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Denominate Numbers-Surface Measure. 333. In the measurement of land it is more convenient to use a decimal scale ; hence the invention of the Gunter Chain. This chain is 4 rods long and is divided into 100 links.

Observe that links are hundredths of chains.
Observe that square chains are tenths of acres.

acres.

acres.

acres.

acres.

EXERCISE.
1. Land, 3 chains by 4 chains contains

acres.
2. Land, 5 chains by 4 chains contains
3. Land, 3 chains by 8 chains contains
4. Land, 5 chains by 7 chains contains
5. Land, 8 chains by 6 chains contains
6. Two chains 20 links equals chains.
7. Two chains 35 links equals chains.
8. Two chains 75 links equals chains.
9. Two chains 5 links equals chains.
10. Two chains 9 links equals chains.
11. Land, 4 ch. by 4.50 ch. contains acres.
12. Land, 5 ch. by 3.20 ch. contains

acres. 13. Make a rule and find the number of acres in each of the following:

(1) Land, 12 chains 35 links by 9 chains 50 links. (2) Land, 21 chains 8 links by 12 chains 30 links. (3) Land, 32 chains 25 links by 15 chains 6 links.

(a) Find the sum of the area of the ten pieces of land described on this page.

To The TEACHER.-A rod is exactly 25 links. A foot is about 1į links. Hence rods and feet can be easily changed to chains and links by regarding each 4 rods as 1 chain and each additional rod as 25 links and each additional foot as 1į links. The error in any one measurement never exceeds 2 inches. 9 rd. 12 ft. 2 chains 43, (25 +18), links.

Denominate Numbers-Surface Measure.

334. To determine the amount of carpet necessary for a given room several minor problems must be solved which can be best studied by means of an

EXAMPLE.

1. How many yards of carpet must be purchased for a room 16 ft. by 20 ft. if the carpet is 1 yd. wide ?

(1) How many breadths will be necessary if the carpet is put down lengthwise of the room? How much must be cut off or turned under from one breadth in this case ?

(2) How many breadths will be necessary if the carpet is put down crosswise of the roo How much must be cut off or turned under from one breadth in this case ?

(3) Make two diagrams of the room on a scale of 1 inch to the foot and show the breadths of carpet in each case.

(4) How many yards must be purchased in each case ?

(5) If in the first case there is no waste in matching the figure and in the second case there is a waste of 8 inches on each breadth except the first,* which plan of putting down the carpet will require the greater number of yards?

(6) If the carpet costs 90¢ a yard and the conditions are as stated in No. 5, what is the cost of the carpet in each case ?

2. How many yards of carpet must be purchased for a room 16 ft. by 20 ft. if the carpet is į of a yard wide and there is no waste in matching the figure ?

3. How many yards of carpet must be purchased for a room that is 15 ft. 6 in. by 16 ft. 4 in. if the carpet is of a yard wide, is put down lengthwise of the room, and there is no waste in matching the figure ?

* Why except the first breadth ?

Denominate Numbers.

335. PLASTERING AND PAPERING.

1. How many square yards of plastering in a room (walls and ceiling) that is 15 ft. by 18 ft. and 12 ft. high, an allowance of 12 square yards being made for openings?

NOTE.-In estimating the cost of plastering, allowance is made for “openings” (windows and doors) only when they are very large in proportion to the wall to be covered. Why are p'asterers unwilling to deduct the entire area of all the openings?

2. At 24¢ a square yard how much will it cost to plaster a room that is 17 ft. by 20 ft. and 10 feet from the floor to the ceiling, deducting 16 square yards for openings?

3. How many “double rolls" of paper will be required for the walls of a room that is 14 ft. by 16 ft. and 11 ft. high above the baseboards, if an allowance of 1 full “ double roll” is made for openings?

NOTE. --Wall paper is usually 18 inches wide. A “single roll” is 24 ft. long. A "double roll” is 48 ft. long. In papering a room 11 ft. high it would be safe to count on 4 full strips from each “double roll,” The remnant would be valueless unless it could be used over windows or doors. Since each strip is 18 inches wide, a “double roll” will cover 72 inches (6 ft.) of wall measured horizontally.

4. At 12¢ a “single roll,” how much will the paper cost for the walls of a room that is 12 ft. by 14 ft. and 7 ft. above the baseboards, if the area of the openings is equivalent to the surface of 2 “single rolls" of paper ?

5. Find the cost, at 25° a square yard, of plastering the walls of a room that is 48 ft. by 60 ft. and 18 feet high, deducting 30 square yards for openings.

Denominate Numbers.

336. FARM PROBLEMS.

Find how many acres in

1. A piece of land 1 rod by 160 rods.
2. A piece of land 7 rods by 160 rods.
3. A piece of land 13 rods by 160 rods.
4. A piece of land 22 feet * by 160 rods.
5. A piece of land 84 yards * by 160 rods.

(a) F'ind the sum of the five results.
6. A piece of land 8 rods by 80 rods.
7. A piece of land 17 rods by 80 rods.
8. A piece of land 371, rods by 80 rods,
9. A piece of land 618 feet * by 80 rods.
10. A piece of land 550 yards * by 80 rods.

(b) Find the sum of the five results.

11. A piece of land 12 rods by 40 rods. 12. A piece of land 27 rods by 40 rods. 13. A piece of land 46 rods by 20 rods. 14. A piece of land 36 rods by 20 rods. 15. A piece of land 264 feet * by 20 rods.

(c) Find the sum of the five results. 16. A piece of land 1 rod by 1 mile. 17. A piece of land 11 rods by 1 mile. 18. A piece of land 66 feet * by 1 mile. 19. A piece of land 99 yards * by 1 mile. 20. A piece of land 198 feet * by } of a mile.

(d) Find the sum of the five results.

21. A piece of land of a mile long and as wide as the schoolroom.

• Change to rods.

Denominate Numbers.

337. FARM PROBLEMS.

1. A piece of land 1 foot wide and 43560 feet long is how many acres ?

How many

2. Change 43560 feet to miles.

3. A piece of land 1 foot wide must be how many miles in length to contain 1 acre?

4. Some country roads are 66 feet wide. acres in 84 miles of such road ?

5. How many acres in 1 mile of road that is 4 rods wide ?

6. A farmer walking behind a plow that makes a furrow 1 foot wide will travel how far in plowing 1 acre?

7. A farmer walking behind a plow that makes a furrow 16 inches wide will travel how far in plowing 1 acre?

8. If a mowing machine cuts a swath that averages 4 feet in width how far does it move in cutting 1 acre?

9. If potatoes are planted in rows that are 3 feet apart (a) how many miles of row to each acre? (b) How many rods of row to each acre? (c) If 4 rods of row on the average yield 1 bushel, what is the yield per acre?

10. Strawberry plants are set in rows that are 2 feet apart. (a) How many miles of row to the acre? (b) How many rods of row to the acre ? (c) How many feet of row to the acre ?

11. If corn is planted in rows 31 feet apart and if the “hills” are 3} feet apart in the row, how many hills to each acre ? *

* Think of each “hill" as occupying a piece of land 3; ft. by 34 ft.

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