4i6 



NATURE 



[July 25, 1918 



disappointing. The latter include some of the best- 

 known deposits, such as the famous. Sheba Mine; the 

 deposits do not show definite walls, and the auriferous 

 rock does not differ from the surrounding country 

 except by its impregnation with iron pyrites and with 

 gold, often very finely disseminated, so that the work- 

 able limits of the deposits can be established only by 

 continual assays. It is pointed out that the zone of 

 contact between the granite and the adjoining stratified 

 rocks is the area within which most of the important 

 gold-bearing deposits are situated, and it is suggested 

 that "gold occurrences are far more likely to be ex- 

 pected within the sphere of influence of the intrusive 

 granite," this forming a belt of country averaging 

 about three miles in width. Furthermore, in prospect- 

 ing, it should, not be forgotten that many of the pay- 

 able deposits "of the Barberton district take the form, 

 not of the well-defined quartz reef, with which most 

 prospectors are familiar, but of " mineralised zones of 

 impregnation, sometimes almost indistinguishable from 

 countrv rock." 



THE SPINNING-TOP IN HARNESS A 



THE gyroscopic theory of the lecture and its 

 applications was illustrated by experiments with 

 apparatus designed to show the chief principles of 

 gjTOScopic motion on a large scale, so as to be visible 

 to an audience ; some bicycle-wheels and a Maxwell 

 dynamical top were used. 



The lecture began with a quotation of the initial 

 sentence of Maxwell's own description of his top, as 

 given to the Royal Society of Edinburgh, April, 1857, 

 and the phrase "the perplexities of men who had 

 successfully threaded the mazes of the planetary 

 motions " was interpreted as a sly, malicious dig at 

 Newton and his struggle in the " Principia " with the 

 gyroscopic theory of precession. 



Twirled by the left hand, the dynamical top gives 

 the appropriate precession in direction ; called preces- 

 sion because the seasons come up in consequence 

 of it twenty minutes earlier each year than otherwise, 

 and twenty minutes a year gives the twenty-six 

 thousand years required for a complete revolution 

 among the stars. 



Two large 52-in. bicycle-wheels were employed as 

 spinning-tops on the floor, made originally by Prof. 

 C. V. Boys for his Otto bicycle. A hub was fitted 

 with ball-bearings, carrying a spike and a long stalk. 

 Spun by hand, with the spike resting in a small cup 

 raised about 3 ft. from the floor, the evolutions of 

 the wheel could be watched as they became more 

 violent, and finally extinguished when the rim reached 

 the floor. 



When the stalk was grasped and raised horizontal 

 and the wheel spun, the gyroscopic eff^ect was very 

 marked if the wheel was allowed to drop or the stalk 

 was brandished. Letting the spike rest in the hand, 

 the wheel moved round in precession, and Kelvin's 

 rule could be shown off in the alteration of the inclina- 

 tion of the axle. 



According to this rule, " Hurry the precession, and 

 the axle rises against gravity." This is observed 

 instinctively in riding a bicycle on the road. To avoid 

 an object the bicycle must be steered towards it in a 

 smaller circle, so as to rise and swerve away. A 

 bicvcle cannot run straight. 



The stability of the axle was shown by hammering 

 the wheel-rim with a stick, causing it to flinch only 

 slightly, but hurrying the precession. 



The mathematical theory was too complicated to be 

 undertaken in the course of ah hour's lecture, even 



I Abstract of a discour';e delivered at the Royal Institution on May 3 by 

 Sir George Greenhill, F.R.S. 



NO. 2543, VOL. lOl] 



when stated in Poinsot's concise manner, "which has 

 brought the subject under the power of a more search- 

 ing analysis than the calculus, in which ideas take 

 the place of symbols and intelligible propositions super- 

 sede equations." 



The elliptic function theory arises in all its com- 

 plexity, and appears as if created to speak the lan- 

 guage of gyroscopic theory. 



Two special cases of motion were suggested to 

 interest the mathematicians in the audience, where the 

 equations are quasi-algebraical, and may be employed 

 as typical illustrations in the wilderness of general 

 theory : — 



{i) Project the axle of the gyroscope horizontally 

 with no spin of the wheel ; this gives a spherical 

 pendulum motion, as of the bob of a simple pendulum 

 projected so as to move ih a spherical curve, and not 

 in plane oscillation. 



(2) Spin the wheel and hold the axle up at an angle 

 above the level, such that when let drop the 

 axle reaches the horizontal and rises again, and so 

 on to a series of cusps. 



This motion was illustrated on the gyroscopic ap- 

 paratus exhibited, an ordinary 28-in. bicycle-wheel and 

 hub screwed to a stalk, a short length of steel rifle- 

 barrel, suspended in altazimuth freedom from a 

 vertical spindle, another bicycle hub, fastened to an 

 iron bracket, bolted to the underside of a w-ooden 

 sleeper supported on brackets — not a thin lath, as I 

 found them trying in Rome wnth the specimen I had 

 sent to the Mathematical Congress in 1908. All details 

 to be bought cheap or easily constructed. 



The three angles, 6, yjr, 0, introduced into the treat- 

 ment by Euler (1750), were shown in the altazimuth 

 suspension : 6 is the angle of the axle with the nadir 

 downward vertical ; yjr is the azimuth ; while (p 

 measures the rubbing angular displacement of the 

 wheel over the axle. 



The exact dynamical interpretation of <^ is rather 

 delicate in its relation to the rotation of the wheel 

 about a moving axle. Thus, starting with the wheel 

 at rest on the axle, we cannot turn it by twirling the 

 axle. But move the axle round in a conical way back 

 to rest at its original start, and we find the wheel has 

 turned round on the axle through an angle ^ propor- 

 tional to the conical angle described by the axle. So 

 here is an answer to the challenge of Aristotle : to 

 turn a sphere round that is perfectly smooth, or spitted 

 along a perfectly smooth diametrical axle. 



In showing the 6 and ylr displacement in altitude 

 and azimuth, the wheel must be held to the axle by 

 the thumb ; as, if free, the angle (p will come into 

 existence. 



Anyone can show this off with a pencil or pen- 

 holder held between finger and thumb. 



The small bicycle-wheel is dismounted by removing 

 the supporting pin, and can then be spun by hand as 

 another top alongside the large wheel, or else super- 

 posed, as in Maxwell's experiment of the "top on the 

 top of a top," thus fortning two links of a gyrostatic 

 chain, standing up like a will o' the wisp, which may 

 be supposed in imagination to reach up to the ceiling, 

 as a mechanical model of the electromagnetic rotary 

 polarisation of light. 



Sir William Thomson gave an elaborate mathe- 

 matical investigation of the vibration and wave propa- 

 gation, but this can be simplified and brought under 

 elementary treatment by considering the gyrostatic 

 chain as a uniform helical polygon rotating uniformly 

 about the vertical, as I have explained in my Report 

 on Gyroscopic Theory (1914). 



Any similar discussion of a double pendulum, as of 

 a bell and clapper, or a chain of links, is simplified in 

 this manner by comparing the oscillation with a 



