Fig. 506.—Circle and angles.
We may now resume our consideration of the angles by means of the circle. Let us recur to our previous figure of the right angles, around which we will describe a circle. We see that the portion of the circumference contained between the sides of the right angle is exactly one-fourth of the whole. This is termed a quadrant, and is divided into 90°—the fourth of 360 equal parts or degrees into which the whole circumference is divided. The angle of 45° so often quoted as an angle of inclination is half a right angle. To measure angles an instrument called a Protractor is used.
Fig. 507.—The Protractor.
The Protractor, as will be seen from the accompanying illustration (fig. 507), is a semi-circle containing 180°. The lower portion is a diagonal scale, the use of which will be explained presently. The Protractor measures any actual angle with accuracy. If we put the vertical point of the angle and the centre point of the circle together, we can arrive at the dimensions of the angle by producing the lines containing it to the circumference. An angle instrument, figured herewith, may be assumed as the basis of most apparatus for measuring angles. An index hand, R R, moves round a dial like the hand of a clock, and the instrument is used by gazing first at one of the two objects, between which the angle we wish to determine is made—like the church steeples (fig. 508) for instance. The centre of the instrument is placed upon the spot where lines, if drawn from the eye to each of the objects, would intersect. The index hand is then put at 0°, and in a line between the observer and the object, A. Then the index is moved into a similar position towards B, and when in line with it the numbers of degrees passed over (in this imaginary case 20), shows the magnitude of the angle.
Fig. 508.—Determination of distance.
Fig. 509.—Measuring angles.