Boston, October 11, 1844.

Messrs. South & Jones,

3 pieces superfine cloth, 5 do. do. do. 10 pairs 3-point blankets, do. 7 pairs 8-4

4 pieces super welsh flannel, 160 yds. at

.50 per yd.

4 do. fine

do. do.

140 66 at

do do. do. furniture chintz,

150 66

150 " at

40 " at

REDUCTION.

§ 50. Reduction teaches to change quantities from one name or denomination to another, still retaining the same value.

It consists of two parts, descending and ascending.

REDUCTION DESCENDING.

§ 51. Reduction Descending teaches to bring quantities from a higher denomination to a lower.

RULE.

1. Multiply the quantity in the highest denomination, by that number of the next lower which will make an integer, or one in that higher, and write down the product.

2. To this product add the number, if any, which was in the lower denomination before, and multiply the sum by the number of the next lower denomination, which makes an integer in the present one.

3. Proceed in the same manner through all the denominations to the lowest, and the sum last found will be the value of all the quantities which were in the higher denominations taken together.

Q. What is reduction?

Q. Of how many parts does it consist?
Q. Give the rule for reduction descending?

EXAMPLES.

1. Reduce 2417. 3s. 4d. 1gr. to farthings.

2. Reduce 271b. 6oz. and 12dwts. to grains, troy weight.

3. Reduce 47hhd. 16gal. 1qt. to quarts, wine measure.

4. Reduce 287b. 11oz. 7dr. 2scr. to grains.

5. Reduce 1cwt. 3qr. 217b. 14oz. to ounces.

6. Reduce 20r. 4yd. 2ft. 6in. to inches.

7. Reduce lyd. 3qr. 2n. lin. to inches.

8. Reduce 1A. 3R. 20p 14 Sq. yd. to square feet.

9. Reduce 56c. 20 S. ft. to solid inches.

10. Reduce 1t. 3hhd. 40gal. 1qt. to quarts, wine measure. 11. Reduce 2mo. 3wk. 5d. 13hr. to hours.

12. Reduce 2chal. 1bu. 2pk. 7qt. to quarts, dry measure. 13. Reduce 7M. 112A. 3R. 2p. to perches.

14. Reduce 36t. 8cwt. 3qr. 15lb. to ounces avoirdupois. 15. Reduce 98lb. 9oz. 18dwt. to grains, troy weight. 16. How many grains of rhubarb are there in 1876. 7oz. 3dr. 2scr. 16gr.?

17. How many grains of gold are there in a cup weighing 4oz. 2dwt.?

18. How many pounds are there in 75t. 12cwt. 3qr. 12lb.? 19. In 73yd. 3qr. 2n. how many nails?

20. How many barleycorns will reach 100 miles?
21. How many yards in 9mi. 2fur. 18p.?
22. How many perches in 368a. 1r. 26p.?
23. In 3507. 16s. 8d. how many farthings?

24. In 81 guineas, how many pence?

25. In a silver teapot, weighing 15oz. 10dwt., how many grains?

26. In 2532 ells Flemish, how many quarters ?

27. In 48mi. 4fur., how many inches?

28. In 246 acres, how many perches?

29. In a pipe of Sherry wine, how many pints? 30. In 208 hogsheads of beer, how many pints?

31. How many seconds in 10 years 3 months 21 days? 32. In 11s. 14° 18' 22", how many seconds?

33 In 18 tons of round timber, how many inches?
34. In 36 chaldrons, how many quarts?

35. How many nails in 70 E. E. 2qr.?
36. In 456 cents, how many mills?
37. In 1878 dimes, how many mills?
38. In 41 dollars, how many cents?
39. How many mills in 12 eagles ?
40. In 32 half-eagles, how many dollars?

REDUCTION ASCENDING.

$52. Reduction Ascending teaches to bring quantities from a lower denomination to a higher.

RULE.

1. Divide the given quantity by as many of that denomination as make one of the next higher, and write down what remains.

2. Divide the quotient by as many of this as make one of the next higher, and write down what remains, as before.

3. Proceed in the same manner through all the denominations to the highest, and the quotient last found, together with the several remainders, if there be any, will be of the same value as the first quantity proposed.

EXAMPLES.

1. In 9184 pennyweights, how many pounds Troy?

20)9184
12)459.. 4

38lbs. 3oz. 4dwt. Ans.

2. Reduce 100003 farthings to pounds.

3. How many pounds Troy in 6530 dwts.?

4. How many ounces and pounds in 3456 scruples? 5. How many yards in 11616 nails?

6. In 2000 nails, how many ells English?

7. In 95040 poles, how many leagues?

8. In 6272640 square inches, how many square yards? 9. In 63113858 seconds, how many days?

10. How many guineas in 37254 pounds? 11. How many pounds in 8870 guineas?

12. How many pounds avoirdupois are there in 98765 drachms?

13. In 19680 perches, how many acres?

14. In 21880 grains of rhubarb, how many pounds? 15. In 3798 quarters, how many Flemish ells?

16. How many boxes of raisins, each containing 24 pounds avoirdupois, can be filled out of 67584 ounces?

17. In 3072960 inches, how many miles?

18. In 6048 pints of wine, how many puncheons? 19. In 373248 pints of beer, how many butts?

20. In 10108 pints of wheat, how many bushels ?

21. In 1296000 cubic inches, how many tons of hewn timber?

22. In 1920 cubic feet, how many cords?

23. In 10800 minutes, how many signs?

24. In 3058560 cubic inches of round timber, how many tons?

25. In 80640 gills, how many tuns of wine?

26. In 1712 gallons of wine, how many hogsheads?
27. Reduce 413280 minutes into weeks.

28. In 190080 barleycorns, how many miles?
29. In 7094 pecks, how many chaldrons?
30. How many cents in 7100 mills?
31. How many dimes in 8264500 mills?
32. How many dollars in 4700 cents?
33. How many eagles in 630000 mills?

34. In 17064 quarts of ale, how many hogsheads?
35. In 2160 pints of oats, how many bushels?
36. In 31556929 seconds, how many years?
37. In 36481 halfpence, how many pounds?

MISCELLANEOUS EXERCISES.

1. In 45768 pence, how many crowns, at 64 pence each? 2. In a piece of linen, measuring 21 English ells, how

many shirts can be cut, of 3 yards 3 quarters each?

3. How many hours elapsed from the passage of the first bankrupt law of the United States, April, 4, 1800, to the expiration of the same, April 21, 1806; (3654 days to a year)?

4. In 9 pounds of silk, each 16 ounces, how many drachms? 5. How many packages of 10 ounces, are there in 56 pounds of bark?

6. In 27 bales, each of 14 pieces, and each piece 21 yards, 2 quarters, how many Flemish ells?

7. In 3 fields, measuring respectively, 3 acres, 2 roods, 14 perches; 7 acres, 3 roods, 27 perches; and 10 acres, 1 rood, 36 perches: how many square inches ?

8. In a butt of beer, how many tankards of three pints each?

9. From March 8 to December 29, how many hours?

10. How many half-dollars would extend from the earth to the sun, which is 95 millions of miles distant, 5 half-dollars being equal to 6 inches?

11. How many minutes elapsed from the passage of the second bankrupt law of the United States, August 19, 1841, to its repeal, March 3, 1843; (3654 days to a year)?

COMPOUND MULTIPLICATION.

53. Compound Multiplication teaches to find the amount of any given number of different denominations repeated a certain proposed number of times.

GENERAL RULE.

1. Place the multiplier under the lowest denomination of the given quantity.

2. Multiply the number in the lowest denomination by the multiplier, and find how many integers of the next higher denomination are contained in the product, and write down what remains.

3. Carry the integers thus found to the product of the next higher denomination, with which proceed as before, and so on through all the denominations to the highest; and this product, together with the several remainders, taken as one number, will be the whole amount required.

The proof is the same as in simple multiplication.