_Mrs. B._ You will not in general find this rule hold good; for liquids have scarcely any elasticity, whilst hard bodies are eminent for this property, though the latter are certainly of much greater density than the former; elasticity implies, therefore, not only a susceptibility of compression, but depends upon the power possessed by the body, of resuming its former state after compression, in consequence of the peculiar arrangement of its particles.

_Caroline._ But surely there can be no pores in ivory and metals, Mrs.

B.; how then can they be susceptible of compression?

_Mrs. B._ The pores of such bodies are invisible to the naked eye, but you must not thence conclude that they have none; it is, on the contrary, well ascertained that gold, one of the most dense of all bodies, is extremely porous; and that these pores are sufficiently large to admit water when strongly compressed, to pa.s.s through them. This was shown by a celebrated experiment made many years ago at Florence.

_Emily._ If water can pa.s.s through gold, there must certainly be pores or interstices which afford it a pa.s.sage; and if gold is so porous, what must other bodies be, which are so much less dense than gold!

_Mrs. B._ The chief difference in this respect, is I believe, that the pores in some bodies are larger than in others; in cork, sponge and bread, they form considerable cavities; in wood and stone, when not polished, they are generally perceptible to the naked eye; whilst in ivory, metals, and all varnished and polished bodies, they cannot be discerned. To give you an idea of the extreme porosity of bodies, sir Isaac Newton conjectured that if the earth were so compressed as to be absolutely without pores, its dimensions might possibly not be more than a cubic inch.

_Caroline._ What an idea! Were we not indebted to sir Isaac Newton for the theory of attraction, I should be tempted to laugh at him for such a supposition. What insignificant little creatures we should be!

_Mrs. B._ If our consequence arose from the size of our bodies, we should indeed be but pigmies, but remember that the mind of Newton was not circ.u.mscribed by the dimensions of its envelope.

_Emily._ It is, however, fortunate that heat keeps the pores of matter open and distended, and prevents the attraction of cohesion from squeezing us into a nut-sh.e.l.l.

_Mrs. B._ Let us now return to the subject of reaction, on which we have some further observations to make. It is because reaction is in its direction opposite to action, that _reflected motion_ is produced. If you throw a ball against the wall, it rebounds; this return of the ball is owing to the reaction of the wall against which it struck, and is called _reflected motion_.

_Emily._ And I now understand why b.a.l.l.s filled with air rebound better than those stuffed with bran or wool; air being most susceptible of compression and most elastic, the reaction is more complete.

_Caroline._ I have observed that when I throw a ball straight against the wall, it returns straight to my hand; but if I throw it obliquely upwards, it rebounds still higher, and I catch it when it falls.

_Mrs. B._ You should not say straight, but perpendicularly against the wall; for straight is a general term for lines in all directions which are neither curved nor bent, and is therefore equally applicable to oblique or perpendicular lines.

_Caroline._ I thought that perpendicularly meant either directly upwards or downwards?

_Mrs. B._ In those directions lines are perpendicular to the earth. A perpendicular line has always a reference to something towards which it is perpendicular; that is to say, that it inclines neither to the one side or the other, but makes an equal angle on every side. Do you understand what an angle is?

_Caroline._ Yes, I believe so: it is the s.p.a.ce contained between two lines meeting in a point.

_Mrs. B._ Well then, let the line A B (plate 2. fig. 1.) represent the floor of the room, and the line C D that in which you throw a ball against it; the line C D, you will observe, forms two angles with the line A B, and those two angles are equal.

_Emily._ How can the angles be equal, while the lines which compose them are of unequal length?

_Mrs. B._ An angle is not measured by the length of the lines, but by their opening, or the s.p.a.ce between them.

_Emily._ Yet the longer the lines are, the greater is the opening between them.

_Mrs. B._ Take a pair of compa.s.ses and draw a circle over these s.p.a.ces, making the angular point the centre.

_Emily._ To what extent must I open the compa.s.ses?

_Mrs. B._ You may draw the circle what size you please, provided that it cuts the lines of the angles we are to measure. All circles, of whatever dimensions, are supposed to be divided into 360 equal parts, called degrees; the opening of an angle, being therefore a portion of a circle, must contain a certain number of degrees: the larger the angle the greater is the number of degrees, and two angles are said to be equal, when they contain an equal number of degrees.

_Emily._ Now I understand it. As the dimension of an angle depends upon the number of degrees contained between its lines, it is the opening, and not the length of its lines, which determines the size of the angle.

_Mrs. B._ Very well: now that you have a clear idea of the dimensions of angles, can you tell me how many degrees are contained in the two angles formed by one line falling perpendicularly on another, as in the figure I have just drawn?

_Emily._ You must allow me to put one foot of the compa.s.ses at the point of the angles, and draw a circle round them, and then I think I shall be able to answer your question: the two angles are together just equal to half a circle, they contain therefore 90 degrees each; 90 degrees being a quarter of 360.

_Mrs. B._ An angle of 90 degrees or one-fourth of a circle is called a right angle, and when one line is perpendicular to another, and distant from its ends, it forms, you see, (fig. 1.) a right angle on either side. Angles containing more than 90 degrees are called obtuse angles, (fig. 2.) and those containing less than 90 degrees are called acute angles, (fig. 3.)

_Caroline._ The angles of this square table are right angles, but those of the octagon table are obtuse angles; and the angles of sharp pointed instruments are acute angles.

[Ill.u.s.tration: PLATE II.]

_Mrs. B._ Very well. To return now to your observation, that if a ball is thrown obliquely against the wall, it will not rebound in the same direction; tell me, have you ever played at billiards?

_Caroline._ Yes, frequently; and I have observed that when I push the ball perpendicularly against the cushion, it returns in the same direction; but when I send it obliquely to the cushion, it rebounds obliquely, but on an opposite side; the ball in this latter case describes an angle, the point of which is at the cushion. I have observed too, that the more obliquely the ball is struck against the cushion, the more obliquely it rebounds on the opposite side, so that a billiard player can calculate with great accuracy in what direction it will return.

_Mrs. B._ Very well. This figure (fig. 4. plate 2.) represents a billiard table; now if you draw a line A B from the point where the ball A strikes perpendicular to the cushion, you will find that it will divide the angle which the ball describes into two parts, or two angles; the one will show the obliquity of the direction of the ball in its pa.s.sage towards the cushion, the other its obliquity in its pa.s.sage back from the cushion. The first is called _the angle of incidence_, the other _the angle of reflection_; and these angles are always equal, if the bodies are perfectly elastic.

_Caroline._ This then is the reason why, when I throw a ball obliquely against the wall, it rebounds in an opposite oblique direction, forming equal angles of incidence and of reflection.

_Mrs. B._ Certainly; and you will find that the more obliquely you throw the ball, the more obliquely it will rebound.

We must now conclude; but I shall have some further observations to make upon the laws of motion, at our next meeting.

Questions

1. (Pg. 32) On what is the science of mechanics founded?

2. (Pg. 32) In what does motion consist?

3. (Pg. 33) What is the consequence of inertia, on a body at rest?

4. (Pg. 33) What do we call that which produces motion?

5. (Pg. 33) Give some examples.

6. (Pg. 33) What may we say of gravity, of cohesion, and of heat, as forces?

7. (Pg. 33) How will a body move, if acted on by a single force?

8. (Pg. 33) What is the reason of this?

9. (Pg. 33) What do we intend by the term velocity, and to what is it proportional?

10. (Pg. 33) Velocity is divided into absolute and relative; what is meant by absolute velocity?

11. (Pg. 33) How is relative velocity distinguished?

12. (Pg. 34) How do we measure the velocity of a body?

13. (Pg. 34) The time?

14. (Pg. 34) The s.p.a.ce?