If the radius is three inches, how long is the diameter? [Illustration: Diagram 25.] LESSON THIRTY-FOURTH. ARCS AND DEGREES. What small part of the circumference of circle 1 (DIAGRAM 25.) is marked? It is called an “_arc_.” _An arc is any part of a circumference._ Read five arcs that are marked. Which is longer, the arc _e d_, or the arc _e f_? _b d_, or _b d e_? _a b d_, or _a b d e_? Name an arc which is half of the circumference. It is called a “_semi-circumference_.” “Semi” means “half.” _A semi-circumference is half of a circumference._ Read three arcs, each of which is one-fourth of the circumference. If the whole circumference were divided into three hundred and sixty equal arcs, would each arc be large or small? Each of these arcs would be called a “_degree_.” [Degrees are marked (°).] _A degree of a circumference is a three hundred and sixtieth part of it._ How many degrees in a semi-circumference? How many degrees in one-fourth of a circumference? If a fourth of a circumference were divided into three equal parts, how many degrees would there be in each part? Into how many parts would each third of a quarter have to be again divided to make single degrees? Is an arc of ninety-one degrees greater or less than one-fourth of a circumference? Is an arc of a hundred and seventy-nine degrees greater or less than a semi-circumference? Can there be more than three hundred and sixty degrees in a circumference? If the circumference of circle 1 were divided into degrees, each degree would be so small an arc that it would look like a dot. If a degree were divided into sixty equal parts, each part would be called a minute. If a minute were divided into sixty equal parts, each part would be called a second. How many degrees in the large circle of Fig. 2? How many in the smaller one? Has a large circle any more degrees than a small circle? In the large circle how many degrees from _a_ to _b_? In the small circle how many from _a_ to _b_? Which is greater, an arc of ninety degrees of the large circle, or one of ninety degrees of the small one? Which is greater, an arc of a degree of the large circle, or one of a degree of the small one? The angle _a o b_ has its vertex at what part of the larger circle? At what part of the smaller circle? On how many degrees of the larger circle does the angle stand? On how many degrees of the smaller circle does it stand? Then it is said to be an angle of 90°. If the angle _a o f_ is an angle of 30°, how many degrees must there be in the arc _a f_? If the arc _f e_ is an arc of 60°, what is the size of the angle _f o e_? An angle of 10° stands upon an arc of how many degrees? Of 8°? Of 1°? The angle _a o b_ is what kind of an angle? Upon how many degrees does it stand?