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 Ida, 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.

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

OPERATION.

4632

2553 4735 2863 14783

ANALYSIS. Beginning with the units and tens of the number last written, we add first the tens above, then the units, thus; 63 and 30 are 93, and 5 are 98, and 50 are 148, and 3 are 151, and 30 are 181, and 2 are 183. Of this sum, we write the 83 under the 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.

persons

5. What is the total number of churches, the number of accommodated, and the value of church property in the United

States, as shown by the following statistics?

Pounds of
Butter.

Alabama...... 4,008,811

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

Arkansas...... 1,854,239

SUBTRACTION.

69. Subtraction is the process of taking one number from another of the same kind, equal to or greater than itself.

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 928 take 275.

OPERATION.

Minuend,

Subtrahend,

Remainder,

928
275

653

ANALYSIS. We first subtract 5 units from 8 units, and obtain 3 units for a partial remainder. As we cannot take 7 tens from 2 tens, we add 10 tens to the 2 tens, making 12 tens; then 7 tens from 12 tens leave 5 tens, the second partial remainder. Now, since we added 10 tens, or 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 added to 2 hundreds makes 3 hundreds, and this sum subtracted from 9 hundreds leaves 6 hundreds; and we have for the total remainder, 653.

NOTE. The process of adding 10 to the minuend is sometimes called borrowing 10, and that of adding 1 to 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.