NEXT day, when Mr. Seymour found Tom and his brother

playing at marbles on a smooth piece of ground, he asked Tom to explain why a marble always turns round as it moves along.

"I suppose," said Tom, "it depends upon the motion which I give it by my finger and thumb as it leaves my hand."

"You can doubtless thus impart a spinning motion to your marble; but I fancy you would be quite unable, if you tried ever so much, to make the marble proceed along the ground without revolving."

"I have sometimes, indeed, tried to do that," said Tom, "but I found that even when the marble was pushed along with a flat piece of wood, it would roll."

"Then it is clear that the rotation in other cases is not due to the action of your fingers in projecting the marble. I think a little consideration will show you that if the marble is projected without a rotatory motion, it must acquire one the moment it touches the ground. For the contact of the lowest part of the marble with the ground will check its velocity, while the upper part, not impeded in this way, will be urged forward at its original velocity in obedience to the first law of motion. The result will be that a rolling motion will be set up."

"But do you remember that I told you a few days ago," said Mr. Seymour, "that by giving a revolving body a peculiar spinning motion, certain effects were produced, which I should, on some future occasion, take into consideration?"

"To be sure I do,” replied Tom.

"Well, then, attend to re."

Mr. Seymour took a marble, and placing it on the ground, gave it an impulse forward by pressing his forefinger upon it: the marble darted forward a few paces, after which it rolled back again.

"That is most extraordinary!" cried Tom. "The marble came back to your hand of its own accord, as it were, without having met with any obstacle."

66 And you, no doubt,” said Mr. Seymour, "regard it as contrary to the well-known law that a body once put in motion, in any direction, will continue to move in that direction until some foreign cause oppose it."

66

It really would appear so."

"It is, however, far otherwise: the force which I imparted to the marble gave it two kinds of motion; the one projecting it forward, the other producing a rotatory motion round its axis in a direction opposite to that which it would usually assume by friction against the ground, and in the same direction in which a marble rolling towards me would rotate: the consequence was that when the forward motion on account of the friction of the marble on the ground was destroyed, the rotatory motion continued, and by thus establishing an action in an opposite direction, caused the marble to retrograde. If, however, you will fetch Rosa's hoop, I will demonstrate the fact on a larger scale.” Tom accordingly produced the hoop; and Mr. Seymour projected it forward, giving to it at the same instant a spinning motion in an opposite direction. The hoop proceeded forward

to a certain distance, when it stopped, and then ran back to the hand.

"I have a new toy for you," said Tom's father, "and one which will not only exercise your skill, but will serve to illustrate for us certain remarkable effects produced by rotation."

Mr. Seymour led the way to a part of the grounds where there was an open space of some extent, and then produced a sling. This toy consists, as most readers are doubtless aware, simply of an oblong or rather lozenge-shaped piece of leather, to each end of which a strong cord is attached. The sling is used by placing a stone in the piece of leather, passing one of the fingers through a loop formed in one of the ends, and then holding both cords between the forefinger and thumb so that they are of equal length; the stone is whirled very rapidly round, and when the cord is let go, the stone flies off with amazing velocity.

This feat Mr. Seymour then exhibited to the juvenile party, Louisa and her sisters having joined the others, and they were greatly astonished at the distance to which a stone could thus be hurled.

The children now proceeded to amuse themselves with the sling. Louisa challenged Tom to a trial of skill. She fancied that she could hurl a stone with greater accuracy than her brother; but after several contests she acknowledged herself vanquished, for Tom had succeeded in striking the trunk of a tree at a considerable distance, while his sister was never able to throw the stone within several yards of the mark.

"Well done, Tom!" exclaimed Mr. Seymour; "why, you will soon equal in skill the ancient natives of the Balearic Islands!"

"And were they famous for this art?" asked Louisa.

"With such dexterity," replied her father, "did they use the sling, that we are told their young children were not allowed any food by their mothers except that which they could fling down from the beam where it was placed aloft. I fancy, however, Tom, that you would become very hungry before you could strike an object in yonder poplar."

66

At all events, I will try," said Tom.

He accordingly whirled round his sling and discharged its stone, which flew forward with great velocity, but in a direction very wide from the mark at which it was aimed. In the next moment a violent hallooing was heard: it was from the vicar,

who had narrowly escaped being struck by the falling stone, as he was making his way through the grounds.

"My dear Mr. Goodenough," cried Tom, running towards the vicar, as the latter emerged from the shrubs which had hitherto concealed his approach, "I sincerely hope you have not been struck?"

The

"Oh, no; I have fortunately escaped without hurt. But what new game is this which is now engaging your attention? sling, I see. It seems, then, that I have been in great danger of meeting the fate of the giant of Gath.”

Mr. Seymour said he was about to explain the scientific principle of the sling, and he suggested that the vicar might be able to afford them some information as to its history.

"The art of slinging," replied the vicar, "is of the highest antiquity, and the most amazing skill appears to have been attained by Asiatic nations in the use of the sling as a weapon. It was well known and practised in Europe at a very early period, and our Saxon ancestors appear to have been very expert in hurling such missiles. But pray, Mr. Seymour, proceed with your scientific explanation."

"What we have just seen," Mr. Seymour began, "is simply a result of those laws of motion with which you are already acqainted. The effects here are, however, sufficiently remarkable and interesting to make it worth our while to examine them in detail."

"Are there not certain special forces at work?" asked Louisa, with some surprise. "I am sure I have read that circular motion is always the result of two forces, called the centrifugal and the centripetal."

"Your ideas, my dear," replied her father, "as to the existence of some special and peculiar forces concerned in causing a body to rotate about a centre, are the result of the error into which the readers, and sometimes also the writers, of popular scientific treatises are apt to fall. I allude to that very common error of supposing that for every term which custom or convenience has introduced, there is some corresponding and distinct thing existing in nature. The seeming tendency of a body revolving in a circle, as the stone is forced to do in the sling, is only an instance of the operation of the first law of motion; and since, when the stone is twirled round, it is constantly changing its direction instead of proceeding in a straight line, there must

CONSTRAINED MOTION.

247

be some impressed force at work. Now, let us consider what is it that prevents the stone from obeying the first law."

"The leather hinders the stone from flying away," cried Tom, "and the pressure on the leather causes a pull on the string, which is tightly stretched in consequence."

"Yes," said Mr. Seymour, "it is the tension of the cords which retains the stone in its circular path, and that tension is itself equal, by the law of equality of action and reaction, to the resultant force tending to withdraw the stone directly from the centre of rotation. But observe that when the stone is liberated, it does not fly away in the direction of the prolonged radius of the circle, but in the same direction on which it is moving at the moment of its liberation, namely, along a tangent to the circle."

66

Pray what is meant by a tangent?" asked Louisa.

"A tangent, my dear girl, is a straight line drawn so as just to touch the circumference of a circle without cutting it even if prolonged. The tendency of the revolving stone in our sling to obey the first law has been sometimes described as producing a tangential force; but what we have chiefly to study in these cases of bodies constrained to move round a centre, is the resultant of this tangential force, which must be opposed by an equal force drawing the body to the centre of rotation. Since the body would, if no impressed force acted upon it, move along the tangent, and would by so doing withdraw itself from the centre round which it revolves, there must be a portion of this force resolved in the radial direction; and it is this to which the name of centrifugal force has been given, and which is that opposed by the tension of the cords in the case of the sling. But, now, here is another example of a body constrained to move in a circle. I lay this wooden hoop flat on the ground, and taking Rosa's ball, I cause the ball to go round and round the inside of the hoop. You see there is here no connection whatever between the body and the centre of the circle in which it is revolving; yet it is convenient to employ the terms centrifugal and centripetal to express briefly the results of the operations of the laws of motion in this case. Thus, for instance, while the ball is running briskly round the inside of the hoop, I suddenly raise the latter-away goes the ball in quite a straight line, which is a tangent to the hoop at the precise point at which the ball escaped. Now, this tendency of the ball to escape must have