Artificers estimate their work as follows:

By the square foot; glazing and stone-cutting.

By the square yard; painting, plastering, paving, ceiling, and paper, hanging.

By the square of 100 feet; flooring, partitioning, roofing, slating, and tiling.

Brick-work is generally estimated by the 1000 bricks; sometimes in cubic feet.

1. In estimating the painting of moldings, cornices, etc., the measuring-line is carried into all the moldings and cornices.

2. A brick wall which is a brick and a half thick, is said to be of the standard thickness. Five courses in the height are called a foot.

EXAMPLES FOR PRACTICE.

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

OPERATION.

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

160

1665 sq. rd.

301

4161

49966

503821 sq. yd.

9

4534444 sq. ft.
144

36 = 1 sq. ft.

1813912 with 136 sq. in.

1813776

453444

65296108 sq. in., Ans.

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

How do artisans estimate work?

=

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

=

ANALYSIS. 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, 153. But of a sq. yd. = & of 9 sq. ft. 6 sq. ft.; and 3 of a sq. ft. of 144 sq, in. 108 sq. in. Therefore & q. yd. = 6 sq. ft. 108 sq. in.; and adding 108 sq. in. to 28 sq. in. we have 136 sq. in., and 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.

to

3. Reduce 87 A. 118 sq. rd. 7 sq. yd. 1 sq. ft. 100 sq. in. square inches. Ans. 550355068 sq. in.

5. 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 enclose a farm a mile square? Ans. 1280 rods.

7. How much additional fence will divide it into four equal square fields ? Ans. 640 rods. 8. How many acres of land in Boston, at $1 a square foot, will $100000 purchase?

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. 32 yards.

10. What would be the cost of plastering a room 18 ft. long, 16 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.

SURVEYORS' SQUARE MEASURE.

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

2304000000

SCALE-ascending, 625, 16, 10, 640, 36; descending, 36, 640, 10, 16,

625.

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 FOR PRACTICE.

1. How many poles 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?

4. What will be the cost of a farm containing 4550000 square links, at $50 per acre?

Repeat the table of surveyors' square measure.

Ans. $2275.

Give the scale.

III. CUBIC MEASURE.

198. A Cube is a solid, or body, having six equal square sides, or faces. If each side of a cube be 1 yard, or 3 feet, 1 foot in thickness of this cube will contain 3 x 3 x 1 =9 cubic feet, and the whole cube will contain 3 x 3 x 3 = 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 are found by multiplying the length, breadth, and thickness together.

199. 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. ft.

SCALE-ascending, 1728, 27.

1{

Perch of Stone

or Masonry, ...Pch.

The other numbers are not in a regular scale, but are merely so many times 1 foot. The unit equivalents, being fractional, are consequently omitted.

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 feet long, 4 feet wide, and 4 feet 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 feet long, 1 feet wide, and 1 foot high.

Define a cube. How are the contents of a cube or rectangular solid found? For what is cubic measure used? Repeat the table. Give the scale. How is railroad freight estimated? What is understood by a cord foot? By a perch of stone or masonry?

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 houses, 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.

EXAMPLES FOR PRACTICE.

1. In 125 cu. ft. 840 cu. in. how many cu. in.? Ans. 216840. 2. Reduce 5224 cubic feet to cords. Ans. 4013. 3. In a solid, 3 ft. 2 in. long, 2 ft. 2 in. wide, and 1 ft. 8 in. thick, how many cubic inches? Ans. 19760.

4. How many small cubes, 1 inch on each edge, can be sawed from a cube 6 feet on each edge, allowing no waste for sawing? Ans. 373248.

5. In a pile of wood 60 feet long, 20 feet wide, and 15 feet high, how many cords? Ans. 1405. 6. How many cubic feet in a load of wood 10 feet long, 31 feet wide, and 3 feet high? Ans. 113 cu. ft.

7. If a load of wood be 12 feet long and 3 feet wide, how high must it be to make a cord ? Ans. 3 ft. high. 8. The gray limestone of Central New York weighs 175 pounds a cubic foot. What is the weight of one solid yard? Ans. 2 T. 7 cwt. 25 lb.

9. A cellar wall, 32 ft. by 24 ft., is 6 ft. high and 11⁄2 ft. thick. What did it cost at $1.25 a perch? Ans. $50.909+. 10. What did it cost to dig the same cellar, at 15 cents a cubic yard? Ans. $25.60.

11. My sleeping room is 10 ft. long, 9 ft. wide, and 8 ft. high. If I breathe 10 cu. ft. of air in one minute, in how long a time will I breathe as much air as the room contains? Ans. 72 min.

12. In a school-room 30 ft. long, 20 ft. wide, and 10 ft. high, with 50 persons breathing each 10 cu. ft. of air in one minute, in how long a time will they breathe as much as the room contains? Ans. 12 min.

How are excavations and embankments measured?