1. When hours are to be obtained, reckon from 12 at night, and ff minutes and seconds, write them still at the right of hours.

2. In finding the difference of time between two dates, 12 mo. are usually considered a year, and 30 days a month.

3. When the time is less than a year, the true number of days in each month and parts of a month is added.

4. The day on which a note, draft, or contract is dated, and that on which they mature, are not both included. The former is generally omitted.

2. The war between England and America was commenced April 19, 1775, and peace was restored Jan. 20, 1783. What length of time did the war continue?

3. The American Civil War began April 11, 1861, and closed April 9, 1865. What time did it continue ?

4. How long has a note to run that is dated Jan. 16, 1873, and made payable July 10, 1875 ?

5. A note dated May 28, 1875, was paid Feb. 10, 1876. What length of time did it run?

6. A person started on a tour of the world at 9 o'clock A.M., Sept. 3, 1874, and returned to the same depot at 3 P.M., July 15, 1876. What time was he absent ?

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

8. How many days from June 20th to the 10th of Jan. following?

9. What length of time elapsed from 12 o'clock M., Jan. 10. 1876, to June 16, 9 o'clock A.M.?

10. What length of time elapsed from 16 min. past 16 o'clock A.M., July 4, 1873, to 22 min. before 8 o'clock P.M., Dec. 12, 1875 ?

11. What length of time will elapse from 40 min. 25 sec. past 12 o'clock M., April 21, 1875, to 4 min. 36 sec. before 5 o'clock P.M., Jan. 1, 1878?

MULTIPLICATION.

WRITTEN EXERCISES.

443. 1. Multiply 28 rd. 2 yd. 2 ft. by 7.

OPERATION.

28 rd. 2 yd. 2 ft. ry

199

1 (1) 2

=1

6 in.

199

2

0

6

ANALYSIS.-Write the multi plier under the lowest denomination of the multiplicand, and multiply.

7 times 2 ft. are 14 ft., equal to 4 yd. 2 ft. Write the 2 ft. under the feet, and reserve the 4 yd. to add to the product of yards.

7 times 2 yd. are 14 yd., and 4 yd. added make 18 yd., equal to 3 rd. 14 yd. Write the 1 yd. under the yards, and reserve the 3 rd. to add to the product of rods.

7 times 28 rd. are 196 rd., and 3 rd. added make 199 rd., which write under the same denomination.

Theyd. is equal to 1 ft. 6 in., which added to the product, gives 199 rd. 2 yd. 6 in. for the entire product.

1. The multiplier must be an abstract number. (103.)

2. When the multiplier is large and is a composite number, the work may be shortened by multiplying successively by its factors. (109.)

2. In 9 bbl. of walnuts, each containing 2 bu. 3 pk. 6 qt., how many bushels ?

3. If a man cut 3 Cd. 36 cu. ft. of wood in 1 da., how cords can he cut in 12 days?

many

4. Multiply 8 gal. 3 qt. 1 pt. 3.25 gi. by 96.

5. If 1 A. produce 42 bu. 1 pk. 5 qt. 1 pt. of corn, how many bushels will 64 A. produce?

6. Multiply 0.8 f39 £36 m 34 by 24.

7. What will 84 yd. of cloth cost, at £1 8s. 91d. a yd.?

8. If $80 will buy 3 A. 24 P. 20 sq. yd. 4 sq. ft. of land, how much will $4800 buy?

9. How many bushels of grain in 47 bags, each con

10. If a load of coal by the long ton weigh 1 T. 6 cwt. 2 qr. 26 lb. 10 oz., what will be the weight of 67 loads? 11. Multiply 4 yd. 1 ft. 4.7 in. by 125.

12. Multiply 7 T. 15 cwt. 10.5 lb. by 1.7.

13. At $1.37 a gallon, what will be the cost of 5 casks. of wine, each containing 28 gal. 2 qt. 1 pt.?

14. A farmer sold 4 loads of oats, averaging 41 bu. 3 pk. each, at $.75 a bushel. What did he receive for the whole?

DIVISION.

444. 1. Divide 56 lb. 9 oz. 12 pwt. by 6.

OPERATION.

lb. Oz. pwt.

6)56

9

12

9

5

12

ANALYSIS.-Write the divisor at the left of the dividend. The object is to find 1 sixth of a compound number.

of 56 lb. is 9 lb. and a remainder of 2 lb. Write the 9 lb. in the quotient, and reduce

the 2 lb, to ounces, which, added to 9 oz., make 33 oz.

of 33 oz. is 5 cz. and a remainder of 3 oz. Write the 5 oz. in the quotient, and reduce the 3 oz. to pwt., which added to 12 pwt.. make 72 pwt. of 72 pwt. is 12 pwt., which write in the quotient.

2. Divide 358 A. 57 P. 6 sq. yd. 2 sq. ft. by 7.
3. Divide £35 9s. 7d. by 5; by 7; by 8.

4. Divide 282 bu. 3 pk. 1 qt. 1 pt. by 9; by 10; by 12.

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

5. Divide 254 yd. 4 ft. 34 in. by 21; by 42.

6. Divide 196 Cd. 4 cd. ft. 12 cu. ft. by 72.

7. How many iron rails, each 16 ft. long, are required to lay a railroad track 26 mi. long?

8. Divide 24 sq. mi. 140 P., by 221.

9. Divide 202 yd. 1 ft. 6 in. by .

10. Divide 336 bu. 3 pk. 4 qt. by 4 bu. 3 pk. 2 qt.

Reduce both dividend and divisor to the same denomination, and divide as in simple numbers.

11. How many boxes, each holding 1 bu. 1 pk. 7 qt., can be filled from 356 bu. 3 pk. 5 qt. of cranberries ? 12. Divide 311 gal. 1 qt. 1 pt. by 53.

OPERATION.

53)311 gal. 1 qt. 1 pt. (5 gal. 3 qt. I pt.

13. The aggregate weight of 41 hhd. of sugar is 19 T. cwt. 22 lb. What is the average weight?

14. If a town 4 mi. square be equally divided into 62 farms, how much land will each farm contain ?

LONGITUDE AND TIME.

445. The Longitude of a place is its distance east or west from a given meridian, measured on the equator.

The meridian from which longitude is reckoned is called the first meridian, and is marked 0°. All places east of this, within 180°, are in east longitude, and all places west, within 180°, are in west longitude.

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

446. Since the earth revolves on its axis once in 24 hours, the sun appears to pass from east to west around the earth, or through 360° of longitude once in 24 hours of time. Hence in 1 hour the sun appears to pass through of 360°, or 15°; in 1 minute, through of 15°, or 15'; and in 1 second, through of 15', or 15".

1. Since the sun appears to move from east to west, when it is 12 o'clock at one place, it will be past 12 o'clock at all places east, and before 12 at all places west. Hence, knowing the difference of time between two places, and the exact time at one of them, the exact time at the other is found by adding their difference to the given time, if it is east, and by subtracting, if it is west.

2. If one place is in east and the other in west longitude, the difference of longitude is found by adding them, and if the sum is greater than 180°, by subtracting it from 360°.