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being in Maine 31766, in New Hampshire 9280, in Vermont 10212, in Massachusetts 7800, in Rhode Island 1306, and in Connecticut 4674 ?

Ans. 65,038. 12. The estimated population of the above States, in 1855, was as follows; Maine 653000, New Hampshire 338000, Vermont 327000, Massachusetts 1133123, Rhode Island 166500, and Connecticut 384000. What was the entire population ? 13 At the commencement of the year

1858 there were in operation in the New England States, 3751 miles of railroad; in New York, 2590 miles; in Pennsylvania, 2546; in Ohio, 2946; in Virginia, 1233; in Illinois, 2678; and in Georgia, 1233. What was the aggregate number of miles in operation in all these States?

14. The Grand Trunk Railway is 962 miles long, and cost $60000000; the Great Western Railway is 229 miles long, and cost $14000000; the Ontario, Simcoe and Huron, is 95 miles long, and cost $3300000; the Toronto and Hamilton is 38 miles long, and cost $2000000. What is the aggregate length, and what the cost, of these four roads ?

Ans. Length, 1,324 miles; cost, $79,300,000. 15. A man bequeathed his estate as follows; to each of his two sons, $12450 ; to each of his three daughters, $6500; to his wife, $650 more than to both the sons, and the remainder, which was $1000 more than he had left to all his family, he

gave to benevolent institutions. What was the whole amount of his property ?

Ans. $140,900. 16. How many miles from the southern extremity of Lake Michigan to the Gulf of St. Lawrence, passing through Lake Michigan, 330 miles ; Lake Huron, 260 miles; River St. Clair, 24 miles; Lake St. Clair, 20 miles; Detroit River, 23 miles; Lake Erie, 260 miles; Niagara River, 34 miles; Lake Ontario, 180 miles; and the River St. Lawrence, 750 miles ?

17. The United States exported molasses, in the year 1856, to the value of $154630; in 1857, $108003; in 1858, $115893; and tobacco, during the same years respectively, to the value of $1829207, $1458553, and $2410224. What was the entire value of the molasses and tobacco exported in these three years ?

18. The population of Boston, in 1855, was 162629; Providence, 50000; New York, 629810; Philadelphia, 408815; Brooklyn, 127618; Cleveland, 43740; and New Haven, 25000. What was the entire population of these cities? Ans. 1,447,612.

19. Iron was discovered in Greece by the burning of Mount da, B. C. 1406; and the electro-magnetic telegraph was invented by Morse, A. D. 1832. What period of time elapsed between the two events ?

Ans. 3,238 years. 20. The number of pieces of silver coin made at the United States Mint at Philadelphia, in the year 1858, were as follows: 4628000 half dollars, 10600000 quarter dollars, 690000 dimes, 4000000 half dimes, and 1266000 three-cent pieces. What was the total number of pieces coined ?

21. The cigars imported by the United States, in the year 1856, were valued at $3741460; in 1857, at $4221096; and in 1858, at $4123208. What was the total value of the importations for the three years?

Ans. $12,085,764. 22. In the appropriations made by Congress for the year ending June 30, 1860, were the following; for salary and mileage of members of Congress, $1557861; to officers and clerks of both Houses, $157639; for paper and printing of both Houses, $170000; to the President of the United States, $31450; and to the Vice President, $8000. What is the total of these items?

ADDING TWO OR MORE COLUMNS AT ONE OPERATION.

OPERATION.

68. 1. What is the sum of 4632, 2553, 4735, and 2863 ?

ANALYSIS. Beginning with the units and tens of 4632 the number last written, we add first the tens above, 2553 then the units, thus ; 63 and 30 are 93, and 5 are 98, 4735

and 50 are 148, and 3 are 151, and 30 are 181, and 2863

2 are 183. Of this sum, we write the 83 under the 14783 columns added, and carry the 1 to the next columns,

thus ; 28 and 1 are 29, and 40 are 69, and 7 are 76, and 20 are 96, and 5 are 101, and 40 are 141, and 6 are 147, which we write in its place, and we have the whole amount, 14783.

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5. What is the total number of churches, the number of persons accommodated, and the value of church property in the United States, as shown by the following statistics ?

Methodist..
Baptist ....
Presbyterian
Congregational
Episcopal
Roman Catholic.....
Lutheran
Christians..
Friends
Union
Universalist ....
Free Church
Moravian
German Reformed
Dutch Reformed.
Unitarian
Mennonite.
Tunkers
Jewish
Swedenborgian

No. of churches. 12484 8798 4591 1675 1430 1269 1205 812 715 619 494 361 331 327 324 244 110 52 31

No. of persons accommodated. 4220293 3134438 2045516 795677 631613 705983 532100 296050 283023 213552 205462 108605 112185 156932 181986 137867 29900 35075 16575 5070

Value of church property. $14636671 10931382 14469889

7973962 11261970 8973838 2867886

845810 1709867

690065 1767015 252255 443347 965880 4096730 3268122

94245 46025 371600 108100

15

6. Give the amounts of the productions of the United States and Territories for the year 1850, as expressed in the following columns:

Pounds of
Butter.

Pounds of

Cheese.

Pounds of

Wool.

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Bushels of

Wheat. Alabama...... 4,008,811 31,412 657,118 294,044 Arkansas...... 1,854,239,3 30,088 182,595 199,639 California ..... 705

150
5,520

17,228 Columb., Dist. 14,872 1,500

525

17,370 Connecticut... 6,498,119 5,363,277 497,454

41,762 Delaware... 1,055,308 3,187 57,768 482,511 Florida 371,498 18,015

23,247 1,027 Georgia 4,640,559, 46,976 S90,019 1,088,534 Illinois 12,526,5433 1,278,225 2,150,113 9,414,575 Indiana 12,881,535 624,564 2,610,287 6,214,458 Iowa..... 2,171,188 209,810 373,898 1,530,581 Kentucky 9,947,523 213,954 2,297,433 2,142,822 Louisiana... 683,069 1,957 109,897

417 Maine ..... 9,243,811,1 2,434,454 1,364,034 296,259 Maryland ..... 3,086,160 3,975 477,438 4,494,680 Massachusetts 8,071,370 7,088,142 585,138 31,211 Michigan ..... 7,065,878 * 1,011,492 2,043,283 4,925,889 Mississippi... 4,346,234 21,191 559,619 137,990 Missouri...... 7,834,359 203,572 1,627,164 2,981,652 N. Hampshire 6,977,056 3,196,563 1,108,476 185,658 New Jersey... 9,487,210 365,756 375,396 1,601,190 New York.... 79,766,094 49,741,413 10,071,301

10,071,301 13,121,498 N. Carolina... 4,146,290 95,921 970.738 2,130,102 Ohio........... 34,449,379 20,819,542 10,196,371 14,487,351 Pennsylvania 39,878,418 2,505,034 4,481,570 15,367,691 Rhode Island 995,670 316,508 129,692

49 S. Carolina... 2,981,850n 4,970 487,233 1,066,277 Tennessee 8,139,585

1,364,378 1,619,386 Texas......... 2,344,900;; 95,299

131,917 41,729 12,137,980 8,720,834 3,400,717 535,955 Virginia ..... 11,089,359 436,292 2,860,765 11,212,616 Wisconsin 3,633,750 400,283 253,963 4,286,131 Territories ... 295,984 73,826 71,894 517,562

372,10

Vermont ......

2*

SUBTRACTION.

69. Subtraction is the process of determining the difference between two numbers of the same unit value.

70. The Minuend is the number to be subtracted from. 71. The Subtrahend is the number to be subtracted.

72. The Difference or Remainder is the result obtained by the process of subtraction.

73. When the given numbers contain more than one figure each, the method of subtraction depends upon the following principles:

I. If the units of each order in the subtrahend be taken separately from the units of like order in the minuend, the sum of the differences must be equal to the entire difference of the given numbers. (Ax. 10.)

II. If both minuend and subtrahend be equally increased, the remainder will not be changed. 1. From. 926 take 275. OPERATION.

ANALYSIS. We first subtract 5 units from Minuend,

328

8 units, and obtain 3 units for a partial reSubtrahend,

275

mainder. As we cannot take 7 tens from 2 Remainder, 653

tens, we add 10 tens to the 2 tens, making

12 tens; then 7 tens from 12 tens leave 5 tens, the seconü partial remainder. Now, since we added 10 tens, er 1 hundred, to the minuend, we will add 1 hundred to the subtrahend, and the true remainder will not be changed (II); thus, 1 hundred addsd to 2 hundreds makes 3 hundreds, and this sum subtracted from 9 nundreds leaves 6 hundreds; and we have for the total remainder, 553.

Note.-The process of adding 10 to the minuend sometimes called bor. owing 10, and that of adding 1 the next figure of the subtrahend, carrying 1.

74. From these principles and illustrations we deduce the following

RULE. I. Write the less number under the greater, placing units of the same order under each other

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