin- 
 ning of my tops and gyrostats. On the spindle 
 of the motor is fastened a circular piece of wood ; 
 by touching this key I can supply the motor with 
 electric energy, and the wooden disc is now rotat- 
 ing very rapidly. I have only to bring its rim in 
 
 Fig, 52. 
 
 contact with any of these tops or gyrostats to set 
 them spinning, and you see that I can set half a 
 dozen gyrostats a-spinning in a few seconds ; this 
 chain of gyrostats, for instance. Again, this larger 
 motor (Fig. 52), too large to move about in my 
 hand, is fastened to the table, and I have used 
 
 PI 
 
114 SPINNING TOPS. 
 
 it to drive my larger contrivances ; but you under- 
 stand that I use these just as a barber might use 
 them to brush your hair, or Sarah Jane to clean 
 the knives, or just as I would use a little steam- 
 engine if it were more convenient for my purpose. 
 It was more convenient for me to bring from 
 London this battery of accumulators and these 
 motors than to bring sacks of coals, and boilers, 
 and steam-engines. But, indeed, all this has the 
 deeper meaning that we can give to it if we like. 
 Love is as old as the hills, and every day Love's 
 messages are carried by the latest servant of man, 
 the telegraph. These spinning tops were known 
 probably to primeval man, and yet we have not 
 learnt from them more than the most fractional 
 portion of the lesson that they are always sending 
 out to an unobservant world. Toys like these were 
 spun probably by the builders of the Pyramids 
 when they were boys, and here you see them side 
 by side with the very latest of man's contrivances. 
 I feel almost as Mr. Stanley might feel if, with the 
 help of the electric light and a magic-lantern, he 
 described his experiences in that dreadful African 
 forest to the usual company of a London drawing- 
 room. 
 
 The phenomena I have been describing to you 
 play such a very important part in nature, that if 
 time admitted I might go on expounding and ex- 
 
SPINNING TOPS. 115 
 
 plaining without finding any great reason to stop 
 at one place rather than another. The time at my 
 disposal allows me to refer to enly one other 
 matter, namely, the connection between light and 
 magnetism and the behaviour of spinning tops. 
 
 You are all aware that sound takes time to 
 travel. This is a matter of common observation, 
 as one can see a distant woodchopper lift his axe 
 again before one hears the sound of his last stroke. 
 A destructive sea wave is produced on the coast 
 of Japan many hours after an earthquake occurs off 
 the coast of America, the wave motion having taken 
 time to travel across the Pacific. But although light 
 travels more quickly than sound or wave motion in 
 the sea, it does not travel with infinite rapidity, and 
 the appearance of the eclipse of one of Jupiter's 
 satellites is delayed by an observable number of 
 minutes because light takes time to travel. The 
 velocity has been measured by means of such 
 observations, and we know that light travels at the 
 rate of about 187,000 miles per second, or thirty 
 thousand millions of centimetres per second. There 
 is no doubt about this figure being nearly correct, 
 for the velocity of light has been measured in the 
 laboratory by a perfectly independent method. 
 
 Now the most interesting physical work done 
 since Newton's time is the outcome of the experi- 
 ments of Faraday and the theoretical deductions of 
 
Il6 SPINNING TOPS. 
 
 Thomson and Maxwell. It is the theory that light 
 and radiant heat are simply electro-magnetic dis- 
 turbances propagated through space. I dare not 
 do more than just refer to this matter, although 
 it is of enormous importance. I can only say, 
 that of all the observed facts in the sciences of 
 light, electricity, and magnetism, we know of none 
 that is in opposition to Maxwell's theory, and we 
 know of many that support it. The greatest and 
 earliest support that it had was this. If the theory 
 is correct, then a certain electro-magnetic measure- 
 ment ought to result in exactly the same quantity 
 as the velocity of light. Now I want you to under- 
 stand that the electric measurement is one of quan- 
 tities that seem to have nothing whatever to do with 
 light, except that one uses one's eyes in making 
 the measurement ; it requires the use of a two-foot 
 rule and a magnetic needle, and coils of wire and 
 currents of electricity. It seemed to bear a 
 relationship to the velocity of light, which was 
 not very unlike the fabled connection between 
 Tenterden Steeple and the Goodwin Sands. It 
 is a measurement which it is very difficult to 
 make accurately. A number of skilful experi- 
 menters, working independently, and using quite 
 d'fferent methods, arrived at results only one of 
 which is as much as five per cent, different from 
 the observed velocity of light, and some of them, 
 
SPINNING TOPS. 117 
 
 on which the best dependence may be placed, agree 
 exactly with the average value of the measure- 
 ments of the velocity of light. 
 
 There is then a wonderful agreement of the two 
 measurements, but without more explanation than 
 I can give you now, you cannot perhaps under- 
 stand the importance of this agreement between 
 two seemingly unconnected magnitudes. At all 
 events we now know, from the work of Professor 
 Hertz in the last two years, that Maxwell's theory 
 is correct, and that light is an electro-magnetic 
 disturbance; and what is more, we know that 
 electro-magnetic disturbances, incomparably slower 
 than red-light or heat, are passing now through 
 our bodies ; that this now recognized kind of 
 radiation may be reflected and refracted, and yet 
 will pass through brick and stone walls and foggy 
 atmospheres where light cannot pass, and that 
 possibly all military and marine and lighthouse 
 signalling may be conducted in the future through 
 the agency of this new and wonderful kind of 
 radiation, of which what we call light is merely 
 one form. Why at this moment, for all I know, 
 two citizens of Leeds may be signalling to each 
 other in this way through half a mile of houses, 
 including this hall in which we are present. 1 
 
 1 I had applied for a patent for this system of signalling 
 some time before the above words were spoken, but although 
 it was valid I allowed it to lapse in pure shame that I should 
 
If 8 SPINNING TOPS. 
 
 I mention this, the greatest modern philosophical 
 discovery, because the germ of it, which was pub- 
 lished by Thomson in 1856, makes direct reference 
 to the analogy between the behaviour of our spin- 
 ning-tops and magnetic and electrical phenomena. 
 It will be easier, however, for us to consider here 
 a mechanical illustration of the rotation of the 
 plane of polarized light by magnetism which 
 Thomson elaborated in 1874. This phenomenon 
 may, I think, be regarded as the most important 
 of all Faraday's discoveries. It was of enormous 
 scientific importance, because it was made in a 
 direction where a new phenomenon was not even 
 suspected. Of his discovery of induced currents 
 of electricity, to which all electric-lighting com- 
 panies and transmission of power companies of the 
 present day owe their being, Faraday himself said 
 that it was a natural consequence of the discoveries 
 of an earlier experimenter, Oersted. But this 
 magneto-op;. ic discovery was quite unexpected. I 
 will now describe the phenomenon. 
 
 Some of you are aware that when a beam of light 
 is sent through this implement, called a Nichol's 
 Prism, it becomes polarized, or one-sided — that is, 
 all the light that comes through is known to be 
 propagated by vibrations which occur all in one 
 plane. This rope (Fig. 53) hanging from the ceiling 
 
 have so unblushingly patented the use of the work of Fitz- 
 gerald, Hertz, and Lodge. 
 
SPINNING TOPS. 
 
 119 
 
 illustrates the nature of plane polarized light. All 
 points in the rope are vibrating in the same plane. 
 Well, this prism A, Fig. 54, only lets through it light 
 that is polarized in a vertical plane. 
 And here at B I have a similar imple- 
 ment, and I place it so that it also will 
 only allow light to pass through it 
 which is polarized in a vertical plane. 
 Hence most of the light coming 
 through the polarizer, as the first prism 
 is called, will pass readily through 
 the analyzer, as the second is called, 
 and I am now letting this light enter 
 my eye. But when I turn the analyzer 
 round through a right angle, I find 
 that I see no light ; there was a 
 gradual darkening as I rotated the 
 analyzer. The analyzer will now 
 only allow light to pass through which 
 is polarized in a horizontal plane, and 
 it receives no such light. 
 
 You will see in this model (Fig. 55) 
 a good illustration of polarized light. 
 
 ~ B 
 
 a 
 
 Fig. S3. 
 
 A 
 
 P 
 
 Fig. 54. 
 The white, brilliantly illuminated thread M N is 
 
120 SPINNING TOPS. 
 
 pulled by a weight beyond the pulley M, and its 
 end N is fastened to one limb of a tuning-fork. 
 Some ragged-looking pieces of thread round the 
 portion N A prevent its vibrating in any very deter- 
 minate way, but from A to M the thread is free from 
 all encumbrance. A vertical slot at A, through 
 which the thread passes, determines the nature of 
 the vibration of the part A B ; every part of the 
 thread between A and B is vibrating in up and 
 down directions only. A vertical slot in B allows 
 the vertical vibration to be communicated through 
 it, and so we see the part B M vibrating in the same 
 way as A B. I might point out quite a lot of 
 ways in which this is not a perfect illustration of 
 what occurs with light in Fig. 54. But it is quite 
 good enough for my present purpose. A is a 
 polarizer of vibration ; it only allows up and down 
 motion to pass through it, and B also allows up 
 and down motion to pass through. But now, as 
 B is turned round, it lets less and less of the up 
 and down motion pass through it, until when it is 
 in the second position shown in the lower part 
 of the figure, it allows no up and down motion to 
 pass through, and there is no visible motion of the 
 thread between B and M. You will observe that 
 if we did not know in what plane (in the present 
 case the plane is vertical) the vibrations of the 
 thread between A and B occurred, we should only 
 have to turn B round until we found no vibration 
 
SPINNING TOPS. 
 
 121 
 
 5 G oO 
 
 [i agB 
 
122 SPINNING TOPS. 
 
 passing through, to obtain the information. Hence, 
 as in the light case, we may call A a polarizer of 
 vibrations, and B an analyzer. 
 
 Now if polarized light is passing from A to B (Fig. 
 54) through the air, say, and we have the analyzer 
 placed so that there is darkness, we find that if 
 we place in the path of the ray some solution 
 of sugar we shall no longer have darkness at B ; 
 we must turn B round to get things dark again ; 
 this is evidence of the sugar solution having 
 twisted round the plane of polarization of the light. 
 I will now assume that you know something 
 about what is meant by twisting the plane of 
 polarization of light. You know that sugar solution 
 will do it, and the longer the path of the ray 
 through the sugar, the more twist it gets. This 
 phenomenon is taken advantage of in the sugar 
 industries, to find the strengths of sugar solutions. 
 For the thread illustration I am indebted to Pro- 
 fessor Silvanus Thomson, and the next piece of 
 apparatus which I shall show also belongs to him. 
 
 I have here (see Frontispiece) a powerful armour- 
 clad coil, or electro-magnet. There is a central 
 hole through it, through which a beam of light 
 may be passed from an electric lamp, and I have 
 a piece of Faraday's heavy glass nearly filling 
 this hole. I have a polarizer at one end, and an 
 analyzer at the other. You see now that the 
 
SPINNING TOPS. 123 
 
 polarized light passes through the heavy glass and 
 the analyzer, and enters the eye of an observer. 
 I will now turn 13 until the light no longer passes. 
 Until now there has been no magnetism, but I 
 have the means here of producing a most intense 
 magnetic fieM in the direction in which the ray 
 passes, and if your eye were here you would see 
 that there is light passing through the analyzer. 
 The magnetism has done something to the light, 
 it has made it capable of passing where it could 
 not pass before. When I turn the analyzer a 
 little I stop the light again, and now I know that 
 what the magnetism did was to convert the glass 
 into a medium like the sugar, a medium which 
 rotates the plane of polarization of light. 
 
 In this experiment you have had to rely upon 
 my personal measurement of the actual rotation 
 produced. But if I insert between the polarizer 
 and analyzer this disc of Professor Silvanus Thom- 
 son's, built up of twenty-four radial pieces of 
 mica, I shall have a means of showing to this 
 audience the actual rotation of the plane of polar- 
 ization of light. You see now on the screen the 
 light which has passed through the analyzer 
 in the form of a cross, and if the cross rotates 
 it is a sign of the rotation of the plane of polar- 
 ization of the light. By means of this electric key 
 I can create, destroy, and reverse the magnetic 
 
124 SPINNING TOPS. 
 
 field in the glass. As I create magnetism you see 
 the twisting of the cross ; I destroy the magnetism, 
 and it returns to its old position ; I create the 
 opposite kind of magnetism, and you see that 
 the cross twists in the opposite way. I hope it 
 is now known to you that magnetism rotates the 
 plane of polarisation of light as the solution of 
 sugar did. 
 
 As an illustration of what occurs between polar- 
 izer and analyzer, look again at this rope (Fig. 53) 
 fastened to the ceiling. I move the bottom end 
 sharply from east to west, and you see that every 
 part of the rope moves from east to west. Can 
 you imagine a rope such that when the bottom 
 end was moved from east to west, a point some 
 yards up moved from east-north-east to west-sou'- 
 west, that a higher point moved from north-east 
 to south-west, and so on, the direction gradually 
 changing for higher and higher points ? Some of 
 you, knowing what I have done, may be able to 
 imagine it. We should have what we want if this 
 rope were a chain of gyrostats such as you see 
 figured in the diagram ; gyrostats all spinning in 
 the same way looked at from below, with friction- 
 less hinges between them. Here is such a chain 
 (Fig. 56), one of many that I have tried to use in 
 this way for several years. But although I have 
 often believed that I saw the phenomenon occur in 
 
SPINNING TOPS. 
 
 125 
 
 Fig. 56. 
 
126 
 
 SPINNING TOPS. 
 
 such a chain, I must now confess to repeated failures. 
 
 The difficulties I have met with are almost alto- 
 gether mechanical 
 ones. You see that 
 by touching all the 
 gyrostats in succes- 
 sion with this rapidly 
 revolving disc driven 
 by the little electro- 
 motor, I can get them 
 all to spin at the same 
 time ; but you will 
 notice that what with 
 bad mechanism and 
 bad calculation on my 
 part, and want of skill, 
 the phenomenon is 
 completely masked 
 by wild movements 
 of the gyrostats, the 
 causes of which are 
 better known than 
 capable of rectifica- 
 tion. The principle 
 Fig. 57. of the action is very 
 
 visible in this gyrostat 
 
 suspended as the bob of a pendulum (Fig. 57). You 
 
 may imagine this to represent a particle of the 
 
SPINNING TOPS. 
 
 substance which transmits light 
 in the magnetic field, and you 
 see by the trickling thin stream 
 of sand which falls from it on 
 the paper that it is continually 
 changing the plane of polariza- 
 tion. But I am happy to say 
 that I can show you to-night a 
 really successful illustration of 
 Thomson's principle ; it is the 
 very first time that this most 
 suggestive experiment has been 
 shown to an audience. I have 
 a number of double gyrostats 
 (Fig. 58) placed on the same line, 
 joined end to end by short 
 pieces of elastic. Each instru- 
 ment is supported at its centre 
 of gravity, and it can rotate 
 both in horizontal and in vertical 
 planes. 
 
 The end of the vibrating lever 
 A can only get a horizontal 
 motion from my hand, and the 
 motion is transmitted from one 
 gyrostat to the next, until it has 
 travelled to the very end one. 
 Observe that when the gyrostats 
 are not spinning, the motion is 
 
 Fig. 58. 
 
128 SPINNING TOPS. 
 
 everywhere horizontal. Now it is very important 
 not to have any illustration here of a reflected 
 ray of light, and so I have introduced a good deal 
 of friction at all the supports. I will now spin 
 all the gyrostats, and you will observe that when 
 A moves nearly straight horizontally, the next 
 gyrostat moves straight but in a slightly different 
 plane, the second gyrostat moves in another plane, 
 and so on, each gyrostat slightly twisting the plane 
 in which the motion occurs ; and you see that the 
 end one does not by any means receive the hori- 
 zontal motion of A, but a motion nearly vertical. 
 This is a mechanical illustration, the first successful 
 one I have made after many trials, of the effect 
 on light of magnetism. The reason for the action 
 that occurs in this model must be known to 
 everybody who has tried to follow me from the 
 beginning of the lecture. 
 
 And you can all see that we have only to 
 imagine that many particles of the glass are rotat- 
 ing like gyrostats, and that magnetism has par- 
 tially caused an allineation of their axes, to have 
 a dynamical theory of Faraday's discovery. The 
 magnet twists the plane of polarization, and so 
 does the solution of sugar ; but it is found by expe- 
 riment that the magnet does it indifferently for 
 coming and going, whereas the sugar does it in a 
 way that corresponds with a spiral structure of 
 molecules. You see that in this important par- 
 
SPINNING TOPS. 129 
 
 ticular the gyrostat analogue must follow the mag- 
 netic method, and not the sugar method. We 
 must regard this model, then, the analogue to 
 Faraday's experiment, as giving great support to 
 the idea that magnetism consists of rotation. 
 
 I have already exceeded the limits of time 
 usually allowed to a popular lecturer, but you 
 see that I am very far from having exhausted our 
 subject. I am not quite sure that I have accom- 
 plished the object with which I set out. My 
 object was, starting from the very different be- 
 haviour of a top when spinning and when not 
 spinning, to show you that the observation of that 
 very common phenomenon, and a determination to 
 understand it, might lead us to understand very 
 much more complex-looking things. There is no 
 lesson which it is more important to learn than 
 this — That it is in the study of every-day facts that 
 all the great discoveries of the future lie. Three 
 thousand years ago spinning tops were common, 
 but people never studied them. Three thousand 
 years ago people boiled water and made steam, but 
 the steam-engine was unknown to them. They had 
 charcoal and saltpetre and sulphur, but they knew 
 nothing of gunpowder. They saw fossils in rocks, 
 but the wonders of geology were unstudied by 
 them. They had bits of iron and copper, but not 
 one of them thought of any one of the fifty simple 
 
1^0 SPINNING TOPS. 
 
 ways that are now known to us of combining those 
 known things into a telephone. Why, even the 
 simplest kind of signalling by flags or lanterns was 
 unknown to them, and yet a knowledge of this 
 might have changed the fate of the world on one 
 of the great days of battle that we read about. 
 We look on Nature now in an utterly different 
 way, with a great deal more knowledge, with a 
 great deal more reverence, and with much less 
 unreasoning superstitious fear. And what we are 
 to the people of three thousand years ago, so will 
 be the people of one hundred years hence to us ; 
 for indeed the acceleration of the rate of progress 
 in science is itself accelerating. The army of scien- 
 tific workers gets larger and larger every day, and 
 it is my belief that every unit of the population 
 will be a scientific worker before long. And so we 
 are gradually making time and space yield to us 
 and obey us. But just think of it ! Of all the dis- 
 coveries of the next hundred years ; the things 
 that are unknown to us, but which will be so well 
 known to our descendants that they will sneer at 
 us as utterly ignorant, because these things will 
 seem to them such self-evident facts ; I say, of all 
 these things, if one of us to-morrow discovered one 
 of them, he would be regarded as a great dis- 
 coverer. And yet the children of a hundred years 
 hence will know it : it will be brought home to 
 
SPINNING TOPS. 131 
 
 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 ? " x 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 
 
 1 How to see by electricity is perfectly well known, but no 
 rich man seems willing to sacrifice the few thousands of 
 pounds which are necessary for making the apparatus. If I 
 could spare the money and time I would spend them in 
 doing this thing — that is, I think so— but it is just possible 
 that if I could afford to throw away three thousand pounds, 
 I might feel greater pleasure in the growth of a great fortune 
 than in any other natural process. 
 
132 SPINNING TOPS. 
 
 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 glit- 
 tering 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 com- 
 parison 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. 
 
 Introduction, pages 9 — 14, showing the importance of 
 the study of spinning-top behaviour. 
 
 Quasi-rigidiiy induced even in flexible and fluid bodies by 
 rapid motion, 1 4—2 1 . 
 
 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. 
 
 The nature of this quasi-rigidity in spinning bodies is a 
 resistance to change of dircctio?i of the axis of spinning, 
 21—30. 
 
 Illustrations : Cased gyrostat, 21 — 24; tops, biscuits, 
 hats, thrown into the air, 24 — 26 ; quoits, hoops, pro- 
 jectiles 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, 
 
 3°- 
 Study of the crab-like behaviour of a spinning body, 
 
 3Q-49- 
 
 Illustrations: Spinning top, 31 ; cased gyrostat, 32 ; 
 balanced gyrostat, 33 — 36; windage of projectiles from 
 
J 34 SPINNING TOPS. 
 
 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. Pivof or explanation of our simple universal ride, 50 — 54. 
 
 Giving two independent rotations to a body, 50, jji ; 
 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 ; centri- 
 fugal 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 inac- 
 curacy 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 
 
SPINNING TOTS. 135 
 
 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 state- 
 ment made and a sort of apology for making it, 90, 91. 
 1 o. Influence of possible internal fluidity of the earth on its 
 precessional motion, 91 — 98. 
 
 Effect of fluiJs 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 ; beauti- 
 ful behaviour of hollow top filled with water, 95 ; strik- 
 ing 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 sub- 
 terranean regions to know, isl, that the earth rotates ; 
 2nd, the amount of rotatio7i ; 3rd, the direction of true 
 north ; \th, the latitude, 101 — ill. 
 
 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 rota- 
 tion, 105 — 107; to find the true north, 108; all rotating 
 bodes vainly endeavouring to point to the pole star, 
 108; to find the latitude, no; analogies between the 
 gyrostat and the mariner's compass and the dipping 
 needle, no, m; dynamical connection between mag- 
 netism and gyrostatic phenomena, 11 1. 
 
 13. How the lecturer spun his tops, using electro-motors, 
 
 112 — 114. 
 
 14. Light, magnetism, and molecular spinning tops, 1 15 — - 
 
 128. 
 
 Light taVes time to travel, 115 ; the electro-magnetic 
 
1$6 SPINNING TOPS. 
 
 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 tole wished 
 for, 132. 
 
APPENDIX I. 
 
 THE USE OF GYROSTATS. 
 
 In 1874 two famous men made a great mistake in en- 
 deavouring to prevent or diminish the rolling motion of tli2 
 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 prece ss 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 
 
Ij8 SPINNING TOPS. 
 
 such a small correction, and consequently calculation is 
 exceedingly simple. 
 
 Inventors using gyrostats have succeeded in doing the 
 following things— 
 
 (i) Keeping the platform of a gun level on board ship, 
 however the ship may roll or pitch. Keeping a submarine 
 vessel or a flying machine with any plane exactly horizontal 
 or inclined in any specified way. 1 It is easy to effect such 
 objects without the use of a gyrostat, as by means of spirit 
 levels it is possible to command powerful electric or other 
 motors to keep anything always level. The actual methods 
 employed by Mr. Beauchamp Tower (an hydraulic method), 
 and by myself (an electric method), depend upon the use of 
 a- gyrostat, which is really a pendulum, the axis being 
 vertical. 
 
 (2) Greatly reducing the rolling (or pitching) of a ship, or 
 the saloon of a ship. This is the problem which Mr. Schlick 
 has solved with great success, at any rate in the case of 
 torpedo boats. 
 
 (3) In Mr. Brennan's Mono-rail railway, keeping the 
 resultant force due to weight, wind pressure, centrifugal 
 force, etc., exactly in line with the rail, so that, however the 
 load on a wagon may alter in position, and although the 
 wagon may be going round a curve, it is quickly brought to 
 a position such that there are no forces tending to alter its 
 angular position. The wagon leans over towards the wind 
 or towards the centre of the curve of the rail so as to be 
 in equilibrium. 
 
 (4) I need not refer to such matters as the use of gyrostats 
 for the correction of compasses on board ship, ^referred to in 
 page in. 
 
 Problems (2) and (3) are those to which I wish to refer. 
 1 Probably first described by Mr. Brennan. 
 
SPINNING TOPS. 
 
 139 
 
140 SPINNING TOPS. 
 
 For a ship of 6,ooo tons Mr. Schlick would use a large 
 wheel of 10 to 20 tons, revolving about an axis E F (fig. 1) 
 whose mean position is vertical. Its bearings are in a frame 
 E C F D which can move about a thwart-ship axis C D with a 
 precessional motion. Its centre of gravity is below this 
 axis, so that like the ship itself the frame is in stable equi- 
 librium. Let the ship have rolled through an angle R from 
 its upright position, and suppose the axis E F to have pre- 
 cessed through the angle P from a vertical position. Let 
 the angular velocity of rolling be called R, and the angular 
 velocity of precession P ; let the moment of momentum of 
 the wheel be m. For any vibrating body like a ship it is 
 easy to write out the equation of motion ; into this equation 
 we have merely to introduce the moment m P diminishing 
 R ; into the equation for P we merely introduce the moment 
 m R increasing P. As usual we introduce frictional terms ; 
 in the first place F R (F being a constant co-efficient) stilling 
 the roll of the ship; in the second case/"P a fluid friction 
 introduced by a pair of dash pots applied at the pins 
 A and B to still the precessional vibrations of the frame. 
 It will be found that the angular motion P is very much 
 greater than the roll R. Indeed, so great is P that there 
 are stops to prevent its exceeding a certain amount. Of 
 course so long as a stop acts, preventing precession, the 
 roll of the ship proceeds as if the gyrostat wheel were not 
 rotating. Mr. Schlick drives his wheels by steam ; he will 
 probably in future do as Mr. Brennan does, drive them by 
 electromotors, and keep them, in air-tight cases in good 
 vacuums, because the loss of energy by friction against an 
 atmosphere is proportional to the density of the atmosphere. 
 The solution of the equations to find the nature of the R and 
 P motions is sometimes tedious, but requires no great amount 
 of mathematical knowledge. In a case considered by me of 
 
SPINNING TOPS. I4 l 
 
 a 6,000 ton ship, the period of a roll was increased from 14 
 to 20 seconds by the use of the gyrostat, and the roll rapidly 
 diminished in amount. There was accompanying this slow 
 periodic motion, one of a two seconds' period, but if it did 
 appear it was damped out with great rapidity. Of course it 
 is assumed that, by the use of bilge keels and rolling chambers, 
 and as low a metacentre as is allowable, we have already 
 lengthened the time of vibration, and damped the roll R 
 as much as possible, before applying the gyrostat. I take 
 it that everybody knows the importance of lengthening 
 the period of the natural roll of a ship, although he may 
 not know the reason. The reason why modern ships of great 
 tonnage are so steady is because their natural periodic times 
 of rolling vibration are so much greater than the probable 
 periods of any waves of the sea, for if a series of waves acts 
 upon a ship tending to make it roll, if the periodic time of 
 each wave is not very different from the natural periodic time 
 of vibration of the ship, the rolling motion may become 
 dangerously great. 
 
 If we try to apply Mr. Schlick's method to Mr. Brennan's 
 car it is easy to show that there is instability of motion, 
 whether there is or is not friction. If there is no friction, 
 and we make the gyrostat frame unstable by keeping its 
 centre of gravity above the axis C D, there will be vibra- 
 tions, but the smallest amount of friction will cause these 
 vibrations to get greater and greater. Even without friction 
 there will be instability if ;«, the moment of momentum of 
 the wheel, is less than a certain amount. We see, then, 
 that no form of the Schlick method, or modification of it, 
 can be applied to solve the Brennan problem. 
 
 Mr. Brennan's method of working is quite different from 
 that of Mr. Schlick. Fig. 2 shows his model car (about six 
 feet long) ; it is driven by electric accumulators carried by 
 
142 
 
 SPINNING TOPS. 
 
SPINNING TOPS. 143 
 
 the car. His gyrostat wheels are driven by electromotors 
 (not shown in fig. 3); as they are revolving in nearly vacuous 
 spaces they consume but little power, and even if the current 
 were stopped they would continue running at sufficiently 
 high speeds to be effective for a length of time. Still it must 
 not be forgotten that energy is wasted in friction, and work 
 has to be done in bringing the car to a new position of equilib- 
 rium, and this energy is supplied by the electromotors. 
 Should the gyrostats really stop, or fall to a certain low 
 speed, two supports are automatically dropped, one on either 
 side of the car ; each of them drops till it reaches the 
 ground ; one of them dropping, perhaps, much farther than 
 the other. 
 
 The real full-size car, which he is now constructing, may 
 be pulled with other cars by any kind of locomotive using 
 electricity or petrol or steam, or each of the wheels may 
 be a driving wheel. He would prefer to generate electro- 
 power on his train, and to drive every wheel with an electric 
 motor. His wheels are so independent of one another that 
 they can take very quick curves and vertical inequalities of 
 the rail. The rail is fastened to sleepers lying on ground 
 that may have sidelong slope. The model car is supported by 
 a mono-rail bogie at each end ; each bogie has two wheels 
 pivoted both vertically and horizontally ; it runs on a round 
 iron gas pipe, and sometimes on steel wire rope ; the ground 
 is nowhere levelled or cut, and at one place the rail is a 
 steel wire rope spanning a gorge, as shown in fig. 2. It is 
 interesting to stop the car in the middle of this rope and to 
 swing the rope sideways to see the automatic balancing of 
 the car. The car may be left here or elsewhere balancing 
 itself with nobody in charge of it. If the load on the car — 
 great lead weights — be dumped about into new positions, 
 the car adjusts itself to the new conditions with great 
 
144 
 
 SPINiNING TOPS. 
 
 quickness. When the car is stopped, if a person standing 
 on the ground pushes the car sidewise, the car of course 
 pushes in opposition, like an indignant animal, and by 
 ludicious pushing and yielding it is possible to cause a 
 
 %WZ77 r 
 
 77777?y/////////////// 'lA 277777, 
 
 Fig. 3. 
 
 considerable tilt. Left now to itself the car rights itself 
 very quickly. 
 
 Fig. 3 is a diagrammatic representation of Mr. Biennan's 
 pair of gyrostats in sectional elevation and plan. The 
 cases G and G', inside which the wheels F and F' are rotat- 
 ing in vacuo at the same speed and in opposite directions 
 
I46 SPINNING TOPS. 
 
 (driven by electromotors not shown in the figure), are pivoted 
 about vertical axes E J and E' J'. They are connected by 
 spur-toothed segments J J and J' J', so that their precessional 
 motions are equal and opposite. The whole system is 
 pivoted about C, a longitudinal axis. Thus when precessing 
 so that H comes out of the paper, so will H', and when H 
 goes into the paper, so does H'. When the car is in equilib- 
 rium the axes K II and K' H' are in line N O O' N' across 
 the car in the plane of the paper. They are also in a line 
 which is at right angles to the total resultant (vertical or 
 nearly vertical) force on the car. I will call N O O' N' the 
 mid position. Let \m be the moment of momentum of 
 either wheel. Let us suppose that suddenly the car finds 
 that it is not in equilibrium because of a gust of wind, or 
 centrifugal force, or an alteration of loading, so that the shelf 
 D comes up against H, the spinning axis (or a roller revolv- 
 ing with the spinning axis) of the gyrostat. H begins to 
 roll away from me, and if no slipping occurred (but there 
 always is slipping, and, indeed, slipping is a necessary con- 
 dition) it would roll, that is, the gyrostats would precess 
 with a constant angular velocity a, and exert the moment 
 ma upon the shelf D, and therefore on the car. It is to 
 be observed that this is greater as the diameter of the 
 rolling part is greater. This precession continues until the 
 roller and the shelf cease to touch. At first H lifts with 
 the shelf, and afterwards the shelf moving downwards is 
 followed for some distance by the roller. If the tilt had 
 been in the opposite direction the shelf D' would have 
 acted upwards upon the roller H', and caused just the 
 opposite kind of precession, and a moment of the opposite 
 kind. 
 
 We now have the spindles out of their mid position ; how 
 are they brought back from O Q and O' Q' to O N and O' N', 
 
SPINNING TOPS. I47 
 
 but with H permanently lowered just the right amount ? It is 
 the essence of Mr. Brennan's invention that after a restoring 
 moment has been applied to the car the spindles shall go back 
 to the position N O O' N' (with H permanently lowered), so 
 as to be ready to act again. He effects this object in various 
 ways. Some ways described in his patents are quite different 
 from what is used on the model, and the method to be used 
 on the full-size wagon will again be quite different. I will 
 describe one of the methods. Mr. Brennan tells me that he 
 considers this old method to be crude, but he is naturally 
 unwilling to allow me to publish his latest method. 
 
 D' is a circular shelf extending from the mid position in 
 my direction ; D is a similar shelf extending from the mid 
 position into the paper, or away from me. It is on these 
 shelves that H' and H roll, causing precession away from 
 N O O' N', as I have just described. When H' is inside the 
 paper, or when H is outside the paper, they find no shelf to 
 roll upon. There are, however, two other shelves L and L', 
 for two other rollers M and M', which are attached to the 
 frames concentric with the spindles ; they are free to rotate, 
 but are not rotated by the spindles. When they are pressed 
 by their shelves L or L' this causes negative precession, and 
 they roll towards the N O O' N' position. There is, of course, 
 friction at their supports, retarding their rotation, and there- 
 fore the precession. The important thing to remember is 
 that H and H', when they touch their shelves (when one is 
 touching the other is not touching) cause a precession away 
 from the mid position N O O' N' at a rate a, which pro- 
 duces a restoring moment via of nearly constant amount 
 (except for slipping), whereas where M or M' touches its 
 shelf L or L' (when one is touching the other is not touch- 
 ing) the pressure on the shelf and friction determine the 
 rate of the precession towards the mid position N O O' N', 
 
U§ SPINNING TOPS. 
 
 as well as the small vertical motion. The friction at the 
 supports of M and M' is necessary. 
 
 Suppose that the tilt from the equilibrium position to be 
 corrected is R, when D presses H upward. The moment 
 ma, and its time of action (the total momental impulse) are 
 too great, and R is over-corrected ; this causes the roller M' 
 to act on L', and the spindles return to the mid position ; 
 they go beyond the mid position, and now the roller H' acts 
 on D', and there is a return to the mid position, and beyond 
 it a little, and so it goes on, the swings of the gyrostats out of 
 and into the mid position, and the vibrations of the car about 
 its position of equilibrium getting rapidly less and less until 
 again neither H nor H', nor M nor M' is touching a shelf. 
 It is indeed marvellous to see how rapidly the swings decay. 
 Friction accelerates the precession away from N O O' N'. 
 Friction retards the precession towards the middle position. 
 
 It will be seen that by using the two gyrostats instead of 
 one when there is a curve on the line, although the plane 
 N O O' N' rotates, and we may say that the gyrostats 
 precess, the tilting couples which they might exercise are 
 equal and opposite. I do not know if Mr. Brennan has 
 tried a single gyrostat, the mid position of the axis of the 
 wheel being vertical, but even in this case a change of slope, 
 or inequalities in the line, might make it necessary to have 
 a pair. 
 
 It is evident that this method of Mr. Brennan is altogether 
 different in character from that of Mr. Schlick. Work is 
 here actually done which must be supplied by the electro- 
 motors. 
 
 One of the most important things to know is this : the 
 Brennan model is wonderfully successful ; the weight of the 
 apparatus is not a large fraction of the weight of the wagon ; 
 will this also be the case with a car weighing 1,000 times as 
 
SPINNING TOPS. H9 
 
 much ? The calculation is not difficult, but I may not give 
 it here. If we assume that suddenly the wagon finds itself 
 at the angle R from its position of equilibrium, it may be 
 taken that if the size of each dimension of the wagon be 
 multiplied by «, and the size of each dimension of the 
 apparatus be multiplied by ft, then for a sudden gust of 
 wind, or suddenly coming on a curve, or a sudden shift of 
 position of part of the cargo, R may be taken as inversely 
 proportional to n. I need not state the reasonable assump- 
 tion which underlies this calculation, but the result is that if 
 n is 10, ft is T$. That is, if the weight of the wagon is 
 multiplied by 1,000, the weight of the apparatus is only 
 multiplied by 420. In fact, if, in the model, the weight of 
 the apparatus is 10 per cent, of that of the wagon, in the 
 large wagon the weight of the apparatus is only about 4 per 
 cent, of that of the wagon. This is a very satisfactory result. 1 
 
 My calculations seem to show that Mr. Schlick's apparatus 
 will form a larger fraction of the whole weight of a ship, as 
 the ship is larger, but in the present experimental stage of the 
 subject it is unfair to say more than that this seems probable. 
 My own opinion is that large ships are sufficiently steady 
 already. 
 
 In both cases it has to be remembered that if the diameter 
 of the wheel can be increased in greater proportion than the 
 dimensions of ship or wagon, the proportional weight of 
 the apparatus may be diminished. A wheel of twice the 
 diameter, but of the same weight, may have twice the 
 moment of momentum, and may therefore be twice as 
 effective. I assume the stresses in the material to be the 
 
 1 The weight of Mr. Brennan's loaded wagon is 313 lb., including 
 gyrostats and storage cells. His two wheels weigh 13 lb. If made of 
 nickel steel and run at their highest safe speed they would weigh much 
 less. 
 
APPENDIX II. 
 
 Page 23 ; note at line 3. Prof. Osborne Reynolds made 
 the interesting remark {Collected Papers, Vol. ii., p. 154), 
 "That if solid matter had certain kinds of internal motions, . 
 such as the box has, pears differing, say, from apples, the 
 laws of motion would not have been discovered; if discovered 
 for pears they would not have applied to apples." 
 
 Page 38 ; note at line 8. The motion of a rifle bullet is 
 therefore one of precession about the tangent to the path. 
 The mathematical solution is difficult, but Prof. Greenhill 
 has satisfied himself mathematically that air friction damps 
 the precession, and causes the axis of the shot to get nearer 
 the tangential direction, so that fig. 10 illustrates what 
 would occur in a vacuum, but not in air. It is probable that 
 this statement applies only to certain proportions of length 
 to diameter. 
 
 Page 129; note at line 5. Many men wonder how the 
 ether can have the enormous rigidity necessary for light 
 transmission, and yet behave like a frictionless fluid. One 
 way of seeing how this may occur is to imagine that when 
 ordinary matter moves in the ether it only tends to produce 
 motion of translation of the ether particles, and therefore 
 no resistance. But anything such as light, which must operate 
 in turning axes of rotating parts, may encounter enormous 
 elastic resistance. 
 
APPENDIX III. 
 
 THE GYRO-COMPASS FOR SHIPS. 
 (Added January 1916,) 
 
 In page 1 1 1 I speak of the use of a gyrostat as a compass, 
 but I did not dream that the gyro-compass would be in use 
 within fifteen years. The errors of the magnetic compass on 
 board ship are large and very troublesome, but they would 
 not probably have compelled the adoption of the gyro- 
 compass had it not been for the invention of the submarine. 
 A magnetic compass cannot be used at all inside a steel 
 submarine. 
 
 In page 106 the perfectly free gyrostat, whose spinning 
 axis is at first horizontal and pointing due north, would seem 
 gradually to tilt out of the horizontal if left free, and it would 
 point away from the north. In truth the axis would really 
 keep in a constant direction in space, and it is the direction 
 of the north horizontal which is altering, due to the motion 
 of the earth. To keep the axis pointing due north, it is 
 necessary to keep it as nearly horizontal as possible, as is 
 done in Fig. 47. As arranged in Fig. 47, the gyrostat on a 
 firm support finds the due north quite rapidly if there is no 
 friction about the vertical axis, and such a gyro-compass can 
 be used on land. 1 I have used a very accurate one which 
 comes to the north from any position in about half a minute. 
 But on board ship it is not possible to get a firm support, 
 and hence the whole frame of Fig. 47 must be suspended on 
 gymbals, which for stability must be above the centre of 
 
 1 The difficulty as to friction suggested to Lord Kelvin [British 
 Association Report, 1884) that a float might be used to support the 
 gyrostat, and this is the method actually employed in the compass used 
 in the German Navy, and to some extent in our own Navy. 
 
152 SPINNING TOPS. 
 
 gravity of the whole suspended mass. In spite of the rolling 
 and pitching of the ship, gravity causes the average position 
 of the spinning axis to be horizontal, as we wish it to be. If 
 the axis is displaced from its position in the meridian it 
 vibrates into and out of the meridian and into and out of the 
 position of no tilt with a very slow swing. The tilt is always 
 very small, even for great displacement in azimuth. The 
 periodic time is usually 70 or 100 minutes ; the longer this 
 periodic time the less is the evil effect of rolling or pitching 
 of the ship, and the less is another important evil effect due 
 to the ship getting up speed towards the north or south. 
 
 The directive torque towards the north is always exceed- 
 ingly small, because of the slowness of the earth's rotation ; it 
 is proportional to the angular momentum of the wheel, and 
 is less in higher latitudes. The wheel is usually inside a 
 case which contains also the stator of a three-phase electric 
 motor, so that the wheel keeps going at a constant great 
 speed. The speed must not be so great as to cause danger- 
 ous stresses in its material due to centrifugal force. The 
 wheel generates heat by friction against the atmosphere 
 and its speed is limited by rise of temperature. The heat 
 generated per second is proportional to the density of the 
 atmosphere, and, therefore, in one kind of gyro-compass the 
 case is filled with hydrogen, and in another there is air in a 
 partly vacuous state. Inventors aim at getting great direc- 
 tive torque by using large and heavy wheels ; they seem to 
 forget that it might be better to diminish .the resistance to 
 motion about the vertical axis, which may roughly be called 
 a solid friction. With large heavy wheels the expense is 
 great and the friction is great. Again, the use of hydrogen 
 or a partial vacuum introduces another possibility of failure 
 due to accidents, and there are too many of these possibilities 
 already. 
 
SPINNING TOPS. 153 
 
 The vibrations must be damped. It is usual for this pur- 
 pose to introduce a torque about the vertical axis which is 
 proportional to the tilt. This gives good damping, but 
 unfortunately it introduces a considerable error which is 
 different for different latitudes, and it also increases theerror 
 due to change of speed of the ship. It is better to damp 
 the tilting vibration directly in the well-known simplest wav, 
 as this introduces no latitude error and does not increase 
 the error due to constant acceleration. 
 
 The error due to rolling and pitching and uniform 
 acceleration of the ship ; the latitude error ; the serious 
 " quadrantal error" due to the ship rolling when on a north- 
 west or north-east course, and errors due to friction, have 
 caused inventors to introduce numerous and complex methods 
 of correction. It results that the binnacle of the gyro- 
 compass is like a bag-qf -tricks. It is enough to say that in 
 that which is best known, as one part of the complexity, there 
 are three gyrostats rotating in hydrogen. Still, it must be 
 said for these unscientific contrivances that so long as they 
 do not get out of order they are a help to navigators. 
 
 Mr. S. G. Brown proceeds in another way. He first 
 invented a novel method of destruction of the solid friction 
 about the vertical axis ; he is therefore able to dispense 
 with 95 per cent, of the directive torque hitherto supposed to 
 be necessary ; so he can use a small wheel rotating in the 
 ordinary atmosphere. By another invention, which he 
 attributes to my suggestion, he arranges that his pendulum 
 is always as nearly vertical as if the ship did not roll, and 
 therefore there is neither rolling nor quadrantal error. There 
 is no latitude error ; there is no error due to change of speed 
 of the ship. This gyro-compass is a marvel of simplicity in 
 principle and in construction. It is shown in Fig. 4. 
 
 The frame F is supported on gimbals, of which one set G 
 
154 
 
 SPINNING TOPS. 
 .5" 
 
 Fig. 4. — The Gyro-Compass. 
 
SPINNING TOPS. 155 
 
 is shown. Moving relatively to this frame vertically and in 
 azimuth is the ring R, which is rigidly fixed to the vertical 
 spindle S, to which the compass card is attached. The case 
 C contains the wheel, kept rotating on ball-bearings by 
 means of a three-phase electric stator. C is supported by 
 knife-edges E on the ring R. The swinging of C relatively 
 to R is damped by the knife K, which cuts through cobbler's 
 wax in the box B. Solid friction about the vertical spindle 
 is destroyed in the following way. There is a constant 
 current electric motor in M which pumps oil underneath the 
 spindle S, so that S rises and falls rapidly. There are three 
 ring mercury contacts at D to convey current. Two sets of 
 springs (not shown) counteract all effects of rolling or 
 pitching in such a way that S is kept just as nearly vertical 
 as if the ship were steady. 
 

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