3. From 3 T. 15 cwt. 18 lb. take 1 T. 7 cwt. 9 lb. 6 oz. 4. From 340 bu. 2 pk. 4 qt. take 116 bu. 3 pk. 6 qt.

5. From a cask containing 36 gal. 2 qt. of vinegar, 18 gal. 3 qt. 1 pt. was drawn. How much remained?

6. From 25 mi. 150 rd. 12 ft. take 16 mi. 120 rd. 144 ft. 7. From 145 A. 96 P. subtract 120 A. 105 P.

10. 31⁄2 lb. Troy and § lb. Troy. 16. .976 A. and ✯ A.

20. A merchant tailor sold cloth that cost him £228 10s.

10 d. for £300 6s. 10d. What was his profit?

21. From a piece of land containing .75 A., a piece was sold, containing 80 sq. rd. 140 sq. ft. 96 sq. in.; how much remained?

22. From a bin containing 130 bu. 1 pk. 6 qt. of corn, 75 bu. 21 pk. were sold; how much remained unsold?

23. From 1 gross of steel pens, 7 doz. 10 pens were sold; how many were left?

24. From a pile of wood containing 124§ cords, was sold at one time 32 Cd., at another 24 Cd. 5 cd. ft., and at another 28 Cd.; how much remained?

297. To find the time between two dates.

1. What length of time elapsed from 2 o'clock P. M., Sept. 4, 1862, to 10 o'clock A. M., April 15, 1880?

OPERATION.

yr.

mo. da. hr.

1880

4

15

10

1862

9

4

14

17

7 10 20

EXPLANATION. Write the later date for the minuend, and the earlier for the subtrahend, giving the month its number instead of the name. Usually, 12 mo. are reckoned as a year, and 30 da. a month. But to be exact, the true number of days in each month and parts of a month must be reckoned when the time is less than a year. When hours are to be obtained, reckon from 12 o'clock, night.

Find the time

2. From May 12, 1848, to June 1, 1860.

3. From June 1, 1861, to Oct. 20, 1872.

4. From April 1, 1875, to August 16, 1879.

5. From May 10, 1878, to 3 o'clock P. M., Nov. 4, 1881. 6. Money borrowed July 9, 1877, was paid June 26, 1879. How long was it kept?

7. The American civil war began April 11, 1861, and closed April 9, 1865. How long did it continue?

8. How long has a note to run that is dated May 20, 1876, and made payable Sept. 12, 1880 ?

9. How many years, months, and days from your birthday to this date; or what is your age?

10. A note dated July 15, 1879, was paid May 21, 1882; how long did it run?

11. I started on a tour around the world at 10 o'clock A. M., Aug. 8, 1879, and returned to the same depot at 4 o'clock P. M., May 10, 1881. How long was I absent?

12. The construction of the Brooklyn Suspension Bridge was commenced Jan. 3, 1870, and opened for travel July 4, 1882. How long was it in building?

298. To multiply a denominate number by an ab

stract number.

1. Multiply 7 bu. 3 pk. 6 qt. 1 pt. by 6.

EXPLANATION.-Write the multiplier under the lowest denomination of the multiplicand, and multiply as in simple numbers. Thus, 6 times 1 pt.

OPERATION.

7 bu. 3 pk. 6 qt. 1 pt. 6

are 6 pt., equal to 3 qt. Write a cipher 47 bu. 2 pk. 7 qt. 0 pt. under the pints, and reserve the 3 qt.

to be added to the product of quarts. 6 times 6 qt. are 36 qt., and 3 qt. added make 39 qt., equal to 4 pk. and 7 qt. Write the 7 qt. in the product under the quarts, and reserve the 4 pk. to be added to the product of pecks. Proceed in the same manner with each denomination until the entire product is found.

When the multiplier is large and a composite number, multiply successively by its factors. (81.)

2. Multiply 5 lb. 8 oz. 10 pwt. by 6; by 7; by 8. 3. Multiply 7 T. 12 cwt. 10.5 lb. by 8; by 9; by 7. 4. How many bushels of corn will 12 A. produce, if 1 A. yield 38 bu. 2 pk. 6 qt.?

5. What is the weight of 2 doz. spoons, if each spoon weighs 3 oz. 12 pwt. 15 gr.?

6. How much land in 5 farms, each farm divided into 8 fields, and each field containing 12 A. 120 P.?

7. Find the weight of 32 carloads of coal, by the long ton, each weighing 5 T. 7 cwt. 2 qr. 24 lb. 10 oz.

8. If 1 hhd. of sugar weighs 6 cwt. 28 lb., what is the weight of 8 hhd., and their value, at 9 cts a pound?

Find the product in integers of lower denominations of

9. 5 A. by 16. 10. mi. by 9. 11. 8.125 pk. by 24. 12. 6 lb. Troy by 36. 13. 8.84 T. by .9.

14. 2 da. 9.48 hr. by 42. 15. 7.125 cwt. by 1.6. 16. 4g hhd. by 15.

17. 5.2 wk. by 28.

18. 2 bu. 2.45 pk. by 10.

299. To divide a denominate number into equal parts.

1. Divide 47 bu. 3 pk. 6 qt. by 7.

OPERATION.

7) 47 bu. 3 pk. 6 qt.

6 bu. 3 pk. 34 qt.

EXPLANATION.- -Write the divisor at the left of the dividend, and proceed to find one seventh of the given number. Thus, of 47 bu. is 6 bu. and a remainder of 5 bu. Write the 6 bu. in the quotient, and reduce the 5 bu. to pecks, which added to 3 pk. make 23 pk. of 23 pk. is 3 pk. and a remainder of 2 pk. Write the 3 pk. in the quotient, and reduce the 2 pk. to quarts, which added to 6 qt. make 22 qt. of 22 qt. is 34 qt., which write in the quotient.

2. Divide 15 lb. 9 oz. 12 pwt. 17 gr. by 4; by 6; by 8. 3. Divide 3 T. 12 cwt. 14 lb. 13 oz. by 3; by 9; by 7 4. Divide b69 36 32 00 gr. 18 by 9; by 4; by 12. 5. Divide 1946 gal. 3 qt. 1 pt. by 35; by 42.

When the divisor is large and a composite number, the work may be shortened by dividing successively by its factors. (103.)

weighing 1 lb. 10 oz. 6 pwt.;

16. Bought 12 spoons, what was the weight of each spoon?

17. A town containing 16 sq. miles was equally divided into 120 farms. What was the size of each farm?

18. From the sum of 61 gal. 3 qt. 1 pt., and 36 gal. 1 pt., take 28 gal. 2 qt., and divide the result by 18; by 24; by 30. 19. In excavating a cellar 3240 cu. ft. of earth was removed by 3 men in 8 days. How many cubic yards did each man remove daily?

20. How many times is £5 1s. 8d. contained in £25 8s. 4d.? Reduce both dividend and divisor to the same denomination; then divide as in simple numbers.

21. How long will 5 bu. 2 pk. 4 qt. of oats feed a horse, if he eats 1 pk. 4 qt. a day? If 1 pk. 6 qt.?

300. The Meridian of any place is an imaginary line passing from the North Pole to the South Pole through that place.

301. The Longitude of any place is its distance east or west from some assumed meridian.

The English and Americans usually reckon longitude from the meridian of Greenwich, England.

Since the earth turns upon its axis once in 24 hours, it follows that of 360°, or 15° of longitude passes under the sun in 1 hr., and of 15°, or 15', passes under the sun in 1 min., and of 15', or 15", passes under the sun in 1 sec. of time. Hence, the following

As the earth revolves from west to east, places east of a given meridian have midday sooner, and are said to have earlier, or faster time, because the sun appears to them earlier; and for similar reasons places west are said to have later or slower time.