“Certainly; that has, doubtless, its influence: but the resistance of the air is also a powerful force upon this occasion. A top has been made to spin in vacuo as long as two hours and sixteen minutes.[24] But come, Tom, spin your top once more. Observe,” exclaimed Mr. Seymour, “how obliquely the top is spinning. It is now gradually rising out of an oblique position;--now it is steadily spinning on a vertical axis;--and now its motion is so steady, that it scarcely seems to move.” “It is _sleeping_, as we call it,” said Tom. “Its centre of gravity is now situated perpendicularly over its point of support, which is the extremity of the axis of rotation: but attend to me,” continued Mr. Seymour, “for I am about to attempt the explanation of a phenomenon which has puzzled many older and wiser philosophers than yourselves. It is evident that the top, in rising from an oblique to a vertical position, must have its centre of gravity raised; what can have been the force which effected this change?” “Was it the centrifugal force?” asked Tom. “Certainly not,” said Mr. Seymour, “as I will presently convince you.” “Then it must have been the resistance of the air,” said Louisa. “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.” [Illustration: A toy top, diagonal to a surface.] “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