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8. There is a fence enclosing a circular field 48 feet in diameter. What will be the area of a square field which the same fence will exactly surround ?

9. A loans $ 325.50 for 3 y. 4 mo. 24 d., and receives for interest $ 77.469. B loans $ 1.80, and his money amounts in the same time to $ 2.259. Which receives the greater per cent?

10. Find the difference between the square root and the cube root of .0064

462. 1. What will 377 bushels of salt cost, if 133 bushels cost $ 11.75 ?

2. How many stones 10 inches long, 9 inches wide, and 4 inches thick, will it take to build a wall 80 feet long, 20 feet high, and 24 feet thick ?

3. If you buy eggs for 12ų cents, and sell them for 15 cents per dozen, for how much must wood be sold, that cost you $ 4.20 per cord, to gain in the same ratio ?

4. What must I pay for 25 shares of bank stock, at 7 per cent advance, the par value being $ 250 per share ?

5. For how much less than its face should a note of $ 840 be sold, if payable in 4 months ?

6. What is the value of a lot of land in the form of a rightangled triangle, the base being 15 yards and the hypothenuse 25 yards, at 8} cents per square foot ?

7. In a school-room 35 feet long, 30 feet wide, and 12 feet high, there are 40 pupils, each breathing 10 cubic feet of air per minute. In what time will the air be unfit for respiration, if no pure air be admitted ?

8. A man bought 3 loads of hay. The first load weighed 4832 lb., tare 1124 lb.; the second weighed 4628 lb., tare 1136 1b.; the third weighed 4976 lb., tare 1142 lb. What did it cost him at $33.37} per ton ?

9. A cargo of 4000 bushels of wheat, worth $1.20 per bushel, is insured at of 1} per cent on of its value. If the cargo be lost, how much will the owner of the wheat lose ?

10. Mr. B. mortgaged his farm for $6000, Oct. 1, 1879, to be paid in 6 years, with interest at 8 per cent. Three months from date he paid $500; Sept. 10, 1880, $ 1126; March 31, 1881, $ 2000; and Aug. 10, 1881, $ 876.50. How much was due at the expiration of the time ?

463. 1. What cost a piece of land 70 rods 5) feet long, 52 rods 81 feet wide, at $ 256 per acre ?

2. What is the interest of $ 725 for 9 months 4 days, at 5 per cent ?

3. Bought a farm for $ 4200, agreeing to pay $ 600 down and the rest in six equal semi-annual installments. When could I justly make one payment for the whole ?

4. A chimney 5 ft. square and 50 ft. high has two flues, each 1 ft. square. How many bricks, 8 in. by 4 in. by 2 in., were used in its construction ?

5. Having used my carriage three years, I am willing to sell it at a loss of 20 per cent. If I receive $ 250 for it, what was the cost ?

6. What is the circumference of the largest wheel that can be got through a door 5 ft. wide and 12 ft. high ?

7. A, B, C, and D hired a pasture for $ 75. A put in 7 cows, 6 weeks; B 3 cows, 13 weeks; C 4 cows and 9 sheep, 7 weeks ; D 42 sheep, 5 weeks. A cow would eat as much as 3 sheep. What should each pay ?

8. Divide $ 3000 among A, B, and C, giving A $ 50 more than B, and B $ 250 more than C.

9. If a cistern 6 ft. in diameter hold 80 barrels of water, what must be the diameter of a cistern of the same depth to hold 1280 barrels ?

10. A can do a piece of work in of an hour; B can do of it in one hour. In what time can both do it ?

APPENDIX.

ROMAN NOTATION.

464. Roman Notation uses seven capital letters in ex. pressing numbers :

I, V, X, L, C, D, M.

1, 5, 10, 50, 100, 500, 1000. All other numbers are expressed by repeating or combining these letters, according to the following

465. Principles. 1. Repeating a letter repeats its value.

Thus, I stands for one; II, two; III, three; X, ten; XX, twenty; XXX, thirty, etc.

2. When a letter is placed before another of greater value, the difference of their values is expressed.

Thus, IV stands for four; IX, nine; XL, forty; XC., ninety.

3. When a letter is placed after another of greater value, the sum of their values is expressed.

Thus, VI stands for six; XI, eleven; XV, fifteen; XXV, twenty-five, etc.

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4. A dash (-) over a letter increases the value of the letter a thousand fold.

Thus, V stands for five thousand; X, ten thousand; L, fifty thousand.

466. TABLE
XIV

XC
XV 15 |

100 XVI 16 | CC

200 XVII

CCC
XVIII

400 XIX VII

XX
20

600 VIII XXX 30 | M

1000 IX

MD

1500 X

50

100000 XI

LX
60 M

1000000 XII 12 LXX 70 MDCXX

1620 XIII : 13 LXXX

MDCCCLXXXI 1881

300

o voer A CN

18

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VI

500

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40

10

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Express in letters: 7. Twenty-nine.

10. One hundred sixty-one. 8. Seventy-three. 11. Fifteen hundred eighty. 9. Ninety-eight.

12. Two thousand eight hundred. 13. One thousand seven hundred seventy-six.

FUNDAMENTAL PROCESSES. 467. The Fundamental Processes of arithmetic, or those upon which all others depend, are addition, subtraction, multiplication, and division. · These are also sometimes called the ground rules of arithmetic.

PRIME NUMBERS.

468. No direct method of detecting prime numbers has been discovered.

The prime numbers to 1009 are included in the following

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469. A Circulating Decimal is a decimal in which a figure or a set of figures continually repeats. Thus,

f = 0.666... and I1 = 0.727272... 470. A Repetend is the part of the decimal that continually repeats.

It may be marked, when a single figure repeats, by a dot (.) over it, and when a set of figures, by a dot over the first and the last of the set. Thus,

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