strength for safety against breakage; and the author proposes to call it the Crinal, from the Latin crinis and crinalis. In the Metre-Tonne-Second System the unit of force, likewise derived by the Gaussian method, is 10,000 Crinals, or 100,000,000 Dynes, or is about equal to the gravity of 2 cwt., or of of a ton. This force would be properly borne as a pull by a moderately-sized rope; and the author proposes to call it the Funal, from the Latin funis and funalis. 10 Then we have One Horse-Power, of 33,000 foot-pounds per minute, about equal to 75,000 Decimetre-Crinals per second; and the Horse-Power is also about equal to 75 of a Metre-Funal per second. Also 1 Metre-Funal = 100,000 Decimetre-Crinals, = 10,000,000,000 Centimetre-Dynes, or Ergs, = Also 1 Horse-Power is about 7,500,000,000 Centimetre-Dynes per second, or as the same may be written 75×10 Centimetre-Dynes per second. The number 7,500,000,000, for expressing a Horse-Power under the CentimetreGram-Second System, is an exceedingly unmanageable one; and it gives a very decisive indication that the Centimetre and Gram are too small to be suitable as fundamental units of length and of mass for ordinary engineering purposes; and that there is great need for the establishment of systems having larger units, such as those which have been recommended in the present paper, and for which a convenient nomenclature has been offered. It is to be observed that the provision made by the British Association Committee, in the Report already referred to, of a multiple of the Dyne, such as the Megadyne, or million of Dynes, as a larger unit of force, does not accomplish all that is to be desired, because various important formulas, or convenient methods of statement, will not hold good when any of the units are so derived. Thus, for instance, if the Megadyne be the unit of force, while the Gram and Second are the units of mass and time, the ordinary formulas for giving the so-called "centrifugal force" of a revolving mass, F= and F=mw3r, will not hold good; and, as another instance, we may notice that the proposition that, in respect to a jet of water, the reaction force on the vessel is equal numerically to the momentum generated per second, will not hold good; and numberless other instances might readily be cited, but those given may suffice. On the Precessional Motion of a Liquid. By Sir W. THOMSON, D.C.L., F.R.S. The formulas expressing this motion were briefly explained, but the analytical treatment of them was reserved for a paper "On the Nutation of a Solid Shell containing Liquid." The chief object of the present communication was to illustrate experimentally a conclusion from this theory which has 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 the 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 ordinary 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 theory, produce very approximately the same precession in the thin shell filled with liquid as in the rotating solid. Accordingly the main pre cessional 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 observation without measurement might show very sensible differences between the performances of the liquid and the solid gyrostat in the way of nutational tremors produced 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 interesting illustration of that very interesting result of mathematical hydrokinetics, 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 Precession of the Equinoxes, and the Pendulum," by Brevet-Major Gen. J. G. Barnard, College 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. 1, 1872); so far as regards fluidity or imperfect rigidity, within an infinitely 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 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 mean time. Addendum. Solid and Liquid Gyrostats.-The solid gyrostat has been regularly shown for many years in the 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 and Edinburgh at conversaziones of the Royal Societies and of the Society of Telegraph Engineers, but no account of it has yet been published. The following is a brief description of it. 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 encloses it. Fig. 1 represents a section 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 containingcase is fitted with a thin projecting edge in the plane of the fly-wheel, which is called the bearing-edge. Its 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 greater than the distance of the corners from the centre. The friction of the fly-wheel would, if the bearing-edge were circular, cause the case to roll along it like a hoop; and it is to prevent this effect that the curved polygonal form described above and represented in the drawing is given to the bearing-edge. To spin the solid gyrostat a piece of stout cord about forty feet long and a place where a clear run of about 60 feet can be obtained are convenient. The gyrostat having been placed with the axis of its fly-wheel vertical, the cord is passed in through an aperture in the case two and a half times round the bobbin-shaped part of the shaft and out again at an aperture on the opposite side. Having taken care that the slack cord is placed clear of all obstacles, and that it is free from kinks, the operator holds the gyrostat steady, so that its case is prevented from turning, while an assistant pulls the cord through by running, at a gradually increasing pace, away from the instrument, while holding the end of the cord in his hand. Sufficient tension is applied to the entering cord to prevent it from slipping round on the shaft. In this way a very great angular velocity is communicated to the flywheel, sufficient, indeed, to keep it spinning for upwards of twenty minutes. If, when the gyrostat has been spun, it be set on its bearing-edge with the centre of gravity exactly over the bearing point, on a smooth horizontal plane such as a piece of plate-glass lying on a table, it will continue apparently stationary and in stable equilibrium. If while it is in this position a couple round a horizontal axis in the plane of the fly-wheel be applied to the wheel, no deflection of this plane from the vertical is produced, but it rotates slowly round a vertical axis. If a heavy blow with the fist be given to the side of the case, it is met by what seems to the senses the resistance of a very stiff elastic body, and, for a few seconds after the blow, the gyrostat is in a state of violent tremor, which, however, subsides rapidly. As the rotational velocity gradually diminishes, the rapidity of the tremors produced by the blow also diminishes. It is very curious to notice the tottering condition, and slow, seemingly palsied tremulousness of the gyrostat when the flywheel bas nearly ceased to spin. In the liquid gyrostat the fly-wheel is replaced by an oblate spheroid, made of thin sheet-copper and filled with water. The ellipticity of this shell in the instrument exhibited is that is to say, the equatorial diameter exceeds the polar by that fraction of either. It is pivoted on the two ends of its polar axis in bearings fixed in a circular ring of brass surrounding the spheroid. This circle of brass is rigidly connected with the curved polygonal bearing-edge which lies in the equatorial plane of the instrument, thus forming a framework for the support of the spheroidal shell. In fig. 3 a section is represented through the polar axis to show the ellipticity, and fig. 4 gives a view of the gyrostat as seen from a point in the prolongation of the axis. To prevent accident to the shell, when the gyrostat falls down at the end of its spin, cage-bars are fitted round it in such a way that no plane can touch the shell. The method of spinning the liquid gyrostat is similar to that described for the solid gyrostat, differing only in the use of a very much longer cord and of a large wheel for the purpose of pulling it, The cord is first wound on a bobbin free to rotate round a fixed pin. The end of it is then passed two and a half times round a little pulley, and thence to a point in the circumference of a large wheel to which it is fixed. An assistant then turns the wheel with gradually increasing velocity, while the frame of the gyrostat is firmly held, and the requisite tension applied to the entering cord to prevent it from slipping round the pulley. Secular Illustration of the Laws of the Diffusion of Liquids. On a new case of Instability of Steady Motion. On the Nutation of a Solid Shell containing Liquid. |