Mrs. B. An angle is not measured by the length of the lines, but by their opening, or the space between them.

Emily.

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

Mrs. B. Take a pair of compasses and draw a circle over these spaces, making the angular point the centre.

Emily. To what extent must I open the compasses?

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 compasses 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.

Mrs. B. Very well. To return now to your observation, that

57. Have the length of the lines which meet in a point, any thing to do with the measurement of an angle? 58. What use can we make of compasses in measuring an angle? 59. Into what number of parts do we suppose a whole circle divided, and what are these parts called? 60. When are two angles said to be equal? 61. Upon what does the dimension of an angle depend? 62. What number of degrees, and what portion of a circle is there in a right angle? 63. How must one line be situated on another to form two right angles? (fig. 1.) 64. Figure 2 represents an angle of more than 90 degrees, what is that called? 65. What are those of less than 90 degrees called as in fig. 3?

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 passage towards the cushion, the other its obliquity in its passage 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.

66. If you make an elastic ball strike a body at right angles, how will it return? 67. How if it strikes obliquely? 68. Explain by fig. 4 what is meant by the angles of incidence and of reflection.

CONVERSATION IV.

ON COMPOUND MOTION.

COMPOUND MOTION, THE RESULT OF TWO OPPOSITE FORCES.-OF CURVILINEAR MOTION, THE RESULT OF TWO FORCES.-CENTRE OF MOTION, THE POINT AT REST WHILE THE OTHER PARTS OF THE BODY MOVE ROUND IT.-CENTRE OF MAGNITUDE, THE MIDDLE OF A BODY.-CENTRIPETAL FORCE, THAT WHICH IMPELS A BODY TOWARDS A FIXED CENTRAL POINT.-CENTRIFUGAL FORCE, THAT WHICH IMPELS A BODY TO FLY FROM THE CENTRE.-FALL OF BODIES IN A PARABOLA.-CENTRE OF GRAVITY, THE POINT ABOUT WHICH THE PARTS BALANCE EACH OTHER.

MRS. B.

I MUST now explain to you the nature of compound motion. Let us suppose a body to be struck by two equal forces in opposite directions, how will it move?

Emily. If the forces are equal, and their directions are in exact opposition to each other, I suppose the body would not move at all.

Mrs. B. You are perfectly right; but suppose the forces instead of acting upon the body in direct opposition to each other, were to move in lines forming an angle of ninety degrees, as the lines YA, XA, (fig. 5. plate 2.) and were to strike the ball A, at the same instant; would it not move?

Emily. The force X alone, would send it towards B, and the force Y towards C; and since these forces are equal, I do not know how the body can obey one impulse rather than the other; and yet I think the ball would move, because as the two forces do not act in direct opposition, they cannot entirely destroy the effect of each other.

Mrs. B. Very true; the ball therefore will not follow the direction of either of the forces, but will move in a line between them, and will reach D in the same space of time, that the force X would have sent it to B, and the force Y would have sent it to C. Now if you draw two lines, one from B, parallel to A C, and the other from C, parallel to A B, they will meet in D, and

1. If a body be struck by two equal forces in opposite directions, what will be the result? 2. What is fig. 5. plate 2. intended to represent?