2. Reduce these farthings to pounds, shillings, and pence: 1000000; 2751486; 918743; 211000; 1740031; 4180426.

3. How many halfpenny buns can be bought for £171, 18s. 64d.; and how many pounds, shillings, and pence in 212121 halfpence? 4. How many farthings in 27514 half-crowns; and how many halfpence in 381 guineas?

5. How many sixpences in £128, 17s. 6d.; and in 413464 pence? 6. Reduce £217, 17s. 6d. to half-crowns, and 1000000 pence to

crowns.

7. Bring 31084 threepenny pieces to half-crowns, and 21304 florins to pounds and farthings.

8. In 81327 half-sovereigns, how many half-crowns and farthings? also bring a million halfpence to half-sovereigns.

AVOIRDUPOIS WEIGHT.

9. Reduce the following to pounds: 3 tons 3 cwt.; 1 ton 1 cwt. 3 qrs. 17 lbs.; 241 tons; 41 tons 4 qrs. 11 lbs.

10. Reduce the annexed to tons, cwt., etc.: 2000000 lbs.; 217846 lbs.; 9817311 lbs. ; 8000981 lbs.

11. Bring 813841 oz. to tons; and 9 tons 2 cwt. 14 lbs. to oz.

TROY WEIGHT.

12. Reduce the following to pounds, etc.: 1841732 gr.; 984731 gr.; 27341 oz.; 8473216 gr.

13. Reduce to grains 21 lbs. 8 oz. 19 dwt. 25 gr.; 41 lbs. 17 dwt. 16 gr.; 408 lbs.

14. A gold ornament weighs 10000 gr.; express its weight in pounds, etc.

APOTHECARIES' WEIGHT.

15. Convert 91371 sc. to pounds; and 71387 gr. to pounds. 16. In 101 oz. 4 dr. 1 sc. how many grains? and in 71384 gr. how many ounces?

LONG MEASURE.

17. Bring the following into inches: 81 ft. 17 in.; 7 m.; 17 m. 400 yds.; 86 leag. 100 po.; 184 m. 3 fur.; 15 po. 4 ft.

18. Convert the annexed into miles, etc.: 18473186 in.; 217421 in.; 9000000 in.; 71384216 in.

CAPACITY.

19. In 314 bus. 2 pks. how many pecks? 187 qrs. how many pints? 20. Bring 21871 pts. to quarters; and 17 qrs. 4 gals. to pints. 21. Bring 3 hhds. 17 gal. to gills; and 1845732 gal. to hogsheads. 22. Bring 1000000 pts. to bushels; and 41784 gal. to quarters.

TIME.

23. Reduce 21 wks. 4 da. 11 hrs. 45 min. to seconds.

24. Find how many weeks, etc., are contained in 171486491 secs. 25. Bring 365 da. to seconds, and 2 yrs. 17 wks. 3 da. to hours. 26. Reduce 1000000 min. to weeks, and 5310000 sec. to days, etc.

CLOTH MEASURE.

27. I have 156 yds. of woollen cloth; find how many nails there are in the piece.

28. In 17343 in. how many nails of cloth?

29. You are required to reduce the two following quantities to inches: 91 ells En. 3 qrs. 3 na. 14 in.; 241 yds. 2 qrs. 2 na. 14 in.

PAPER MEASURE.

30. Bring 40 rms. 15 qrs. 18 sheets into sheets. 31. Reduce 17841 sheets to reams.

ANGULAR MEASURE.

32. In an arc of 25 deg. find the number of seconds.

33. In an arc of 17846 sec. find how many degrees, minutes, and seconds.

34. Bring 25° 25′ 25′′; 171° 18′ 11′′; 29° 17′ 12′′; 90° 0′ 0′′ to seconds.

SURFACE.

35. Reduce 674 sq. yds. to inches, and 1100000 sq. in. to yards. 36. Find how many square inches are contained in an acre, a rood, and a perch separately.

37. Reduce ro. 16 po. 11 yds. to feet, and 9 sq. m. to roods. 38. Find how many acres are in a square mile, and bring the answer to yards.

39. A lake has a surface of 3 ac. 2 ro. 20 po.; find how many persons can bathe in it at once, allowing each bather 5 sq. yds.

40. A field of 4 ac. 3 ro. is divided into lots of 20 per. each; find how many allotments it will make.

41. Bring 8475806 sq. ft. into acres, and 481 ac. 19 po. into feet.

CUBIC.

42. Bring the following into cubic inches: 21 yds.; 7 yds. 18 ft. 275 in.; 19 yds. 2 ft. 11 in.; 365 yds. 26 ft. 1627 in.

43. Convert the annexed into cubic yards: 71384216 in.; 7000000 in.; 81486 ft.; 913274 in.

44. How many inches are there in 1 cub. yd., then convert 1728432 cub. in. into yards.

45. Find how many tons of rough timber are in 37486 cub. ft. 46. How many loads of hewn timber are there in a cargo of 365427 cub. ft.

EXERCISES.-XIV.

MISCELLANEOUS.

1. In £71, 13s. 4d. find how many eightpences. 2. In a ton how many parcels of 4 lbs. each.

3. The length of a street is a mile 25 yds. and 2 ft.; find how many inches in the length of the street.

4. Forty bags of coals were brought to a house, each bag contained 79 lbs.; find how many tons, cwt., etc., were delivered.

5. Find how many minims there are in 14 gal. 2 qts. 1 pt. of quinine.

6. I have a dozen silver spoons, each weighing 1 oz. 9 dwt. 13 gr.; what is the weight of my spoons in grains?

7. Suppose a foot of ground to produce a gill of wheat; how many bushels will a field of 4 ac. 3 ro. 10 po. yield?

8. A tierce of wine is drawn out in half-pints; how many times did the cellarman open the tap? (tierce=42 gallons.)

9. How many oranges at a farthing each can be purchased for £59, 13s. 6d. ?

10. Taking a year of 365 dys. 6 hrs., how many years are there in ten million minutes?

11. If a pendulum vibrates 5 times in 2 sec., how many times will it vibrate in 24 hrs.? Reduce 2 tons 7 cwt. 2 qrs. 11 lbs. to

ounces.

12. How many hours are there in ten years, the first of which is 1852?

13. If a silver tankard weighing 100 oz. 16 dwts. is made into spoons weighing 2 oz. 16 dwt. each, how many spoons are there? 14. In 807438 gr. of gold, how many pounds, ounces, etc.? 15. In 1,388,402 in., how many miles, furlongs, etc.?

16. A tank holds 5360 gal. of water; find the weight of the water (in tons, etc.), knowing that a gallon of water weighs 10 lbs. 17. Bring 500,000,000 in. to poles.

18. If soldiers on the march take 32 steps of 32 in. each in 16 sec., how many miles will they march in an hour?

19. Express 864275 in. in miles, yards, etc.

20. How many yards of land at half-a-crown each, can be bought for £2049, 17s. 6d., and how many guineas in 16254 pence?

21. How many square yards are there in a field of 17 ac. 3 ro. 16 po.?

22. How many tons, hundredweights, etc., are there in 76409 oz. avoirdupois ?

23. How many pound packets of sugar can be made out of 1 ton 1 cwt. 1 qr. 1 lb.

24. In 2 ac. 1 ro. 3 per. 9 yds., how many square feet?

25. Reduce £104, 3s. 3 d. to farthings, and explain, as you would to a class, each step of the process.

26. How many ounces are there in 2 tons 3 cwt. 1 qr. 17 lbs. 1 oz. ?

27. In 13832568 sq. ft., how many acres, roods, etc.?

28. In 6040982 sec., how many weeks, days, etc.?

29. Find how many pounds there are in 1234 tons, and the value at d. per pound.

30. Reduce 12 lea. 2 m. 3 fur. 10 yds. 2 ft. to inches, and find how many seconds in a year (365 da. 5 ho. 48 min. 47 sec.).

31. Find in what time a body moving with a velocity of 1100 ft. per second would pass from the earth to the sun, a distance of 91,404,000 miles.

32. How many pence are there in 39 half-crowns, and how many feet in 47 yds.?

33. Reduce 384986 ft. to furlongs, and explain the mode of dividing by 5.

34. Reduce 785447 sq. ft. to acres.

35. A gentleman determines to give half-a-crown to each poor person in his parish, and finds that in doing so he must spend 52 guineas and a half; how many poor people are there in the parish?

36. How many miles will a wheel, which is 16 feet in circumference, traverse in 7825 revolutions?

37. How many parcels of 4 oz. are there in 17 cwt. 2 qrs. 17 lbs.? 38. Reduce 2 m. 16 po. 44 yds. to yards.

39. Reduce 3 ro. 23 po. 14 sq. yds. to square feet.

40. How many fourpenny pieces are there in three ten pound notes, five sovereigns, seven half-sovereigns, three crowns, three half-crowns, nine shillings, and sixpence ?

41. What number of times can you fill a gill measure out of a quarter of wheat?

42. Reduce 527895 in. to poles.

43. Three pennies weigh exactly one ounce; find the weight of 427859700 pence, and also their value.

44. Reduce £351, 13s. 0 d. to farthings, and prove your answer by returning it to pounds, shillings, and pence.

45. Reduce 24000 pence to fourpenny pieces, shillings, florins, crowns, and pounds.

46. Bring 59 lbs. 13 dwts. 5 gr. to grains, and 340157 gr. to pounds, etc.

47. In 136334 inches how many miles, etc., and in 15 yds. 3 qrs. 1 na., how many nails?

48. Bring 27 ac. 1 ro. 32 po. to poles, and 4406 po. to acres. 49. The synodical period of the moon's rotation is 29 da. 12 ho. 44 min. 3 sec., and the sidereal period 27 da. 7 ho. 43 min. 11 sec.; bring both into seconds.

50. In 14365925 sec., how many weeks, days, hours, etc.?

51. Reduce 3 lbs. 3 oz. 3 dwts. to grains.

52. How many pounds, ounces, etc., are there in 853478 gr. of gold?

53. Find the number of inches in the length 1 m. 1 fur. 3 po. 54. What sum must be taken from £47, 17s. 24d. to make it exactly divisible into parts, each equal to £1, 3s. 24d.?

55. Find the difference in inches between 5 m. and 9125 yds. 56. How many seconds are there in the months of January and June respectively?

57. There are two fields, one containing 7 ac. 1 ro. 8 po., the other 10 ac.; find the difference in square yards.

58. Find how many chains between two towns 9 m. 2 fur. apart. 59. How many minutes are there between 12 o'clock of the 2d June 1875, and 5 o'clock in the afternoon of the 20th August 1875 ?

60. A postman visits 300 houses in a day; the average distance between the houses is 7 yds. 2 ft. 3 in.; find how far he travelled in miles, etc., if he had to go half-a-mile before he came to the first house, and stopped at the last.

61. A set of females have 1428964 sheets of paper to make up into quires and reams; how many reams did they produce?

62. How many persons can receive 6s. 8d. each out of £5, 13s. 4d.! work this sum by division.

63. If 4 casks of raisins at £3, 10s. per cwt. cost £21, what is the weight of each cask?

64. How many pieces of cloth 9 yds. 2 qrs. 3 na. long can be cut from a piece 58 yds. 0 qrs. 2 na. in length?

DUODECIMALS, OR CROSS MULTIPLICATION. DUODECIMALS are introduced thus early because of their simplicity and great importance. The origin of the word is from duodecim, twelve, because in multiplying by feet and inches the radix is 12, just the same as when 421 is multiplied by 37, we proceed by tens, so in duodecimals we proceed by twelves. By a very simple rule practical men are accustomed to find the admeasurement of surfaces and solids, such as walls, floors, rooms, gardens, land, timber, blocks of stone, etc.

Surfaces have two dimensions, length and breadth. In the words of Euclid: "A superficies is that which has only length and breadth." Its unit is square inches or square feet.

Solids have length, breadth, and thickness-three dimensions. Solids have for a unit, cubic inches or cubic feet.

The following example will show how the questions are worked out:

Multiply 8 ft. 4 in. by 7 ft. 5 in. Suppose a floor to be 8 ft. 4 in. long, and 7 ft. 5 in. wide, it is required to find the area

B