perpendicular to the axis; but, as they are all equal, and as they pass all round with rapidity by the rotation, the result must be that the top is in equilibrio on its point of support, or on the extremity of the axis on which it turns. But see, your top is down."

"And what is the reason," asked Tom, "of its motion being stopped?"

"I can answer that question, papa," said Louisa ; " is it not owing to the friction of the ground?"

"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.* 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?"

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"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."

Short on 'Serson's Horizontal Top,' Phil. Trans. xlvii. 352.

"Still humming on, their drowsy course they keep,

And lash'd so long like tops, are lash'd to sleep."

-POPE

Plain matter-of-fact persons, like you and the author, gentle reader, will be content to regard the term, "sleeping," as simply expressive of that quiescent state which the top thus assumes. Not 80, however; Mr Prybabel, while smiling at our simplicity, informs us that the phrase is derived from the Italian word topo, a mouse, from which the Italian proverb, "Il dormo comme un topo,"-He sleeps like a dormouse-has been corruptly translated into, "He sleeps like a top."

Many similar instances of verbal corruption might be given. We will adduce one which may be interesting to our juvenile readers, as it will explain the true meaning of the glass-slipper of Cinderella. "Vair," the skin of the gray squirrel, (Peltis gris,) was the fur held next in estimation to ermine, in the fourteenth century. It was so called from its variety of colour, the back of the squirrel being gray, the underneath part of its body white. Cinderella's slipper was of this fur, a "Pantouffle de vair," which being wrongly written verre," gave rise to the rendering of a glass slipper. (Arts of the Middle Ages, by M. Jul. Labarte.)

"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, ▲ and B, by a plane passing through the

line x c, and suppose that at any moment during its spinning the connexion 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 в 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

F

position, terminating in a very short point with a hemispherical shoulder, Pa 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

Op 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 r 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 м 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, 66 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." (26.)

MR SEYMOUR, having observed his children busily engaged at the game of Trap and Ball, determined, as usual, to make it subservient to scientific instruction. With this view he hastily sketched a diagram, and proceeded with it to the scene of sport.

"Now, Tom, let me see how far you have profited by our late conversation. I have some questions to ask you about the action of your Trap and Ball," said his father.

"I do not suppose there is much philosophy in the game," observed Tom.

"Of that we shall judge presently. Can you tell me the direction which the ball takes after it flies from the spoon of the trap, in consequence of the blow of the bat upon the trigger ?"

"It flies upwards, to be sure, and allows me to strike it with my bat," answered the boy.

"Very true; but at what angle? I see you hesitate; look, there

fore, at the diagram I have prepared, and attend to my explanation of it."

Mr Seymour produced the sketch which we here present to our readers.

A B represent the spoon and trigger in their quiescent position. Upon striking the end в with the bat, they are brought into the position C D. The spoon will thus have described the small arc a C, when it will be suddenly stopped by the end of the trigger D coming into contact with the shoe. The motion of the ball, however, will not be arrested, and it will consequently be projected forward out of the spoon."

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Exactly," exclaimed Louisa, " in the same manner as the shilling flew off the wine-glass, or a person on a galloping horse would be thrown over the head by its suddenly stopping."

"I thank you, Louisa; your memory, I perceive, has not suffered from the drenching you received from the water-cart; but can you tell me," continued Mr Seymour, "the direction which the ball will take after its release from the spoon?"

This was a step beyond Louisa's knowledge, and her father, in order to assist her, begged her to consider in what direction it was moving before it left the spoon.

"You have just told us," said Tom, "that it described an arc, or portion of a circle.”

"Very well," said Mr Seymour; "and did not the philosophy of your sling teach you that, when a body revolving in a circle is suddenly disengaged, it will fly off in a right line in the direction in which it was moving at the instant of its release ?—the ball, therefore, will dedescribe the tangent c E.

"It is all clear enough to me now," said Tom, evidently vexed

* See page 50.