CHAPTER LVII.
THE MAGIC TOP—THE GYROSCOPE AND SCIENTIFIC GAMES
We will not do our readers the injustice to suppose that they are not familiar with the ordinary top,—the delight of all school-boys and young people,—of which, therefore, we forbear giving any description; but we now desire to give some details of the construction of the wonderful magic top. It is composed of a large disc, with an axis turning on two pivots connected with a circle of iron. When in repose, this plaything exhibits nothing of a remarkable character; it is completely inert, obeying, like all other bodies, the laws of gravity. But when we come to give the disc a movement of rapid rotation, this inert instrument seems to assume a vitality of its own if we attempt to move it; it resists, and seems to thrust back the hand, and executes movements even in a contrary direction. Besides this, it appears to be freed, in a certain measure, from the laws of gravity; if we place it on its pivot, instead of falling, as it would when the disc is motionless, it preserves the upright or inclined position in which we place it, the upper extremity of the axis slowly describing a horizontal circle round the fulcrum of the other extremity.
Few persons are sufficiently familiar with the theory of mechanics to understand these phenomena, and it often happens that such a top purchased to amuse a child becomes an object of wonder and interest to his seniors. We do not pretend here to explain mathematically the reason of the facts before us, but the mechanical principle on which this top is constructed is of such great scientific importance, that we will, in a few words, explain it to our readers. It is sufficient to have a little knowledge of mechanics to be aware that a body in motion, subjected to the action of a force tending to give it a directly contrary motion, will follow a movement in a third direction, which is termed the resultant of the two others; and this resultant approaches nearer to one of the original directions, in proportion as the corresponding movement is more rapid in relation to the other. If, for example, you strike a billiard ball, which is rolling past you, in such a manner that you drive it regularly along in the same direction, it appears only to obey a part of the given impulsion, and continues its course in an oblique direction, the speed with which it commenced rolling combining with the impulsion to produce a resultant movement. If it is rolling very quickly, and you strike it gently, it will scarcely turn out of its course. If, on the contrary, it is moving slowly, and receives a violent shock, it will run off almost exactly in the direction in which it has been struck.
Fig. 871.—The magic top.
Now that which occurs in this example of a body tending to two movements at the same time, is also produced when it is a question of movements of rotation, so that if a force acts upon a body in rotation in such a manner as to give it a movement of the same kind round another axis, a third movement will be originated round a third axis, the direction of which will be nearest to that in which the rotation is most rapid. Let us apply this very simple principle to our top, and we shall see that magic has nothing whatever to do with these movements, which at first glance appears so extraordinary. Having set it in motion, we rest it on its pivot, its axis in a horizontal position; we then find that we have two movements before us; first, that which we gave the top ourselves, and secondly, the movement of rotation which occurs round a second axis equally horizontal passing through the fulcrum and perpendicular line to the first. A movement of rotation therefore originates round a third axis placed between the two first, but whilst the real axis of the top, obeying this resultant movement, takes up its new position, the law of gravity continuing to act, displaces and moves it a little further, so that in endeavouring to reach its centre of gravity, it turns round its fulcrum (fig. 871). From this explanation, it will be easily seen that the more rapid the movement given to the top,—that due to gravity remaining constant,—the nearer will be the axis of the resultant movement to its real axis, and consequently the slower will be the movement of rotation of the whole round the pivot. Thus this apparently incomprehensible phenomenon is easily explained by gravity, vertical force producing a movement of rotation in a horizontal plane. One can also explain by analogous reasoning, and calculation of passive resistance, why the axis of the top gradually inclines in proportion as the speed of the latter diminishes, and the speed of rotation round the fulcrum increases; why it falls immediately if an obstacle is opposed to the latter movement, and finally, why it produces on the hand which holds it, movements which astonish persons so intensely who behold it for the first time.
The principle we have just described is often enunciated, by saying that every body in rapid rotation rests in its plane, and can only be driven out by a considerable force; this, however, is a defective formula. The principle should be stated in the following manner. A body in rapid rotation tends to remain in its plane; that is, its axis rests parallel with itself, and instead of obeying any force tending to divert its direction, it produces in consequence of the combination of two simultaneous movements, a displacement of the axis, generally much feebler and of a different kind from that which this force exercises on the same body in repose. One of the most charming applications of this theory is due to M. Foucault. The Gyroscope, which bears his name, is a heavy disc, the axis of which is supported by a “Cardan” balance, so that, whatever is the position of the contrivance, it is possible to preserve it in a constant direction. Therefore if the disc is, by means of special mechanism, put in rapid rotation, we may give it all kinds of possible displacement without changing the plane in which the gyroscope moves. Supposing then that its connection with the suspension is fixed in a relatively immovable manner, but attracted by a movement towards the ground, the plane of rotation of the disc will not entirely participate in this movement. It is true, it will be carried into the movement of general removal, but it will remain constantly parallel with itself, and only appears displaced in comparison with the surrounding objects, which obey more completely than itself the movement of the globe’s rotation round its poles. Thus can we demonstrate the movement of our planet. In virtue of the same principle, we see every day passing before our eyes a crowd of phenomena with which we are so familiar that they do not excite our attention. Thus it is because the hoop tends to remain in its plane of rotation that it rolls on without falling or deviating, and for the same reason that tops rotate vertically on their points, or when they are running down, describe a series of concentric circles; and for the same reason again, a juggler is able so easily to hold on the point of a stick a plate which he puts in rapid rotation, etc. It is also owing to this property of rotating bodies that we have been enabled to make use of cylindrical or conical projectiles in artillery. The coiled riflings of the cannon causing the projectiles to turn round very rapidly, their axis preserves an invariable direction during their whole course, until they finally strike the object at which they are aimed. Without this rotation they would pirouette in an irregular manner in the air, and besides any precision in firing being impossible, the resistance of the air would diminish their range to an enormous extent.