Feb. I, 1877] 



NATURE 



297 



ON THE PRECESSTONAL MOTION OF A 

 LIQUID * 



THE formulas expressing this motion were laid before 

 the meeting and briefly explained, but the analytical 

 treatment of them was reserved for a more mathematical 

 paper to be communicated to the Section on Satur- 

 day. The chief object of the present communication 

 was to illustrate experimentally a conclusion from this 

 theory which had been announced by the author in his 

 opening address to the Section, to the effect, that, if the 

 period of the precession of an oblate spheroidal rigid shell 

 full of liquid is a much greater multiple of the rotational 

 period of the liquid than any diameter of the spheroid is 

 of the difference between the greatest and least diameters, 

 the precessional effect of a given couple acting on the 

 shell is approximately the same as if ihe whole were a 

 solid rotating with the same rotational velocity. The 

 experiment consisted in showing a liquid gyrostat, in 

 which an oblate spheroid of thin sheet copper filled with 

 water was substituted for the solid fly-wheel of the ordi- 

 nary gyrostat. In the instrument actually exhibited, the 

 equatorial diameter of the liquid shell exceeded the polar 

 axis by about one-tenth of either. 



Supposing the rotational speed to be thirty turns per 

 second, the effect of any motive which, if acting on a 

 rotating solid of the same mass and dimensions, would 

 produce a precession having its period a considerable 

 multiple of ^ of a second, must, according to the theory, 

 produce very approximately the same precession in the 

 thin shell filled with liquid as in the rotating solid. 

 Accordingly the main precessional phenomena of the 

 liquid gyrostat were not noticeably different from those of 

 ordinary solid gyrostats which were shown in action for 

 the sake of comparison. It is probable that careful ob- 

 servation without measurement might show very sensible 

 differences between the performances of the liquid and 

 the solid gyrostat in the way of nutational tremors pro- 

 duced by striking the case of the instrument with the 

 fist. 



No attempt at measurement either of speeds or forces 

 was included in the communication, and the author 

 merely showed the liquid gyrostat as a rough general 

 illustration, which he hoped might be regarded as an in- 

 teresting illustration of that very interesting result of 

 mathematical hydro-kinetics the quasi-rigidity produced 

 in a frictionless liquid by rotation. 



P.S. — Since the communication of this paper to the 

 Association, and the delivery of my opening address 

 which preceded it on the same day, I have received from 

 Prof. Henry No. 240 of the Smithsonian Contributions to 

 Knowledge, of date October, 1871, entitled " Problems of 

 Rotatory Motion presented by the Gyroscope, the Pre- 

 cession of the Equinoxes and the Pendulum," by Brevet 

 Major-Gen. J. G. Barnard, Col. of Engineers, U.S.A., in 

 which I find a dissent, from the portion of my previously- 

 published statements which I had taken the occasion of 

 my address to correct, expressed in the following terms : — 



" I do not concur with Sir William Thomson in the 

 opinions quoted in note p. 38, from Thomson and Tait, 

 and expressed in his letter to Mr. G. Poulett Scrope 

 (Nature, Feb. i, 1872). So far as regards fluidity, or 

 imperfect rigidity, within anmtinitely rigid envelope, I do 

 not think the rate of precession would be affected." 



Elsewhere in the same paper Gen. Barnard speaks of 

 " the practical rigidity conferred by rotation." Thus he 

 has anticipated my correction of the statements contained 

 in my paper on the Rigidity of the Earth, so far as regards 

 the effect of interior fluidity on the precessional motion of 

 a perfectly rigid ellipsoidal shell filled with fluid. 



I regret to see that the other error of that paper, which 

 I corrected in my opening address, had not been corrected 



' Communicated to Section A of the British Association, Thursday, Sep- 

 tember 7, 1876. 



by Gen. Barnard, and that the plausible reasoning which 

 had led me to it had also seemed to him convincing. 

 For myself, I can only say that I took the very earliest 

 opportunity to correct the errors after I found them to be 

 errors, and that I deeply regret any mischief they may 

 have done in the meantime. 



Addendum. — Salid and Liquid Gyrostats. — The solid 

 gyrostat has been regularly shown for many years in the 



/^.i 



Natural Philosophy Class of the University of Glasgow 

 as a mechanical illustration of the dynamics of rotating 

 solids, and it has also been exhibited in London ard Edin- 

 burgh at conversaziones of the Royal Societies and of the 

 Society of Telegraph Engineers, but no account of it has 

 yet been published. The following brief description and 

 drawing may therefore even now be acceptable to readers 

 of Nature : — 



The solid gyrostat consists essentially of a massive fly- 

 wheel possessing great moment of inertia, pivoted on the 

 two ends of its axis in bearings attached to an outer case 

 which completely incloses it. Fig. i represents a section 



Frsf.S. 



by a plane through the axis of the fly-wheel, and Fig. 2 

 a section by a plane at right-angles to the axis and cutting 

 through the case just above the fly-wheel. The contain- 

 ing case is fitted with a thin projecting edge in the plane 

 of the fly-wheel, which is called the bearing edge. lis 

 boundary forms a regular curvilinear polygon of sixteen 

 sides with its centre at the centre of the fly-wheel. Each 

 side of the polygon is a small arc of a circle of radius 



