712 



NATURE 



[February 25, 1915 



ecliptic. On this ring, which represents the ecliptic, 

 you have the intersections with it of the earth's 

 equator — that is, the equinoxes — and so, as the earth 

 turns, the two intersections move along the ecliptic, 

 the equinoxes precess. The earth, in fact, is a top on 

 which we happen to live, the spin is one turn in 

 24 sidereal hours, and the conical motion is completed 

 in a period of 26,000 years (Fig. 3), One of our 

 problems was to calculate the diameter of this pin for 

 the earth, or, as it was sometimes put, to find the 

 diameter of the north or south pole ! If I remember 

 aright the diameter is about 21 inches. 



These were our first gyrostatic experiments and 

 illustrations. I must not omit to mention that the 

 spinning of the ellipsoid was attempted also with each 

 of two eggs, and that with one the experiment always 

 succeeded, and with the other always failed. The 

 reason of this failure and success was interesting ; and 

 although some students laughed at the experiment, it 

 nevertheless arrested the attention of all. The con- 

 tents of one egg were a viscid liquid, the contents of 

 the other had been subjected to a process of coagulation 

 by prolonged exposure to an elevated temperature. In 

 other words, one ^^g,, the one that would not spin on 

 end, was raw, the other had been boiled hard. I now 

 repeat this experiment, which is the scientific solution 



of the famous problem of Christopher Columbus, to 

 make an egg stand on end. 



It is very easy to show, on principles which I hope 

 to explain later, why the solid prolate ellipsoid, the 

 piece of wood, or the hard-boiled egg, sets itself on 

 end when it is spun about one of the shortest dia- 

 meters ; it is not at all easy to show why the raw egg 

 does not. 



I shall now say something of Lord Kelvin's papers 

 and work on gyrostatics, taking the various topics 

 more or less in chronological order. 



\\.— Dynamical Theory of Rotation of Plane of 

 Polarised Light. 



The first paper in which Lord Kelvin dealt with 

 what may be regarded as a gyrostatic problem is that 

 published by him in the Proceedings of the Royal 

 Society,^ entitled " Dynamical Illustrations of the Mag- 

 netic and the Helicjoidal Rotatory Effects of Trans- 

 parent Bodies in Polarised Light." He does not in 

 that paper use the term "gyrostat" or "gyroscope," 

 but the equations which are arrived at in the dis- 

 cussion of the dynamical illustrations referred to are 



2 Proceedings of the Royal Society, vol. viii, p. 150, 1856. 



NO. 2365, VOL. 94] 



in form essentially of the kind which he afterwards 

 called gyrostatic. 



The fundamental idea of this paper is one which he 

 developed a good deal in later papers and, from time 

 to time, in his lectures to his students. It is that the 

 rotation of the plane of polarised light transmitted 

 through a solution of sugar or tartaric acid, or across 

 a plate of quartz cut at right angles to the axis of 

 the crystal, is to be explained by a helical structure 

 of the medium ; while what appears at first sight to 

 be the exactly similar rotation of that plane, by 

 passage of the light through a piece of heavy glass 

 along the lines of force of a magnetic field, is due to 

 rotational motion already existing in the medium and 

 compounded with the motion produced by the wave of 

 light. 



Think (as I heard him once say) of a transparent 

 elastic medium full of little helical hollows of the order 

 of 1/40,000 in. in dimensions, having all their axes 

 turned the same way, so that to an observer looking 

 along them the helices are all right-handed or all left- 

 handed, or at least are preponderatingly in one direc- 

 tion or the other. Such a medium would have the 

 property of transmitting, in the direction of the axes 

 of the helices, waves of torsional displacement at 

 different speeds according as the torsion is right- 

 handed or left-handed. 



On the other hand, let us think of a transparent 

 elastic medium in which are embedded in a homogene- 



A. 9 .B 



IN 6500 

 YEARS 



NOV^ \ 



IN 13000 

 Y^ARS 



"o 



Fig. 3. 



o 



Fu;. 4. 



ous manner innumerable particles describing circular 

 orbits, all of which, or a majority of which, face the 

 same way, and are traversed by the particles in the 

 same direction round. Now let a wave of turning 

 motion of the medium be propagated in one direction 

 or the other, parallel to the axes of the circles. A 

 wave-motion of a certain rapidity in one direction 

 round, say that of the motion of the particles in the 

 circular orbits, will call for the same centreward 

 force, applied to the particles by the medium, as a 

 motion of greater rapidity applied in the contrary 

 direction round. Thus oppositely directed circular 

 motions will, for the same displacements of the 

 medium, have different rapidities of turning (in 

 planes perpendicular to the direction of propagation 

 of the wave) ; the corresponding waves will travel at 

 different rates, and one will gain on the other. 



The illustration proposed was a double pendulum. 

 A cord (see Fig. 4) is attached at the two ends of a 

 horizontal rod A B, and to the middle point of this 

 cord is fastened a simple pendulum, of length I as 

 indicated. The distance of the bob from the rod is 

 V, that is l+OC. The rod is made to turn with 

 uniform angular speed w about a vertical axis through 

 its middle point O. The cords are supposed to be of 

 negligible mass and quite flexible, and the bob is a 

 massive particle. 



