_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. [Illustration: 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.