SURVEYORS' CHAIN.

162. Surveyors use, in measuring distances, a chain 4 rds. long and containing 100 links.

The links can be written as decimals of a chain.

Ex. 107. (Oral.)

1. How many chains make a mile?

2. In 10 mi. how many chains?

3. How many rods in 9 chains?

4. How many yards in 1 chain? how many feet?

5. How many chains in 48 rods?

6. In 0.75 of a mile how many chains?

7. How many chains in of a mile?

8. If a square field measures 1 chain on a side, how many square rods does it contain? How many square rods then in a square chain?

9. If a square chain contains 16 sq. rds., how many square chains make an acre?

10. What part of an acre are 4 sq. chains? 5 sq. chains? 8 sq. chains?

11. What part of a chain are 50 links? 25 links? 20 links? 12. How many square rods in a square garden-plot measuring 75 links on a side?

13. How many inches long is a link?

14. The distance between two places is found to be 320 chains. Express the distance in miles.

Ex. 108.

1. Reduce 38 chains 80 links to the decimal of a mile.

2. The four sides of a field are 23 chains 19 links, 17 chains 34 links, 6 chains 85 links, and 24 chains 62 links. How many yards around the field?

3. One field contains 3 sq. chains, and another is 3 chains square. How many acres in both fields together?

4. A field is crossed by a driveway 15 links wide, and 13 chains 43 links long. How many square rods in the driveway?

5. From a field of 4 A. a rectangular piece 3 chains 25 links long and 2 chains 75 links wide is reserved. How much of the field is left?

6. The sides of a triangular field measure 21 chains, 14 chains 11 links, and 8 chains 10 links respectively. By how many yards is the longest side less than the sum of the other two?

BOARD MEASURE.

163. Boards one inch or less in thickness are sold by the square foot.

Boards more than one inch in thickness, and all squared lumber, are sold by the number of square feet of boards one inch in thickness to which they are equivalent.

Thus, a board 16 ft. long, 1 ft. wide, and 1 in. thick, contains 16 ft. board measure. If only 3, 3, or of an inch thick, it still contains 16 ft.; but, if 14 in. thick, it contains 20 ft. board measure.

Ex. 109.

How many feet board measure in

1. A board 18 ft. long, 6 in. wide,

:

in. thick?

2. A board 16 ft. long, 12 in. wide, 1 in. thick?

3. Forty boards 14 ft. long, 10 in. wide,

in. thick? 4. A stick of square timber 8 in. by 9 in., and 30 ft. long? 5. Six joists, each 3 in. by 4 in., and 11 ft. long?

6. Ten joists, each 6 in. by 4 in., and 14 ft. long?

7. A stick of square timber 10 in. by 12 in., and 36 ft. long?

8. Ten 2-in. planks, each 13 ft. long, 15 in. wide?

9. Thirty 3-in. planks, each 12 ft. long, 10 in. wide? 10. A board 24 ft. long, 23 in. wide at one end, and 17 in. at the other, and 1 in. thick?

11. In a stick of timber 40 ft. long and 15 in. square? 12. Ten 4-in. planks 16 ft. long and 10 in. wide?

MEASURES OF VOLUME.

164. A rectangular solid is a solid bounded by six rectangles.

165. If the rectangles are all squares, the solid is called a cube.

166. In the figure represented in the margin, let the length contain 5, the breadth 3, and the height 7 in.

The base may be divided into square inches; there will be three rows of 5 sq. in. each; in all 15 sq. in.

inch may be placed a

Upon each square

pile of 7 cu. in., so

that the solid will contain 15 x 7 cu. in.;

that is, 3 x 5 x 7 cu. in.

Hence, to find the volume of a rectangular solid,

Express its length, breadth, and height in the same linear unit; the product of these numbers will express its volume in cubic units of the same name as the linear unit.

UNITS OF VOLUME.

167. 1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.).

1 cubic yard (cu. yd.).

The units of volume are cubes of the linear units. Thus, 1728-123, 27 = 33.

168. In measuring wood, a pile 8 ft. long, 4 ft. wide, and 4 ft. high, is called a cord.

Hence,

1 cord foot (cd. ft.) = 16 cu. ft.

8 cord feet

=

= 1 cord (cd.).

Ex. 110.

(Oral.)

1. A brick is 2 by 4 by 8 in.

Find its volume.

2. How many cubic feet in 2 cu. yds.?

3. How many cubic yards in 81 cu. ft.?

4. Twelve cubic feet are what part of a cubic yard? 5. How many cords in 40 cd. ft.? in 16 cd. ft.

6. How many cords in a pile of wood 32 ft. long, 4 ft. wide, and 4 ft. high?

7. How many loads of earth, each 1 cu. yd., must be removed in digging a ditch 21 ft. long, 3 ft. wide, and 3 ft. deep?

8. How many cubic feet in a stick of timber 12 in. wide, 9 in. thick, and 24 ft. long?

9. How many feet board measure in a cubic foot?

10. How many cubic feet in a stick of timber 16 in. wide, 9 in. thick, and 21 ft. long?

Ex. 111.

1. Reduce 15 cu. yds. 13 cu. ft. to cubic inches.

2. Reduce 150,000 cu. in. to cubic yards.

3. Subtract 28 cu. yds. 25 cu. ft. 1500 cu. in. from 47 cu. yds. 13 cu. ft. 1236 cu. in.

4. Multiply 17 cu. yds. 17 cu. ft. 187 cu. in. by 11.

5. Divide 22 cu. yds. 10 cu. ft. 933 cu. in. by 7.

6. How many cubic inches can be cut out of a cubic foot?

7. How many cubic feet of water will a cistern hold whose three dimensions are each 4 ft.?