31. What fraction of the year is contained in the months of July and August, 1896?

32. The greatest depth of the Atlantic telegraph cable is 2 mi. 250 rd. 5 yd. 1 ft. How many feet is it?

33. How many statute miles in 45° 22′ 30′′, measured on the equator?

34. On an average when walking, Isaac steps 24 inches twice every second. How many minutes will it take him

to walk 11⁄2 miles?

35. Reduce of an acre to square rods and decimals of a square rod.

36. A silversmith in making spoons uses 2 lb. 3 oz. 19 pwt. of silver in one day, 3 lb. 18 pwt. 20 grs. on the second day, and 11 oz. 19 pwt. 23 gr. on the third day. How much silver does he use altogether?

37. What decimal of a pound Troy are 4 oz. 14 pwt.?

38. Reduce 18 pwt. 164 gr. to the fraction of a pound. 39. Find the difference between lb. and 4 lb. 7.84 oz. Troy.

40. Find the cost of 2 doz. spoons, each weighing 9 oz. 8.76 pwt., at $.045 a pennyweight.

41. What decimal part of a grain is 7240 of a pound?

42. What part of an acre is 3 rd. ?

43. Multiply 16 bu. 9 pk. 8 qt. by 3.

44. What is the product of 20 bu. 9 oz. 11 pwt. 15. gr. multiplied by ?

MEASUREMENTS.

162. An Angle is the difference in direction of two lines.

163. A Right Angle is the angle of a square.

164. Anything that has length and breadth, but not thickness, is a Surface.

165. A surface that does not change its direction is a Plane Surface.

166. A figure having four straight sides and four right angles is a Rectangle.

167. A Square is a rectangle having equal sides.

A Rectangle.

An Angle.

A Right Angle.

168. A Square Foot is a square 1 foot long and 1 foot wide.

169. A Square Yard is a square 1 yd. long and 1 yd. wide.

170. The Area of a surface is the number of square units that it contains.

and the unit of the product must be the same as the unit of the multiplicand.

171. The length and breadth of a rectangle are called its Dimensions.

172. A figure having three straight sides and three angles is a Triangle.

The Base of a triangle is the line upon which it stands, and the Altitude is its height above the base, or the base extended. Thus, AC is the base, and BD the altitude, of the triangle shown below.

173. It is evident from the accompanying figure that the area of a triangle is equal to one-half the area of a rectangle of the same base and altitude.

Every circle may be regarded as composed of many equal triangles, the radius of the circle forming the altitudes, and the circumference forming the sum of the bases. Therefore, the area of a circle is equal to the prod uct of the circumference and radius.

PRINCIPLE. The circumference of a circle is 3.1416 times the diameter, or about 34.

Find the diameters having the following circumferences: NOTE. - Indicate only.

27. 78 ft. 28. 19 ft. 29. 316.14 rd. 30. 189.68 ch.

Written.

Find areas.

31. Circumference 37.6992 ft., radius 6 ft.

32. Circumference 47.124 ft., diameter 15 ft.

33. Circumference 62.832 ft., diameter 20 ft. 34. Circumference 94.248 ft., diameter 30 ft.

41. How many square yards are there in a floor 24 ft. long and 15 ft. wide?

42. The base of a triangle is 20 ft. and the altitude 18 ft. What is the area?

43. The circumference of a circle is 31.416 ft. and its radius is 5 ft. What is its area?

44. When the diameter of a circle is 50 ft., what is the circumference?

45. When the radius is 6 ft., what is the circumference? 46. When the circumference is 78.54 ft., what is the radius?

47. Mr. Clark's farm is 35 ch. long and 25 ch. wide. How many acres does it contain?

48. A certain field is 70 rd. long and 65 rd. wide. How many acres are there in the field?

49. A piece of land is 65 rods wide. How long must it be to contain 567 acres?

50. How many sods 10 inches square will be required to turf a lawn 100 ft. long and 50 ft. 6 in. wide?

51. A building lot measures 60 feet in front. What must be its depth to contain of an acre?

52. How many tiles, each 8 inches square, will be required for the floor of a room 24 ft. by 30 ft.?

53. How many shingles will be required for a roof 45 ft. long, and each of its two sides 20 ft. wide, allowing 8 shingles to the square foot ?