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to add ? Why? Why are the tens of one column carried as units to the next column to the left? What is an integer ? See p.

15. What is a fraction? What is a decimal fraction? Are decimal fractions added differently from integers ? Are the tens carried from the column of tenths to that of units in the same manner as from one rank of integers to the next? Why? To what rank does the right hand column belong, in a number consisting wholly of integers ? Is this the case when a number consists partly or wholly of decimal fractions ? How, then, is the local value of the figures ascertained ? Explain the two methods of proving addition.

Practical Exercises.

1. By a census taken in the year 1841, the population of the British Islands was as follows : England, 14,995,138; Wales, 911,603; Scotland, 2,620,184; Ireland, 8,175,124 ; army, navy, &c., 193,469; islands in the British seas, 124,040. What is the total population of these islands ?

Ans. 27,019,558. 2. In the same year, the number of emigrants that left the United Kingdom of Great Britain was as follows: to their North American colonies, 38,164; to the United States, 45,017; to the Australian colonies and New Zealand, 32,625 ; to all other places, 2786. What was the whole number of emigrants from the kingdom that year? Ans. 118,592.

3. The value of the principal articles of manufacture in Great Britain for that year is estimated as follows : cotton, £35,000,000 ;* woollen, £24,000,000 ; iron and hardware, £20,000,000; watches, jewelry, &c., £3,000,000; leather, £13,500,000; linen, £8,000,000; silk, £10,000,000; glass and earthenware, £4,250,000; paper, £2,000,000; hats, £2,000,000. What was the gross amount in pounds sterling ?

Ans. £121,750,000. 4. The white population of the United States, according to the census of 1840, classed according to ages, was as follows: Males, under five years of age, 1,270,790; of five and under ten, 1,024,072 ; of ten and under fifteen, 879,499; of fifteen and under twenty, 756,022; of twenty and under thirty, 1,322,440; of thirty and under forty, 866,431; of forty and

* This character, £, stands for pounds in money.

under fifty, 536,568; of fifty and under sixty, 314,505; of sixty and under seventy, 174,226; of seventy and under eighty, 80,051 ; of eighty and under ninety, 21,679; of ninety and under a hundred, 2,507; of a hundred and upwards, 476. Females, under five, 1,203,349; of five and under ten, 986,921; of ten and under fifteen, 836,588; of fifteen and under twenty, 792,168; of twenty and under thirty, 1,253,395; of thirty and under forty, 779,097; of forty and under fifty, 502,143; of fifty and under sixty, 304,810 ; of sixty and under seventy, 173,299; of seventy and under eighty, 80,562; of eighty and under ninety, 23,964; of ninety and under a hundred, 3,231; of a hundred and upwards, 315. What was the number of free white males? Of free white females ? Total of free whites?

Ans. to the last question, 14,189,108. 5. The number of free people of color in the United States, according to the census of 1840, was as follows: Males, under ten years of age, 56,323; of ten and under twenty-four, 52,799 ; of twenty-four and under thirty-six, 35,308; of thirtysix and under fifty-five, 28,258; of fifty-five and under a hundred,13,493; of a hundred and upwards, 286. Females, under ten, 55,069; of ten and under twenty-four, 56,562; of twenty-four and under thirty-six, 41,673; of thirty-six and under fifty-five, 30,385; of fifty-five and under a hundred, 15,728; of a hundred and upwards, 361. What was the number of free males of color? Of free females of color ? Of free persons of color ?

Ans. to the last question, 386,245. 6. The number of slaves in the United States, according to the census of 1840, was as follows : Males, under ten years of age, 422,599; of ten and under twenty-four, 391,131 ; of twenty-four and under thirty-six, 235,373; of thirty-six and under fifty-five, 145,264; of fifty-five and under a hundred, 51,288; of a hundred and upwards, 753. Females, under ten, 421,470; of ten and under twenty-four, 390,075; of twentyfour and under thirty-six, 239,787; of thirty-six and under fifty-five, 139,201; of fifty-five and under a hundred, 49,692; of a hundred and upwards, 580. What was the number of male slaves? Of female slaves? Of slaves of both sexes ?

Ans, to the last question, 2,487,213. 7. What was the whole population of the United States by the census of 1840, including 6100 persons of the navy of the United States, who were not reckoned in either of the last three enumerations ?

Ans. 17,068,666.

8. The following table exhibits the territorial area of the states of Europe and of North America. Find the aggregate, which will be correct if it amounts to 11,658,480.

AREA OF EUROPE.

&c.

Square miles. 2,000,000

257,368 203,736

Russian Empire, including Poland.
Austrian Empire, including Lombardy,
France, including Corsica
Great Britain and Ireland, British Islands, and

Malta
Prussia
Spain
Turkish Empire
Sweden and Norway
Belgium
Portugal
Holland
Denmark.
Germany
Italy
Swiss Confederation
Greece
Ionian Islands
Cracow
Andorre

.

120,500 107,921 182,270 10,585 91,164 13,214 36,510 13,598 21,856 90,620 100,953 14,950 17,900

999 488 200

AREA OF NORTH AMERICA.

United States

3,306,865 New Britain 2,598,837

Upper and Lower
British America, Canada

346,860
N. Scotia, N. Bruns-
wick, C. Breton, &c. 104,701

3,050,398 Mexico

1,038,834 Central America

203,551 Russian America

394,000 Danish America (Greenland)

380,000

Aggregate

9. The following is a statement of the white population of each of the states and territories of the United States and of the District of Columbia, according to the census of 1850, followed by tables of the free colored and slave population for the same period. Find the sum of each of the columns of males and females, which will be correct if they agree with the several given aggregates.

Then take the sum of the aggregates, which will be correct if it amounts to 23,190,998.

.

STATES, &c.
Maine
New Hampshire
Vermont
Massachusetts .
Rhode Island
Connecticut
New York.
New Jersey
Pennsylvania
Delaware
Maryland
Dist. of Columbia
Virginia
North Carolina
South Carolina
Georgia
Florida
Alabama
Mississippi .
Louisiana
Texas
Arkansas
Tennessee
Kentucky
Missouri
Illinois
Indiana .
Ohio.
Michigan
Wisconsin
Iowa.
California

Males.
296,745
155,960
159,658
484,093

70,340
179,884
1,544,489

233,452 1,142,734

35,746 211,187

18,494 451,300 273,025 137,747 266,233

25,705 219,483 156,287 141,243 84,839 85,874 382,235 392,804 312,987 445,544 506,178 1,004,117 208,465 164,351 100,887 84,708

Females.
285,068
161,496
153,744
501,357

73,535
183,215
1,503,836

232,057 1,115,426

35,423 206,756

19,447 443,500 280,003 136,816 255,339

21,498 207,031 139,431 114,248 69,195 76,315 374,601 368,609 279,017 400,490 470,976 950,933 186,606 140,405 90,994 6,627

Aggregate. 581,813 317,456 313,402 985,450 143,875 363,099 3,048,325

465,509 2,258,160

71,169 417,943

37,941 894,800 553,028 274,563 521,572

47,203 426,514 295,718 255,491 154,034 162,189 756,836 761,413 592,004 846,034

977,154 1,955,050

395,071 304,756 191,881 91,335

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TERRITORIES.
Minnesota
Oregon
Utah.
New Mexico

3,695 8,138 6,020 31,725

2,343 4,949 5,310 29,800

6,038 13,087 11,330 61,525

19,552,768

Aggregate,

FREE COLORED POPULATION.

Males. Under 10

59,125 10 and under 15

26,061 15 and under 20 20,395 20 and under 30

35,782 30 and under 40 26,153 40 and under 50

18,199 50 and under 60

11,771 60 and under 70

6,671 70 and under 80

2,878 80 and under 90.

1,106 90 and under 100

319 100 and upwards.

114 Age unknown.

150

Females.

59,748 26,247 23,399 41,765 29,072 19,741 12,572 7,362 3,438 1,512

549 229 137

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434,495

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Total
Aggregate.

SLAVE POPULATION.

Males. Under 10

506,251 10 and under 15 221,480 15 and under 20 176,169 20 and under 30 289,595 30 and under 40 175,300 40 and under 50 109,152 50 and under 60

65,254 60 and under 70 38,102 70 and under 80 13,166 80 and under 90

4,378 90 and under 100.

Females. 513,331 214,712 181,113 282,615 178,355 110,780 61,762 36,569 13,688

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4,740

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1,211 100 and upwards

606 Age unknown

1,581

1,473

819 1,533

Total
Aggregate

3,203,735

12*

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