EXAMPLES.

1. In 10 A. 65 sq. rd. 16 sq. yd. 4 sq. ft. 136 sq. in. how many square inches are there?

OPERATION.

10 A. 65 sq. rd. 16 sq. yd. 4 sq. ft. 136 sq. in.

=

SOLUTION. Since there are 160 sq. rd. in an acre, in 10 A. there are 10 times 160 sq. rd. 1600 sq. rd. + 65 sq. rd. = 1665 sq. rd. Since there are 30 sq. yd. in one sq. rd., in 30 sq. rd. there are 1665 times 30 sq. yd. 50366 sq. yd. + 16 sq. yd.= 50382 sq. yd. Since there are 9 sq. ft. in one sq. yd., in 50382 sq. yd. there are 50382 times 9 sq. ft. 4534404 sq. ft.+ 4 sq. ft. = 453444 sq. ft. Since there are 144 sq. in. in 1 sq. ft., in 453444 sq. ft. there are 453444 times 144 sq. in. = 65295972 sq. in. +136 sq. in. = 65296108 sq. in., Ans.

=

65296108 sq. in., Ans.

2. In 65296108 sq. in. how many acres are there?

Or

in.

10 A. 65 sq. rd. 16 sq. yd. 4 sq. ft. 136 sq. SOLUTION. - Dividing by the numbers in the ascending scale, and arranging the remainders according to their order in a line below, we find the square yards a mixed number, 15. But of a sq. yd. of 9 sq. ft. 63 sq. ft.; and of a sq. ft. = 2 of 144 sq. in. 108 sq. in. Therefore sq. yd. 6 sq. ft. 108 sq. in.;

=

=

=

=

and adding 108 sq. in. to 28 sq. in. we have 136 sq. in., and adding 6 sq. ft. to 7 sq. ft. we have 13 sq. ft.: 1 sq. yd. 4 sq. ft., and writing the 4 sq. ft. in the result, and adding 1 sq. yd. to 15 sq. yd. we have for the reduced result, 10 A. 65 sq. rd. 16 sq. yd. 4 sq. ft. 136 sq. in.

3. Reduce 87 A. 118 sq. rd. 7 sq. yd. 1 sq. in. to square inches.

ft. 100 sq.

Ans. 550355068 sq. in.

4. Reduce 550355068 square inches to acres. 5. A field 100 rods long and 30 rods wide contains how many acres? Ans. 18 A. 120 sq. rd. 6. How many rods of fence will inclose a farm a mile square? Ans. 1280 rods. 7. How much additional fence will divide it into Ans. 640 rd. 8. How many acres of land in Boston, at $1 a square foot, will $100000 purchase?

four equal square fields?

Ans. 2 A. 47 sq. rd. 9 sq. yd. 31 sq. ft. 9. How many yards of carpeting, 1 yd. wide, will be required to carpet a room 18 ft. long and 16 ft. wide? Ans. 328 yd.

10. What would be the cost of plastering a room 18 ft. long, 161 ft. wide, and 9 ft. high, at 22 cents a sq. yd.? Ans. $22.44.

11. What will be the expense of slating a roof 40 feet long and each of the two sides 20 feet wide, at $10 per square? Ans. $160.

12. How many square inches are there in a board 3 feet long and 20 inches wide? Ans. 720. 13. A man bought a farm 198 rods long and 150 rods wide, and agreed to pay $32 an acre for it. How much did the farm cost him? Ans. $5940. 14. A certain rectangular piece of land measures 1000 links by 100. How many acres does it contain?

Ans. 1 A.

15. How many square yards are there in a triangle whose base is 148 ft. and altitude 45 feet? Ans. 370 sq. yd. 16. What is the area of a triangle whose base is 100 ft. and whose altitude is 60 ft.?

17. How many acres of land are there in a parallelogram, the length of which is 240 rods and the breadth (corresponding to altitudes in the figure, see 196) 84 rods? 18. What is the value of 4 acres of land at $2 per sq. meter?

19. In 9.375 hectares, how many sq. meters are there? 20. How many hectares are there in 25.635 sq. kilometers?

SURVEYOR'S SQUARE MEASURE.

199. This measure is used by surveyors in computing the area or contents of land.

1. A square mile of land is also called a section.

2. Engineers commonly use a chain, or measuring tape, 100 feet long, each foot divided into tenths.

3. The contents of land are commonly estimated in square miles, acres, and hundredths; the denomination, rood, is no longer used.

EXAMPLES.

1. How many poles are there in a township of land? 2. Reduce 3686400 P. to sq. mi.

3. In 94 A. 7 sq. ch. 12 P. 118 sq. 1. how many square links are there?

CUBIC MEASURE.

200. A Cube is a solid, or body, having six equal square sides, or faces. If each side of a cube is 1 yard or 3 feet, 1 foot in thick

ness of this cube will contain 3x3x1-9 cubic feet, and the whole cube will contain 3 x 3 x3=27 cubic feet.

A solid, or body, may

have the three dimensions

all alike or all different. A body 4 ft. long, 3 ft. wide, and 2 ft. thick contains 4 x 3 x 2=24 cubic or solid feet. Hence,

The cubic or solid contents of a body is the product of the length by the breadth by the thickness.

201. Cubic Measure, also called Solid Measure, is used in estimating the contents of solids, or bodies; as timber, wood, stone, etc.

TABLE.

1728 Cubic Inches (cu. in.) make 1 Cubic Foot

cu. yd. cd. ft.

Cd.

128 Cubic Feet

24 Cubic Feet

PRAC. AR.

1 Cord of Wood.

Perch of Stone}

or Masonry

66

1

{

12

1. A cubic yard of earth is called a load.

2. Railroad and transportation companies estimate light freight by the space it occupies in cubic feet, and heavy freight by weight.

3. A pile of wood 8 ft. long, 4 ft. wide, and 4 ft. high, contains 1 cord; and a cord foot is 1 foot in length of such a pile.

4. A perch of stone or of masonry is 16 ft. long, 14 ft. wide, and 1 ft, hign. 5. Joiners, bricklayers, and masons make no allowance for windows, doors, etc. Bricklayers and masons, in estimating their work by cubic measure, make no allowance for the corners of the walls of hou es, cellars, etc., but estimate their work by the girt; that is, the entire length of the wall on the outside.

6. Engineers, in making estimates for excavations and embankments, take the dimensions with a line or measure divided into feet and decimals of a foot. The estimates are made in feet and decimals, and the results are reduced to cubic yards.

METRIC CUBIC MEASURE.

202. The cubic meter is the unit of solid measure.

TABLE.

1000 Cu. Millimeters (cu. mm.)=1 Cu. Centimeter = .061 + cu. in. 1000 Cu. Centimeters (cu. cm.)=1 Cu. Decimeter

1000 Cu. Decimeters (cu. dm.)=1{

Cu. Meter

or Stere

= 61.026 cu. in.

=

'} =35.316+ cu. ft.

1. In measuring wood the cubic meter is called a stere, and is equal to .2759 of a cord.

2. Since in cubic measure 1000 of each denomination make one of the next higher, in reducing to higher or lower denominations we must move the decimal point three places to the left or right for each denomination.

EXAMPLES.

1. In 125 cu. ft. 840 cu. in. how many cu. in. are there? Ans. 216840 cu. in.

2.

Reduce 5224 cubic feet to cords. Ans. 401% cords. 3. In a solid 3 ft. 2 in. long, 2 ft. 2 in. wide, and 1 ft. 8 in. thick, how many cubic inches are there?

Ans. 19760 cu. in.

4. How many small cubes, 1 in. on each edge, can be sawed from a cube 6 ft. on each edge, allowing no waste for sawing? Ans. 373248. 5. In a pile of wood 60 ft. long, 20 ft. wide, and 15 ft. high, how many cords are there? Ans. 140 cords.

6. How many cubic ft. are there in 10 ft. long, 31 ft. wide, and 34 ft. high?

a load of wood Ans. 113 cu. ft.