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DENOMINATE NUMBERS.

Linear Measure.

Note.-In part to provide for ready reference, and in part to give further application of the principles presented on the preceding pages, the remaining pages of this book are devoted chiefly to denominate numbers.

331. The English and United States standard unit of length is the Imperial yard arbitrarily fixed by Act of Parliament and afterward adopted in the United States. It is about $$1$$ f of the length of a pendulum that vibrates once a second at the level of the sea in the latitude of London. It is $34 of a meter.

TABLE.

164 feet

12 inches (in.) = 1 foot (ft)
3 feet

= 1 yard (yd.)
51 yards = 1 rod (rd.)

= l rod. 320 rods

1 mile (mi.) 1760 yards

1 mile. 5280 feet

- 1 mile. 1 fathom (used in measuring the depth of the sea) = 6 feet. 1 knot (used in navigation)

- 1.15 + miles. 1 league (used in navigation)

3 knots. 1 hand (used in measuring the heights of horses) = 4 inches. 1 chain (used by civil engineers)

100 feet. 1 chain (used by land surveyors)

- 66 feet. 1 pace (used in measuring approximately) = } of a rod. 1 barleycorn (used in grading length of shoes) = { of an inch. 1 furlong (a term nearly obsolete)

= f of a mile.

Denominate Numbers - Linear Measure.

EXERCISE.

1. Mont Blanc is 15810 feet, or about miles high. 2. Mt. Everest is 29000 feet, or about miles high.

3. Commodore Dewey opened fire on the enemy at a distance of 5000 yards, or about miles.

4. My horse, measured over the front feet, is 161 hands, or

feet inches high. 5. The vessel seemed to be about three leagues, or miles distant.

6. On sounding, they found the depth of the water to be 15 fathoms, or feet.

7. The cruiser made 20 knots or about miles, an hour.

8. The length of the lot was 36 paces, or about rods. 9. 10000 feet is nearly

miles. 10. 15000 feet is nearly miles. 11. 1000 yards is about of a mile. 12. 100 feet is rods foot. 13. 200 feet is rods feet. 14. 300 feet is rods feet. 15. A kilometer is about rods. 16. A Civil Engineer's chain is rods foot.

PROBLEMS.

1. A seven-foot drive wheel of a locomotive makes how many revolutions to the mile ?

2. Which is the longest distance, 5 miles 319 rods 16 feet 6 inches, 5 miles 319 rods 5 yards 1 foot 6 inches, or 6 miles ?

3. Reduce 40 rd. 4 ft. 5 in. to inches.
4. Reduce 1100 inches to yards, feet, and inches.

Denominate Numbers-Surface Measure

332. The standard unit of surface measure is a square yard which is the equivalent of a 1-yard square.* This unit, like the square foot, square inch, square rod, and square mile, is derived from the corresponding unit of linear measure.

TABLE.
144 square inches (sq. in.)= 1 square foot (sq. ft.),
9 square feet

- 1 square yard (sq. yd.).
301 square yards

1 square rod (sq. rd.). 2724 square feet

1 square rod. 160 square rods

1 acre' (A.).
4840 square yards

1 acre.
43560 square feet
640 acres

1 square mile (sq. mi.).

1 acre.

EXERCISE.

1. Show by a drawing that there are 144 square inches in a 1-foot

square. 2. Show by a drawing that there are 9 square feet in a 1-yard square.

3. Show by a drawing that there are 304 square yards in a 1-rod square.

4. Estimate the number of square yards of blackboard in the room; the number of square feet of blackboard.

5. Estimate the number of square feet in the floor of the schoolroom ; the number of square yards.

6. Estimate the square yards of plastering on the walls of the schoolroom.

7. Estimate the number of square rods in the schoolhouse lot.

Is the lot more or less than £ of an acre ?

* A surface that is 9 ft, long and i st. wide is a square yard though it is not itself a square. It is the equivalent of a l-yard square.

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.

EXERCISE.

acres.

acres.

acres.

acres.

1. Land, 3 chains by 4 chains contains
2. Land, 5 chains by 4 chains contains
3. Land, 3 chains by 8 chains contains
4. Land, 5 chains by 7 chains contains acres.
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
12. Land, 5 ch. by 3.20 ch. contains

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.

acres.

acres.

To THE TEACHER.-A rod is exactly 25 links. A foot is about 14 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 1j 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 room? 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 904 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 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?

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