“No; nor was it the resistance of the air,” replied her father: “for the same effect takes place in vacuo.”
“Then pray inform us, by what means the top was raised.”
“It entirely depended upon the form of the extremity of the peg, and not upon any simple effect connected with the rotatory or centrifugal force of the top. I will first satisfy you that, were the peg to terminate in a fine, that is to say, in a mathematical point, the top never could raise itself. Let A B C be a top spinning in an oblique position, having the end of the peg, on which it spins, brought to a fine point. It will continue to spin in the direction in which it reaches the ground, without the least tendency to rise into a more vertical position; and it is by its rotatory or centrifugal force that it is kept in this original position: for if we conceive the top divided into two equal parts A and B, by a plane passing through the line X C, and suppose that at any moment during its spinning, the connection between these two parts were suddenly dissolved, then would any point in the part A fly off with the given force in the direction of the tangent, and any corresponding point in the part B with an equal force in an opposite direction; whilst, therefore, these two parts remain connected together, during the spinning of the top, these two equal and opposite forces A and B will balance each other, and the top will continue to spin on its original axis. Having thus shown that the rotatory or centrifugal force can never make the top rise from an oblique to a vertical position, I shall proceed to explain the true cause of this change, and I trust you will be satisfied that it depends upon the bluntness of the point.
Let A B C be a top spinning in an oblique position, terminating in a very short point with a hemispherical shoulder P a M. It is evident that, in this case, the top will not spin upon a the end of the true axis X a, but upon P, a point in the circle P M, to which the floor I F is a tangent. Instead, therefore, of revolving upon a fixed and stationary point, the top will roll round upon the small circle P M on its blunt point, with very considerable friction, the force of which may be represented by a line O P at right angles to the floor I F, and to the spherical end of the peg of the top: now it is the action of this force, by its pressure on one side of the blunt point of the top, which causes it to rise in a vertical direction. Produce the line O P till it meets the axis C; from the point C draw the line C t perpendicular to the axis a X, and T O parallel to it; and then, by a resolution of forces, the line T C will represent that part of the friction which presses at right angles to the axis, so as gradually to raise it in a vertical position; in which operation the circle P M gradually diminishes by the approach of the point P to a, as the axis becomes more perpendicular, and vanishes when the point P coincides with the point a, that is to say, when the top has arrived at its vertical position, where it will continue to sleep, without much friction, or any other disturbing force, until its rotatory motion fails, and its side is brought to the earth by the force of gravity.”
“I think I understand it,” said Tom, “although I have some doubt about it; but if you would be so kind as to give me the demonstration in writing, I will diligently study it.”
“Most readily,” said Mr. Seymour. “Indeed I cannot expect that you should comprehend so difficult a subject, without the most patient investigation; and, in the present state of your knowledge, I am compelled to omit the relation of several very important circumstances, to which I may, hereafter, direct your attention. When, for instance, you have become acquainted with the elements of astronomy, I shall be able to show you that the gyration of the top depends upon the same principles as the precession of the equinoxes.”[(22)]
