Let us take that of a spinning top. When the string which has been wrappedround a top's axis is violently drawn off, and the top falls on to the table,it usually happens that besides the rapid rotation two other movements aregiven to it. A slight horizontal momentum, unavoidably impressed on it whenleaving the handle, carries it. away bodily from the place on which it drops;and in consequence of its axis being more or less inclined, it falls intoa certain oscillation, described by the expressive though inelegant word"wabbling." These two subordinate motions, variable in their proportionsto each other and to the chief motion, are commonly soon brought to a closeby separate processes of equilibrium. The momentum which carries the topbodily along the table, resisted somewhat by the air but mainly by the irregularitiesof the surface, shortly disappears; and the top thereafter continues to spinon one spot. Meanwhile, in consequence of that opposition which the axialmomentum of a rotating body makes to any change in the plane of rotation,(so beautifully exhibited by the gyroscope,) the "wabbling" diminishes,and like the other is quickly ended. These minor motions having been dissipated,the rotatory motion, interfered with only by atmospheric resistance and thefriction of the pivot, continues some time with such uniformity that thetop appears stationary: there being thus temporary established a conditionwhich the French mathematicians have termed equilibrium mobile. It is truethat when the velocity of rotation sinks below a certain point, new motionscommence and increase till the top falls; but these are merely incidentalto a case in which the centre of gravity is above the point of support. Werethe top, having an axis of steel, to be suspended from a surface adequatelymagnetized, the moving equilibrium would continue until the top became motionless,without any further change of attitude. Now the facts which it behoves ushere to observe are these. First, that the various motions which an aggregatepossesses are separately equilibrated: those which are smallest, or whichmeet with the greatest resistance, or both, disappearing first; and leavingat last that which is greatest, or meets with least resistance, or both.
Second, that when the aggregate has a movement of its parts with respectto each other which encounters but little external resistance, there is aptto be established a moving equilibrium. Third, that this moving equilibriumeventually lapses into complete equilibrium.
Fully to comprehend the process of equilibration, is not easy; since wehave simultaneously to contemplate various phases of it. The best coursewill be to glance separately at what we may conveniently regard as its fourdifferent orders. The first order includes the comparatively simple motions,as those of projectiles, which are not prolonged enough to exhibit theirrhythmical character, but which, being quickly divided and subdivided intomotions communicated to other portions of matter, are presently dissipatedin the rhythm of ethereal undulations. In the second order, comprehendingvarious kinds of ordinary vibration or oscillation, the implied energy isused up in generating a tension which, having become equal to it or momentarilyequilibrated with it, thereupon produces a motion in the opposite direction,that is subsequently equilibrated in like manner: thus causing a visiblerhythm which is presently lost in invisible rhythms. The third order of equilibration,not hitherto noticed, obtains in those aggregates which continually receiveas much energy as they expend. The steam-engine (and especially that kindwhich feeds its own furnace and boiler) supplies an example. Here the energyfrom moment to moment dissipated in overcoming the resistance of the machinerydriven, is from moment to moment re-placed from the fuel; and the balanceof the two is maintained by a raising or lowering of the expenditure accordingto the variation of the supply: each increase or decrease in the quantityof steam, resulting in a rise or fall of the engine's movement, such as bringsit to a balance with the increased or decreased resistance. This, which wemay fitly call the dependent moving equilibrium, should be specify noted;since it is one that we shall commonly meet with throughout various phasesof Evolution. The equilibrium to be distinguished as of the fourth order,is the independent or perfect moving equilibrium. This we see illustratedin the rhythmical motions of the Solar System, which, being resisted onlyby a medium of inappreciable density, undergo no sensible diminution in suchperiods of time as we can measure.
