each dividend, on the left hand, place such a number for a divisor, as will bring it to the next superior name, and draw a line between them. Begin at the highest, and write the quotient of each division, as decimal parts, on the right of the dividend next below it, and so on, till they are all divided; and the last quotient will be the decimal required.

Ans. .45.

2. Reduce 9s. to the fraction of a pound.
3. Reduce 15cwt. 3чr. 14lb. to the decimal of a ton.

Ans. .79375.

4. Reduce 2qr. 21lb. 8oz. 12dr. to the decimal of a cwt. Ans. .6923828125.

5. Reduce 1qr. Sna. to the decimal of a yard. Ans. .4375. 6. Reduce 5fur. 35rd. 2yd. 2ft. 9in. to the decima' of a mile. Ans. .73603219+.

7. Reduce 3gal. 2qt. 1pt. of wine to the decimal of a hogshead. Ans. .0575396 +.

8. Reduce 1pt. to the decimal of a bushel. Ans. .015625. 9. Reduce 2R. 16p. to the decimal of an acre.

Ans. .6.

CASE III.

To find the decimal of any number of shillings, pence, and farthings by inspection.

NOTE.-A demonstration of this case has been given, page 57.

RULE.

Write half of the greatest number of shillings for the first decimal figure, and if there be an odd shilling, annex a 5 to the half number of shillings, let the farthings in the given pence and farthings, occupy the second and third places, observing to increase their number by 1, if they exceed 12, and by 2, if they exceed 36.

EXAMPLES.

1. Find the decimal of 15s. 94d. by inspection.

2. Find the value of 13s. 6d. by inspection. 3. Find the value of 19s. 84d. by inspection.

Ans. .678.

Ans. .984.

4. Value the following sums by inspection, and find their total-19s. 11 d., 16s. 94d., 1s. 11d., 3s. Cad., 17s. 5 d., 18s. 4 d., 18s. Sid., 19s. 11 d., 13s. 34d., 16s. 0‡d., 17s. 7ąd. Ans. 7.91£.

CASE IV.

To find the value of any given decimal in the terms of the integer.

1. What is the value of .790625 £. ?

Ans. 15s. 9ąd.

As a lower denomination consists of more units than the same value in a higher one, therefore to bring pounds to farthings, we must multiply by the same numbers as in common Reduction.

Hence we deduce the following

RULE.

Multiply the given decimal by that number which it takes of the next denomination to make one of that greater, and cut off as many places for a REMAINDER on the right, as there are places in the given deci mal. Multiply the REMAINDER by the next lower denomination, and cut off for a remainder as before, and so proceed, until the decimal is reduced to the denomination required; the several denominations, standing at the left hand, are the answers required.

2. What is the value of .625 of a shilling? 8. What is the value of .6725 of a cwt.?

Ans. 74d.

Ans. 2qr. 191b. 5oz.
Ans. Sqr. Sna.

4. What is the value of .9375 of a yard? 5. What is the value of .7895 of a mile ?

Ans. 6fur. 12rd. 10ft. 6 in.

6. What is the value of .9378 of an acre?

Ans. SR. 30p. 13ft. 9 in.

7. Reduce .5615 of a hogshead of wine to its value in gallors,

& c.

Ans. 35 gal. 1qt. Opt. 3133g1.

8. Reduce .367 of a year to its value in days, &c.

Ans. 134da. 1h. 7m. 19 sec.

9. What is the value of .6923828125 of a cwt. ?

Ans. 2qr. 21lb. 8oz. 12dr.

10. What is the value of .015625 of a bushel?

11. What is the value of .55 of an ell English?

12. What is the value of .6 of an acre?

Ans. 1 pint.

Ans. 2qr. 3na.
Ans. 2R. 16p.

SECTION XXII.

MISCELLANEOUS EXAMPLES.

Ans. $90.01.3

1. What is the value of 7cwt. 2qr. 18lb. of sugar, at $11.75 per cwt.? 2. What cost 19cwt. Sqr. 14lb. of iron, at $9.25 per cwt.? Ans. $133.84.3.

3. What cost 39A. 2R. 15p. of land, at $87.37.5 per acre? Ans. $3459.50.33.

4. What would be the expense of making a turnpike 87m. 3fur. 15rds., at $578.75 per mile? Ans. $50595.41 1. 5. What is the cost of a board 18ft. 9in. long, and 2ft. 3 in. wide, at $.05.3 per foot? Ans. $2.27.71.

6. Goliah of Gath was 64 cubits high; what was his height in feet, the cubit being 1ft. 7.168in. ?

Ans. 10ft. 4.592in. 7. If a man travel 4.816 miles in an hour; how long would he be in travelling from Bradford to Boston, the distance being 294 Iniles? Ans. 6h. 50m. 6sec.+ 8. What is the cost of 5yd. 1qr. 2na. of broadcloth, at $ 5.62} per yard? Ans. $30.23.4}. 9. Bought 17 bags of hops, each weighing 4cwt. Sqr. 7lb., at $5.87 per cwt.; what was the cost? Ans. $480.64.87. 10. Purchased a farm, containing 176A. SR. 25rds., at $75.37 per acre: what did it cost? Ans. $13334.30.819.

11. What cost 17625 feet of boards, at $ 12.75 per thousand? Ans. $224.71.83. 12. How many square feet in a floor 19ft. Sin. long, and 15ft. 9in. wide? Ans. 303ft. 27in.

13. How many square yards of paper will it take to cover a room 14ft. 6in. long, 12ft. 6in. wide, and 8ft. 9in. high?

Ans. 52 yd.

14. How many solid feet in a pile of wood 10ft. 7in. long, 4ft. wide, and 5ft. 10in. high?

Ans. 24617ft.

15. How many garments, each containing 4yd. 2qr. 3na., can be made from 112yd. 2qr. of cloth?

Ans. 24.

16. Bought 1gal. 2qt. 1pt. of wine for $1.82; what would be the price of a hogshead? Ans. $70.56.

17. Bought 1254yd. of lace for $15.06; what was the price of 1 yard? Ans. $0.12.

18. What cost 17cwt. Sqr. of wool, at $35.75 per cwt.?

Ans. $634.56.2.

19. What cost 7hhd. 47gal. of wine, at $87.25 per hhd.?

Ans. $675.84

20. How many solid feet in a stick of timber 34ft. 9in. long,

1ft. Sin. wide, and 1ft. 6in. deep?

Ans. 65.15625ft.

21. How many cwt. of coffee in 17 bags, each bag containing 2cwt. 1qr. 7lb.? Ahs. 41cwt. Oqr. 54lb. 22. If 18yd. 1qr. of cloth cost $36.50, what is the price of 1 yard?

Ans. $2.00. 23. If $477.72 be equally divided among 9 men, what will be each man's share? Ans. $53.08. 24. A man bought a barrel of flour for $5.37.5, 7gal. of molasses for $1.78, 9 gal. of vinegar for $1.1875, 1 gal. of wine for $1.125, 14lb. of sugar for $1.275, and 5lb. of tea, for $2.625 ; what did the whole amount to?

25. A man purchased 3 loads of hay; tons, the second 83 tons, and the third 1 value of the whole, at $ 17.625 a ton? 26. At $13.625 per cwt., what cost 3cwt.

27. At $125.75 per acre, what cost 37A.

Ans. $13.36.7. the first contained 2} tons; what was the Ans. $128.88.21. 2qr. 7lb. of sugar? Ans. $48.53.91. 3R. 35rds. ? Ans. $4774.57.0

28. At $11.25 per cwt. what cost 17cwt. 2qr. 21lb. of rice ?

Ans. $198.98.4.

29. What cost 7 bales of cotton, each weighing 3.37cwt., at $9.37 per cwt.? Ans. $244.85.1 30. What cost 7hhd. 49gal. of wine, at $97.625 per hhd. ? Ans. $759.30.535

31. What cost 7yd. 3qr. 3na. of cloth, at $ 4.75 per yard? Ans. $37.70.3}. 82. What cost 27T. 15cwt. 1qr. Slb. of hemp, at $183.62 per ton? Ans. $5098.03.75 33. What is the cost of constructing a railroad 17m. 3fur. 15rd., at $1725.87.5 per mile? Ans. $30067.97.833.

32

SECTION XXIII.

EXCHANGE OF CURRENCIES.

PREVIOUS to the year 1776, all accounts in this country were kept in pounds, shillings, perce, and farthings; but owing to the depreciation of the currency, a dollar was estimated differently in different countries.

In New England, Virginia, Kentucky, Tennessee, and Ohio, the dollar is valued at

6s. Od.

New York. North Carolina, and New Jersey,

8s. Od.

Pennsylvania, Delaware, and Maryland,

7s. 6d.

South Carolina and Georgia,

4s. 8d.

Canada and Nova Scotia,

5s. Od.

England and Newfoundland (sterling),

4s. 6d.

In order, therefore to change any of the above currencies to federal money, the shillings, pence and farthings, if there be any, must first be reduced to decimals of a pound, and annexed to the pounds. We then adopt this general

RULE.

Divide the pounds by the value of a dollar in the given currency, EXPRESSED BY A FRACTION OF A POUND; that is, to change the old New England currency to federal money, divide by because 6 shillings is of a pound.

10

To change the old currency of New York, &c., to federal money, divide by ; because 8 shillings is of a pound.

To change the old currency of Pennsylvania, &c., to federal money, divide by ; because 7 shillings and 6 pence is of a pound.

To change the old currency of South Carolina and Georgia to federal money, divide by; because 4 shillings and 8 pence is of a pound.

To change Canada and Nova Scotia currency to federal money, divide by ; because 5 shillings is of a pound.

To change English (sterling) money to federal money, divide by; because 4 shillings and 6 pence is of a pound.

To change sterling money to lawful money, add to the sterling, and the sum will be the lawful; because 4 shillings and 6 pence sterling is 6 shillings lawful; and, for the same reason, take from the lawful, and the remainder will be sterling.

To reduce federal money to any of the above currencies, the federal money must be MULTIPLIED by the above fractions.

EXAMPLES.

1. Change 18£. 4s. 6d. of the old New England currency to federal money.

18.225.÷$60.75 Answer.

In this example we reduce the 4 shillings and 6 pence to a decimal of a pound, which we find to be .225. This decimal we annex to the pounds, and multiply the 18.225£. by 10, and divide by 3, and it produces the answer $60.75. The reason for this process has already been shown.

2. Change $ 60.75 to the old currency of New England.

$60.75X18.225=18£. 4s. 6d. Answer.

=

'The decimal .225 is reduced to shillings and pence by Case IV. of Decimal Fractions.