THE PROTRACTOR. 



47? 



Any line from the centre to the circumference is called a radius, and a line 

 through the centre to each side of the circumference is the diameter, or double 

 the radius. The circumference is three (3 '14) times the diameter. Any 

 portion, say k i I, is an arc, and the line, k /, is the chord of that arc. A line 

 like ;;/ n is a secant, and op is a tangent, or a line touching at one point only. 

 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 con- 

 tained 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 



Fig. 506. -Circle and angles. ft j n 



called a Protractor is used. 



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 



Fig. 507. The Protractor. 



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 



