19. A boat starts with 1652 bushels of wheat aboard; 43 miles down the river, it receives 27 barrels of flour and 3335 bushels of wheat. How many bushels of wheat are then aboard? Ans. 4987 bushels.

43. The sum of a column may consist of more than one figure. In this case, place the right-hand figure under the column added, and add the left-hand figure or figures to the next left-hand column.

If the sum of a column is 64, write down 4 and add 6 to the figures of the next left-hand column; if it is 127, write down 7 and add 12 to the next column.

EXAMPLE.-Add 3658, 4903, 7006, and 734.

Write the numbers, units under units, tens under The sum of the tens, &c. Begin to add at the right. units is 21,-2 tens and 1 unit. Write the 1 unit in the units' place, and add the 2 tens to the tens in the next column.

2 and 3 are 5, and 5 are 10. 10 tens are 1 hundred and 0 tens. Write 0 in the tens' place, and add the 1 hundred to the hundreds in the next column.

1 and 7 are 8, and 9 are 17, and 6 are 23. 23 hundreds are 2 thousands and 3 hundreds. Write 3 in the hundreds' place, and add the 2 thousands to the thousands in the next column.

Ten-thousands.

Hundreds.

Co Thousands.

Tens.

∞ Units.

3658

4903

7006 734

2 and 7 are 9, and 4 are 13, and 3 are 16. 16 thou- Ans. 1 6301 sands are 1 ten-thousand and 6 thousands. This being the last column, write them down. Ans. 16301.

Read and add the following numbers; prove each example:

43. When the sum of a column consists of more than one figure, what must we do? If the sum of a column is 64, what do we do? If it is 93? If it is 127? If the sum of a column is expressed by three figures, how many do we write down, and how many do we add to the next column? Add the numbers in the given example.

44. Rule for Addition,

1. Write units under units, tens under tens, &c.

2. Beginning at the right, find the sum of each column. 3. If the sum is expressed by one figure, write it under the column added; if not, place the right-hand figure there, and add the left-hand figure or figures to the next column.

4. Prove by adding in the opposite direction.

EXAMPLES FOR PRACTICE.

1. Add 123405, 2354210, 354, 794327, and 36547.
2. Add 27562, 345607, 2461, 4567801, and 365.
3. Add 1034001, 78954, 379205, 367001, and 45637.
4. Add 11, 4562, 773, 15266, 8958, and 66666.

5. Add 100375, 406780, 4673005, 4112, 18365791, 2478, and 164357. Ans. 23716898.

6. What is the sum of three hundred thousand, six hundred and fifty; seven thousand, eight hundred and thirty-two; eleven thousand, five hundred and sixty-seven; ten thousand and fiftysix; four hundred and seventy-two? Ans. 330577.

7. A man drew five loads of bricks. In the first load, he had 1209; in the second, 1458; in the third, 1101; in the fourth, 1212; in the fifth, 1303. How many bricks were there in all?

8. If there are shipped from the United States, 15624 barrels of flour to Sweden, 250 barrels to Holland, 205154 to England, 6401 to Cuba, and 19602 to Mexico, how many barrels are shipped altogether?

9. Find the sum of eighty-eight million, and nineteen; fortyseven thousand, and sixty-eight; nine million, seven hundred and eighty-five thousand; nice hundred and eighty-six; eight billion, seven million. Ans. 8104833073.

10. How many square miles in British America, there being 2,436,000 square miles in the Hudson's Bay Territories, 357822 in Canada, 27704 in New Brunswick, 18746 in Nova Scotia, 2134 in

2

Prince Edward's Island, 35913 in Newfoundland, and 19 in the
Bermuda Islands?
Ans. 2878338 square miles.

11. It is computed that there are two million pagans in North America, two million in South America, one million in Europe, five hundred and ten million in Asia, sixty-five million in Africa, and twenty-four million in Oceania. How many pagans are there in the world? Ans. 604,000,000.

12. Maine, the largest of the New England States, contains 31766 square miles. New York, the largest of the Middle States, contains 15234 square miles more than Maine. How many square miles in New York?

13. A person has $1557 in one bank, $2343 in another, and in a third as much as in both the other two. How much has he in the third bank? How much in all three?

14. A lady gave $3445 for a house and $1055 for furniture. She then bought some adjoining land for as much as both house and furniture cost. What did she give for the whole?

15. Wellington's army at Waterloo consisted of 49608 infantry, 12402 cavalry, and 5645 artillery-men. How many men

did it contain in all?

16. Napoleon's army at Waterloo consisted of 48950 infantry, 15765 cavalry, and 7232 artillery-men. How many men did it contain in all?

17. How many men did both Wellington's and Napoleon's army at Waterloo contain? Ans. 139602 men. 18. How many bushels of wheat are there on four boats, each of which contains 5250 bushels of wheat and 45 barrels of flour?

Ans. 21000 bushels.

19. President Madison was born in 1751, and attained the age

of eighty-five; in what year did he die?

20. How many strokes does a clock strike in 24 hours? 21. A lady gave each of her three daughters $9250, and her son $8345. How much did she distribute among them?

22. The earth is 95298260 miles from the sun. The planet Neptune is 2767105740 miles farther. What is Neptune's distance from the sun?

23. A has $4250; B has $375 more than A; C has as much as A and B together. What are all three worth? Ans. $17750.

24. How far is it from New York to Buffalo, the distance from New York to Albany being 150 miles, from Albany to Rochester 251 miles, and from Rochester to Buffalo 75 miles?

25. A man worth $12500 makes as much more, and has $5490 left to him. What is he then worth? Ans. $30490.

26. Required the whole population of the world, that of N. America being estimated at 46000000; S. America, 20000000; Europe, 280000000; Asia, 680000000; Africa, 80000000; and Oceania, 28000000.

27. How many men in an army consisting of four regiments, two of nine hundred and eighty men each, and two of twelve hundred and forty? Ans. 4440 men.

28. A merchant bought $1786 worth of books, and $875 worth of stationery. On the books he gained $549, and on the stationery $228. What did he sell the books for? What did he sell the stationery for? What was his whole gain?

Ans. Books, $2335. Stationery, $1103. Gain, $777. 29. In 1862, the postal revenue of the U. S. amounted to $8299820; in 1863, it was $2863969 more. What did it then amount to?

30. If I invest $2356 in pork, and $1977 in beef, and sell them so as to gain $395, how much do I receive for the whole? 31. A man left his wife $95000; each of his three sons, $15000; his daughter, $34000; and the rest of his property, which amounted to $47250, to charitable societies. What was the whole value of his estate? Ans. $221250.

32. A's orchard contains 146 apple-trees; B's, 22 pear-trees, 9 plum-trees, and 27 apple-trees; C's, 18 plum-trees, 139 appletrees, and 38 pear-trees. How many apple-trees in all three orchards? How many pear-trees? How many plum-trees? How many trees altogether?

33. The salary of the Vice-President of the United States is $8000 a year; that of the President is $17000 more. What do the yearly salaries of both amount to?

34. A certain school opens with 78 boys and 129 girls, Within 30 days there is an addition of 42 boys and 39 girls. How many does the school then contain?

Ans. 1807.

35. Add LXVI., MDXIX., CCIV., XVIII. 36. Add MD., VCXXX., XLIV., CXV., X. Ans. 1015789.

45. Practise the following examples till they can be added at sight up and down, naming the results only. Thus, in Example 1:-three, eight, fourteen, sixteen, seventeen, twenty-three, thirty, thirty-four, thirty-sixwrite 6 in the units' place, and add 3 to the next column.