There are 12 calendar months in a year, each of which contains 31 days, except April, June, September, and November, which have 30 days, and February, which has 28. There are really 365 days, 5 hours, 48 minutes, and 49.7 seconds in a year, or nearly 365 days; so one year in four, we give to February 29 days, thereby making the year consist of 366 days; such a year is called leap year. As this allowance is a little too much, we omit 3 leap years in 400 years. Any year, at the end of a century, that can be divided by 400 without a remainder, is leap year, as 1200, 1600, 2000. Any other year that can be divided by 4 without a remainder, is also leap year, as 1836, 1840, 1844. 4 weeks are sometimes called a month.

DIVISION OF CIRCLES.

The circumference of every circle, whether great or small, is considered to be divided into 360 equal parts, called degrees.

How many calendar months are there in a year? How many days does each month contain? What is the real length of the year? What then is done one year in four? What is such a year called? How many leap years do we omit in 400 years? Why? What years are leap years? What are 4 weeks sometimes called?

How is the circumference of every circle, whether great or small, considered to be divided?

REDUCTION, OR CHANGE OF FORM OF COMPOUND NUMBERS.

LESSON 97.

To be performed in the mind.

1. How many ounces of butter are there in 2 pounds 3 ounces ?

2. How many yards, and how many odd feet are there in a pole 10 feet long? 13 feet long?

3. How many quarts are there in 2 bushels? In 1 bushel 2 pecks?

4. A grocer on the 4th of July, retailed 10 quarts 1 pint of wine; how many gallons and odd quarts and pints did he sell?

5. If you are 3 hours and 5 minutes getting your lesson, how many minutes are you?

6. How many weeks are there in 28 days? In 32 days? In 37 days?

7. At 1 dollar an ounce, how much are 2 pounds of old silver worth? 3 pounds? 5 pounds? 1 pound 3 ounces? 8. How many gallons of molasses are there in 16 pints? In 76 pints? In 15 quarts? In 35 quarts;

9. How many square inches are there in 2 square feet 12 square inches ?

10. A man bought 48 pecks of oats at different times, and gave $6 in payment; what price a bushel did he give?

For the Slate.

11. A farmer had 5 cwt. 3 qrs. 12 lbs. of cheese; how many pounds had he?

OPERATION.

5

3

4

20

12

Explanation. There are 4 qrs.

so to

cwt. qrs. lbs. in 1 cwt., so to get the number of
qrs. we multiply the 5 cwt. by 4,
and add the 3 qrs. to the product.
There are 28 lbs. in a qr.,
get the number of lbs. we multi-
ply the 23 qrs. by 28, and add the
12 lbs. to the product.

Add 3 qrs.

23

28

Therefore, to change or reduce a quantity to a lower denomination,

Multiply the highest denomination in it by so many of the next lower as make one of this highest, and add to the product the number in the lower denomination; multiply the result in the same way, and so on until the quantity be brought into a denomination as low as desired.

12. A farmer having 656 lbs. of cheese, wished to know how many cwt. he had; how many had he?

OPERATION.

4

Explanation. There being 28 lbs. in 1 qr., we divide 656

28) 656 (23 ( 5 cwts. lbs. by 28, and get 23 qrs. and

56

20

12 lbs. over.
qrs. in 1 cwt., we divide 23
qrs. by 4, and get 5 cwt. and
3 qrs. over. So 656 lbs. are
5 cwt. 3qrs. 12 lbs.

There being 4

Therefore, to change or reduce a quantity to a higher denomination,

Explain how example 11, lesson 97, is performed.

How do we change or reduce a quantity to a lower denomination? Explain how example 12, lesson 97, is performed.

Divide by as many as it takes to make one of the next higher denomination; divide the quotient in the same way, and so on until the quantity be brought into a denomination as high as desired.

The operations under either of the two preceding rules are proved by reversing them. Thus the operation in example 11 is reversed in example 12, and the operation in example 12 is reversed in example 11

Note. Each example should now be proved.

LESSON 98.

For the Slate.

1. How many tons are there in 36,000 ounces?

Ans. 1 T. 10 lbs 2. How many pounds are there in 5 tons? Ans. 11,200. 3. A jeweller has 4,312 pennyweights of gold, in various pieces; how many pounds has he?

Ans. 17 lbs. 11 oz. 12 pwts. 4. How many grains of silver are there in 6 ounces?

Ans. 2,880. 5. How many grains of ipecacuanha are there in 2lb 43 23 09 1 gr. ? Ans. 13,561. 6. How many ounces of calomel are there in 640 grains ? Ans. 13 23 29.

7. A surveyor has a chain containing 100 links, each link being 7.92 inches long; how many rods are there in the chain?

8. How many fathoms are there in 2 leagues?

Ans. 4.

Ans. 5,280.

9. A man sold a house lot 6 rods long and 4 rods wide, at $.0625 a square foot; what sum did it bring?

Ans. $408.375. See lesson 82, Decimal Fractions. 10. How many square yards of carpeting will cover a floor 18 feet long, and 16 feet wide? Ans. 32.

LESSON 99.

1. How many cubic inches are there in a block of wood 3 feet long, 2 feet wide, and 1 foot thick?

Ans. 10,368.

How do we change or reduce a quantity to a higher denomination? How are the operations under either of the two preceding rules proved? Give some examples.

2. How many cords are there in a pile of wood 37 feet long, 4 feet wide, and 5 feet high?

Ans. 5 C. 6 ft. 4 cubic ft. 3. A trader bought some beans at $.50 a peck; what sum must he pay for 12 bushels and 3 pecks? Ans. $25.50 4. How many chaldrons are there in 112 bushels of Richmond coal? Ans. 3 chal. 4 bu.

5. How many pints of milk are there in 12 gallons 3 quarts 1 pint, and how much is the whole worth, at 2 cents a pint ? Ans. 103 pts., and it is worth $2.06. 6. How many firkins of beer are there in 1,313 quarts? Ans. 36 fir. 4 gals. 1 qt.

7. If a man drinks 2 quarts of wine a day, how long will 2 tierces 5 gallons and 2 quarts last him? Ans. 179 days. 8. How many hogsheads of molasses are there in 2,217 quarts? Ans. 8 hhds. 50 gals. 1 qt. 9. How many weeks are there in 1,000,000 seconds? Ans. 1 w. 4 d. 13 h. 46 m. 40 sec. 10. 20 cubic feet of water run over a mill-dam in a second; how many cubic feet will pass over the dam in 1 week 4 days 7 hours 0 minutes 48 seconds?

LESSON 100.

Ans. 19,512,960.

Ans: 62,774.

1. In 17° 26' 14" how many seconds? 2. How many degrees are there in 5,700"? Ans. 1o 35'. 3. How many days were there between the time of the Declaration of Independence, July 4th, 1776, and the time of the settlement of a general peace, January 20th, 1783 ? Ans. 2,391. Explanation. 1780 can be divided by 4 without a remainder.

4. 4 weeks are often called a month; how many of such months are there in 67 days? Ans. 2 mo. 1 w. 4 d. 5. A man dug a cellar 36 feet long, 24 feet wide, and 6 feet deep; how many cubic yards of earth did he take out of it?

Ans. 192.

6. A farmer sold some oak wood at $1 a foot; how much did he get for 3 cords and 7 feet? Ans. $31. 7. How many rods are there in 1 mile and 33 rods ?

Ans. 353.

8. How many leagues and fathoms are there in 17 miles and 45 fathoms ? Ans. 5 lea. 1,805 fath.