tained 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 perpendicular 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 is called a right angle, and when one line is perpendicular to another, 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. S.)

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 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 the 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 II.) 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.

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.

CONVERSATION IV.

ON COMPOUND MOTION.

Compound Motion, the Result of two Opposite Forces. -Of Circular Motion, the Result of two Forces, one of which confines the Body to a Fixed Point.-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 confines a Body to 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 Centre of Weight, or 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 directions of the forces are in exact opposition to each other, I suppose the body would not move at all.

Mrs. B. You are perfectly right; but if the forces,

instead of acting on the body in opposition, strike it in two directions inclined to each other, at an angle of ninety degrees, if the ball A (fig 5, plate II.) be struck by equal forces at X and at Y, will it not move?

Emily. The force X 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 will therefore follow the direction of neither 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 from D, to join B and C, you will form a square, and the oblique line which the body describes is called the diagonal of the square.

Caroline. That is very clear, but supposing the two forces to be unequal, that the force X, for instance, be twice as great as the force Y?

Mrs. B. Then the force X would drive the ball twice as far as the force Y, consequently you must draw the line A B (fig. 6.), twice as long as the line A C, the body will in this case move to D; and if you draw lines from that point to B and C, you will find that the ball has moved in the diagonal of a rectangle.

Emily. Allow me to put another case? Suppose the two forces are unequal, but do not act on the ball in the direction of a right angle, but in that of an acute angle, what will result ?

Mrs. B. Prolong the lines in the directions of the two forces, and you will soon discover which way the ball will be impelled; it will move from A to D, in the diagonal of a parallelogram, (fig. 7.) Forces acting in the direction of lines forming an obtuse angle, will also produce motion in the diagonal of a parallelogram. For instance, if the body set out from B, instead of A, and was impelled by the forces X and Y, it would move in the dotted diagonal B C.

We may now proceed to circular motion: this is the result of two forces on a body, by one of which it is projected forward in a right line, whilst by the other it is confined to a fixed point. For instance, when I whirl this ball, which is fastened to my hand with a string, the ball moves in a circular direction; because it is acted on by two forces, that which I give it which represents the force of projection, and that of the string which confines it to my hand. If during its motion you were suddenly to cut the string, the ball would fly off in a straight line; being released from confinement to the fixed point, it would be acted on but by one force, and motion produced by one force, you know, is always in a right line.

Caroline. This is a little more difficult to comprehend than compound motion in straight lines.

Mrs. B. You have seen a mop trundled, and have observed, that the threads which compose the head of the mop fly from the centre; but being confined to it at one end, they cannot part from it; whilst the water they contain, being unconfined, is thrown off in straight lines.