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3. In 278. 19° 51' 28" how many seconds ? 4. How many signs in 2987488 seconds ?

1 gross.

12 gross

MISCELLANEOUS TABLE. Art. 100. This table embraces a variety of things in business important to be known. 12 units

make 1 dozen. 12 dozen

1 great gross. 20 units

1 score. 14 pounds of Iron 'or Lead

1 stone. 60 pounds of Wheat

1 bushel. 60 pounds of Clover-seed

1 bushel. 60 pounds of Beans

1 bushel. 60 pounds of Potatoes

1 bushel. 52 pounds of Onions

1 bushel. 70 pounds of Corn on the Cob

1 bushel. 56 pounds of Shelled Corn

1 bushel. 56 pounds of Rye

1 bushel. 56 pounds of Flax-seed

1 bushel. 45 pounds of Timothy-seed

1 bushel. 20 pounds of Bran

1 bushel. 48 pounds of Barley

1 bushel. 52 pounds of Buckwheat

1 bushel in Pa., Ky., &c. 48 pounds of Buckwheat

1 bushel in Mass. 32 pounds of Oats

1 bushel in Ms., Ill., O., &c. 30 pounds of Oats

1 bushel in Me., N.H. &c. 24 pounds of Oats

1 bushel in Pa.

QUESTIONS. - How do you reduce signs to seconds ? Give the reason of the operation. How do you reduce seconds to degrees ? To signs ? Give the reason for the operation. How many degrees in a circle ? - Art. 100. What is embraced in the miscellaneous table ?

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MISCELLANEOUS EXERCISES IN REDUCTION.

1. In $345.18 how many mills ? 2. How many dollars in 345180 mills ? 3. In 46£ 18s. 5d. how many farthings ? 4. How many pounds in 45044 farthings ? 5. Reduce 6116. Ooz. 17pwt. 17gr. troy to grains. 6. In 351785 grains troy how many pounds ? 7. How many scruples in 271 37 13 19 ? 8. In 7852 scruples how many pounds ? 9. In 83T. 11cwt. 3qr. 181b. how many ounces ? 10. How many tons in 2675088 ounces? 11. How many nails in 97yd. 3qr. 3na. ? 12. In 1567 nails how many yards ? 13. In 57 ells English how many yards ? 14. How many ells English in 71yd. lqr. ? 15. How many inches in 15m. 7fur. 18rd. 10ft. 6in. ? 16. In 1009530 inches how many miles ? 17. In 95,000,000 of miles how many inches ? 18. How many miles in 6,019,200,000,000 inches? 19. In 48deg. 18m. 7fur. 18rd. how many feet ? 20. In 17629557 feet how many degrees? 21. How many square feet in 7A. 3R. 16p. 218ft. ? 22. In 342164 square feet how many acres ? 23. How many square inches in 25 square miles ?

QUESTION. —What gives name to the size or form of books ?

24. In 100362240000 square inches how many square miles ? 25. How many cubic inches in 15 tons of timber ? 26. In 1036800 cubic inches how many tons ? 27. How many gills of wine in 5hhd. 17gal. 3qt. ? 28. In 10648 gills how many hogsheads of wine ? 29. How many quarts of beer in 29hhd. 30gal. 3qt. ? 30. In 6387 quarts of beer how many hogsheads ? 31. How many pints in 15ch. 16bu. 3pk. of wheat? 32. In 35632 pints of wheat how many chaldrons ? 33. How many seconds of time in 365 days 6 hours ? 34. In 31557600 seconds how many days ? 35. How many hours in 1842 years (of 365da. 6h. each) ? 36. In 16146972 hours how many years ? 37. How many seconds in 8S. 14° 18' 17" ? 38. In 915497" how many signs ?

39. What will be the cost of 13 gross of steel pens, at 23 cents per pen

Ans. $46.80. 40. Bought 12 reams of paper at 20 cents per quire ; how much did it cost?

Ans. $48. 41. I wish to put 2 hogsheads of wine into bottles that will contain 3 quarts each ; how many bottles are required ?

Ans. 168 bottles. 42. When $1480 are paid for 25 acres of land, what costs 1 acre? What costs 1 rood? What cost 37A. 2R. 18p. ?

Ans. $2226.66. 43. John Webster bought 5cwt. 3qr. 18lb. of sugar at 9 cents per lb., for which he paid 25 barrels of apples at $1.75 per barrel ; how much remains due ?

Ans. $9.62. 44. Bought a silver tankard weighing 21b. 7oz. for $46.50; what did it cost per oz. ? How much per lb. ? Ans. $18.

45. Bought 3T. lcwt. 181b. of leather at 12 cents per lb., and sold it at 9 cents per lb. ; what did I lose ?

Ans. $183.54. 46. Phineas Bailey has agreed to grade a certain railroad at $5.75

per rod; what will he receive for grading a road between two cities, whose distance from each other is 37m. 7fur. 29rd. ?

Ans. $69856.75. 47. If it cost $17.29 per rod to grade a certain piece of railroad, what will be the expense of grading 15m. 6fur. 37rd. ?

Ans. $87,781.33. 48. What is the value of a house-lot, containing 40 square rods and 200 square feet, at $1.50 per square foot ?

Ans. $16635.

49. How many yards of carpeting, that is one yard in width, will be required to carpet a room 18ft. long and 15ft. wide ?

Ans. 30 yards. 50. A certain machine will cut 120 shingle-nails in a minute ; how many will it cut in 47 days 7 hours, admitting the machine to be in operation 10 hours per day? Ans. 3434400 nails.

51. In a field 80 rods long and 50 rods wide, how many square rods? How many acres ?

Ans. 25 acres. 52. How long will it take to count 18 millions, counting at the rate of 90 a minute ?

Ans. 138da. 21h. 20m. 53. A merchant purchased 9 bales of cloth, each containing 15 pieces, each piece 23 yards, at 8 cents per yard; what was the amount paid ?

Ans. $248.40. 54. Suppose a certain township is 6 miles long and 44 miles wide, how many lots of land of 90 acres each does it contain ?

Ans. 192 lots. 55. The pendulum of a certain clock vibrates 47 times in 1 minute; how many times will it vibrate in 196 days 49m. ?

Ans. 13267583 times. 56. How many shingles will it take to cover a building that is 36 feet long and 24 feet wide, with rafters 16 feet long, supposing 1 shingle to cover 27 square inches ?

Ang. 6144 shingles. 57. How many times will the large wheels of an engine turn round in going from Boston to Portland, a distance of 110 miles, supposing the wheels to be 12 feet and 6 inches in circumference ?

Ans. 46464 times. 58. In a certain house there are 25 rooms, in each room 7 bureaus, in each bureau 5 drawers, in each drawer 12 boxes, in each box 15 purses, in each purse 178 sovereigns, each sovereign valued at $4.84; what is the amount of the money ?

Ans. $135689400. 59. In 18rd. 5yd. 2ft. llin. how many inches ?

Ans. 3779 inches. 60. In 3779 inches how many rods ?

Ans. 18rd. 5yd. 2ft. 1lin. 61. Sold 5T. 17cwt. 3qr. 181b. of potash for 3 cents per pound; what was the amount ?

Ans. $353.79. 62. A gentleman purchased a house lot that was 25 rods long and 16 rods wide for $100,000, and sold the same for $1.25 per square foot; what did he gain by his purchase ?

Ans. $36,125.

XI. ADDITION OF COMPOUND NUMBERS.

Art. 101. ADDITION of Compound Numbers is the process of finding the amount of two or more compound numbers.

ENGLISH MONEY.

OPERATION.
£. 8. d.

far.

Ex. 1. Paid a London tailor 7£. 13s. 6d. 2far. for a coat; 2£. 17s. 9d. 1far. for a vest; 3£. 8s. 3d. 3far. for pantaloons ; 9£. 11s. 8d. 3far. for a surtout; what was the amount of the bill ?

Ans. 23£. 11s. 4d. 1far. Having written units of the same de

nomination in the same column, we find 7 -13 6 2

the sum of farthings in the right-hand 2 17 9 1 column to be 9 farthings, equal to 2d. 3 8 3 3 and lfar. We write the lfar. under the 9 11 8 3 column of farthings, and carry the 2d. to

the column of pence; the sum of which is Ans. 23 11 4 1 28d., equal to 25. 4d. We write the 4d.

under the column of

pence,

and
carry

the 28. to the column of shillings; the sum of which is 518., equal to 2£. 1ls. Having written the 1ls. under the column of shillings, we carry the 2£. to the column of pounds, and find the whole amount to be 23£. Ils. 4d. 1far.

The same result can be arrived at by reducing the numbers as they are added in their respective columns. Thus, in working the example, we can, beginning with farthings, add in this way: 3far. and 3far. are 6far., equal to 1d. 2far., and lfar. are ld. 3far., and 2far. are ld. 5far., equal 2d. 1far. Writing the lfar. under the column of farthings, carry the 2d. to the column of pence; add 2d. (carried) and 8d. are 10d., and 3d. are 13d., equal to 1s. ld., and 9d. are' ls. 10d., and 6d. are ls. 16d., equal to 28. 4d. Writing the 4d. under the column of pence, carry the 2s. to the column of shillings ; add 28. (carried) and 11s. are 13s., and 8s. are 218., equal to 1£. 18., and 178. are 1£. 188., and 138. are 1£. 31s., equal to 2£. 11s. Writing lls. under the column of shillings, carry the 2£. to the column of pounds, and so find the whole amount to be, as before, 23£. Ils. 4đ. lfar.

Thus the adding of compound numbers is like that of simple numbers, except in carrying ; which difference holds also in subtracting, multiplying, and dividing of compound numbers.

QUESTIONS. — Art. 101. What is addition of compound numbers? How do you arrange compound numbers for addition ? Why? What is the difference between addition of compound and addition of simple numbers ?

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