LONG MEASURE.

98. LONG MEASURE is used in measuring distances, i. e. where length is required without regard to breadth or thickness.

NOTE 1. The earth not being an exact sphere, the distance round it in different directions is not exactly the same. By the most exact measurements made, a degree is a little less than 69 miles.

NOTE 2. The barleycorn is but little used.

NOTE 3. The 3 before miles in the table is not a part of the scale.

Ans. 528.

3. In 4yd. 2ft. 8in. how many barleycorns?

98. For what is Long Measure used? Table? Scale? A degree upon the

earth, how long?

4. Reduce 473b.c. to higher denominations.

5. The distance through the center of the earth is about 7912 miles; how many rods is it?

6. The distance round the earth is about 8000000 rods; how many miles is it?

CHAIN MEASURE.

99. CHAIN MEASURE is used by engineers and surveyors in measuring roads, canals, boundaries of fields, etc.

NOTE. To measure roads, etc., engineers often use a chain 100 feet long.

99. For what is Chain Measure used? Table? Scale? Note?

3. In 6fur. 2ch. 3rd. 18li, how

many links?

Ans. 6293.

4. Reduce 3879 links to higher denominations.

Ans. 3fur. 8ch. 3rd. 4li.

5. Reduce 17m. 3fur. 5ch. 2rd. 24 li. to links.

6. Reduce 13475 links to higher denominations.

7. From Boston to Andover is 23 miles; how many links is it?

8. From Boston to Fitchburg is 400000 links; how many miles is it?

9. The distance round a field is 7fur. 6ch. 3rd.; what will it cost to fence the field at $2 per rod?

10. How many miles, etc., in 637482 links?

SQUARE MEASURE.

100. SQUARE MEASURE is used for measuring surfaces.

TABLE.

144 Square Inches (sq. in.) make 1 Square Foot,

9 Square Feet

30 Square Yards or

272 Square Feet

40 Square Rods

66

1 Square Yard,

sq. ft. sq. yd

make 1 Square Chain, sq. ch.

2560=102400—3097600-27878400-4014489600

NOTE. In measuring land, surveyors use a 4-rod chain composed of 100 links. Sometimes the half-chain of 50 links is used.

100. For what is Square Measure used? Table? Scale? Table in Chain Measure?

Note?

3. In 14sq. m. 25a. 3r. 30sq. rd. how many square rods?

Ans. 1437750.

4. Reduce 624873sq. rd. to higher denominations. 5. Bought a field containing 3a. 2r. 25sq. rd. at $2 per rod; what did it cost?

101. The manner of finding the area of a surface like Fig. 1, may be understood from the following explanation. Let A B represent (on a reduced scale) a line 5 inches long; then, evidently, if we pass from A to e, a distance of 1 inch, and draw the line e f, the figure A Bfe will contain 5 square inches, i. e. 5 X 1 square inches. So, in like manner, A Bhg will contain 10, or 52 square inches; and

එ

A

FIG. 1.

B

1

2

3 4 5

f

6

7

8

9 10

h

g

D

་

11 12 13 14 15

C

A B C D will contain 15, or 5 × 3 square inches, i. e. we multiply together the numbers representing the length and breadth, and the product will be the number of square inches in the surface.

NOTE. A surface like Fig. 1 is called a rectangle. If the length and breadth are equal, the rectangle is a square. The angles of a rectangle or square are all equal to each other, and each angle is called a right angle.

101. How is the area of a rectangle or square ascertained? What is said of the angles of a rectangle or square? What is each angle called?

102. The area of a rectangle divided by the length will give the breadth, and the area divided by the breadth will give the length; thus, in Fig. 1, 1553 and 1535.

Ex. 6. How many square rods in a field that is 7 rods wide and 9 rods long? Ans. 63. 7. How many square rods in a field that is 25 rods wide and 48 rods long? How many acres? 2d Ans. 7a. 2r. 8. A board containing 36 square feet, is 12 feet long; how wide is it?

9. A flower garden containing 300 square feet is 12 feet wide; how long is it?

10. How many acres in a field that is 20 rods wide and 56 rods long?

SOLID OR CUBIC MEASURE.

Ans. 7.

103. SOLID OR CUBIC MEASURE is used in measuring things which have length, breadth, and thickness.

NOTE 1. The scale in this table only includes 1728 and 27; the other numbers are irregular.

NOTE 2. Transportation companies often estimate freight, especially of light articles, by the space occupied, rather than by the actual weight. In this estimate, from 25 or 30 to 150 or 175 cubic feet are called a ton. This is called arbitrary weight, and it varies with different transportation companies, and somewhat according to the risks of carriage. The Boston and Maine Railroad Co., e. g., considers a thousand of bricks a ton, whereas the actual weight is more than two tons. Again, a horse is estimated at 3000lb.,

102. How is the breadth of a rectangle found when the area and length are known? How the length, when the area and breadth are known? 103. For what is Solid Measure used? Table? Scale? Note 2?