When measure is applied to solids which have length, breadth and thickness, it is called solid or, cubic measure. A solid inch is a body or block, having six sides, each of which is an inch square, and the number of inches in a solid foot is equal to the number of such blocks that would be required to make a pile a foot square and a foot high. Now it would require 144 blocks to cover a square foot one inch high. Hence to raise the pile 12 inches high would require 12 times 144=1728 blocks, or inches. In like manner it would require 9 solid blocks, a foot each way, to cover a square yard to the height of one foot, and 3 times 9=27, to raise it 3 feet, or make one solid yard. A cord of wood is sometimes called 8 feet. In this case four feet in length, four in breadth, and six inches in height, a foot, that is, of a cord is called one foot, &, 2 feet, &c. In measuring lands, roads, &c. the distances are usually taken in chains and links. In ordinary business, feet and inches are the most common measures. By forty feet of round timber, in the table of solid measure, is meant so much round timber as will make forty feet after it is squared.

XII. Beer Measure.

2 pints, pts. make

1 quart,

XIII. Dry Measure. 2 pints, pts. make 1 quart,qt. qt. 4 quarts,

1 gallon, gal.

gal. 8 quarts,

1 peck, pk.

1 bushel, bu.

1 quarter,gr.

4 quarts, 1 gallon, 36 gallons, 1 barrel, bar. 4 pecks, 54 gallons, 1 hogshead,hhd 8 bushels, 282 cubic inches I gallon,gal 4 quarters,

XIV. Circular Measure.*

1 chaldron,ch.

*

Every circle, without regard to its size, is supposed to be divided into 360 equal parts, called degrees, and these again to be subdivided into minutes and seconds; so that the absolute quantity expressed by any of these denominations must always depend upon the size of the circle. In this measure, are reckoned latitude, longitude, the planetary motions," &c. Thompson.

REDUCTION is the changing of numbers from one denomination to another, without altering their value. 1. In £6, 7s. 8d. 2qr., how many farthings?

Operation.

£6, 7s. Sd. 2qr.

20

127

12

1532

4

It is plain, that, if in one pound there are 20s. in six pounds there are 6 times as many, or 120s. ; and in £6, 7s, there are 127s. Again, if, in one shilling there are 12d. in 127s. there are 127 times 12, which with the 8d. added, equals 1532d. Last6130 qr. Ans. ly, it is evident, that, if in 1 penny there are 4 farthings, in 1532d. there are 4 times the number of farthings, or 6130, the 2qrs. in the given question being added. Hence it appears, that in any given number of pounds there are 20 times as many shillings as pounds, 12 times as many pence as shillings, and 4 times

QUESTIONS. 1. What is Reduction? 2. By what numbers do you multiply in question 1st? and why?

as many farthings as pence. This process is called Reduction Descending, because higher denominations are brought into lower.

2. In 6130 farthings, how many pounds?

Operation. 4)6130

12)1532 2qrs.

20)127 8d.

It will be seen that this question is the reverse of the former; and as 4 farthings are equal to 1 penny, so the number of pence in 6130qrs. will equal the number of times it contains 4, or 1532d. and 2qrs. over. Ans. £6 7s. 8d. 2qrs. Again, as 12d. are equal to 1 shilling, so in 1532d. the number of shillings will equal the number of times it contains 12, or 127s. and 8d. over. Lastly, since 20s. is equal to one pound, 127s. must equal 6 pounds and 7s., because 20 is contained in 127s. 6 times, and 7s. over. It is always to be remembered, that the remainder is of the same denomination as the dividend, whatever may be the divisor. This latter process is called Reduction Ascending, because lower denominations are brought into higher. By these examples, it appears that Reduction Ascending and Descending mutually prove each other. From the preceding operations we derive the following RULES:

Reduction Descending.

RULE.

Reduction Ascending.

RULE.

Multiply the highest de- Divide the denomination nomination given by as many given by as many of that deof the next lower, as it takes nomination as it takes to to make one of the higher, make one of the next higher. observing to add the next Divide farthings by as many lower denomination to the farthings as it takes to make product. Multiply pounds a penny; pence by as many by what makes a pound; shil-pence as it takes to make a lings by what makes a shil-shilling, and so on, until you ling, and so on, until you have reduced it to the dehave reduced it to the de- nomination required. nomination sought in the

question.

QUESTIONS. 3. What is the process called? 4. By what numbers do you divide in question 2? and why? 5. What is this process called? 6. What is the rule for Reduction Ascending? 7. For Reduction Descending?

EXAMPLES.

English Money.

3. In 624 pounds, how ma

ny farthings?

EXAMPLES.

4. In 599040 farthings, how many pounds?

5. If 6 shillings make a 6. In 2603 dollars, how dollar, how many dollars in many pounds and shillings? 780£ 18s?

7. How many pence in 24£ 16s 11d?

9. How many guineas, 28s each, in 49£?

8. How many pounds in 5963 pence?

10. How many pounds in 35 guineas?

Troy Weight.

11. In 18lbs. 11oz. 6pwt. 12. In 109122 grains, how 18grs., how many grains? many pounds?

13. Bought jewelry weigh- 14. If I pay $437,60 for jewing 1lb. 10oz. 15pwt. 20grs. elry, at the rate of $0,04 per paid $0,04 per grain. What grain, what was the weight? did I pay?

Avoirdupois Weight.

15. In 5 tons, 16cwt. 3qrs.| 16. Reduce 3350762drs. 12lbs. 14oz. 10drs., how ma- to tons.

ny drams?

18. Bought lead to the 17. What will be the cost amount of $10752, at $0,12 of 40 tons of lead, at $0,12 per pound, what was the per pound? weight?

19. What must I pay for 20. How much hay can be 20 tons, 18 cwt. of hay, at the bought for $234,08 at half a rate of half a cent per pound? cent per pound?

Apothecaries' Weight.

21. Reduce 6lbs. 10oz. 7drs. 2sc. 16grs. to grains.

23. Reduce 21lbs. 11oz. 3drs. 1sc. 13grs. to grains.

22. In 39836 grains, how many pounds?

24. In 126453 grains, how many pounds?

Long Measure.

25. Reduce 640 degrees 26. In 234854400 feet how to feet. many degrees?

NOTE. To reduce degrees NOTE. To divide by 16 to statute miles, multiply first first reduce 16 to halves by 69, and for the in the and the dividend also to

multiplier take of the mul- halves-Thus, 1633 half

tiplicand-Thus :

2)640 degrees

feet; & 234854400-469708800 half feet, which divided by 33 gives 142338 rods.

691

5760

3840

320

44480 miles.

27. How many barley corns will reach across the Indian Ocean, it being 45 degrees?

28. How many degrees in 594475200 barley corns? 29. A teamster, after trav- 30. If a teamster receive elling 20 miles, met a man for his load $264, being paid who offered him as many 55 cents for each revolution of cent pieces for his load, as the larger waggon wheel, the his larger wheel had turned circumference being 20 feet, round since he commenced how far had he travelled? his journey, the wheel being 20 feet in circumference: how much did he get for his load? 31. How many barley corns will reach round the globe, it corns how many degrees? being 360 degrees?

32. In 4755801600 barley

Land, or Square Measure.

33. If in a county there 34. How many square are 1200 square miles, how miles in 122880000 square many square rods are there rods?

in this county?

36. In 2697235200 square 35. How many square inch- inches, how many square es in 430 square acres? acres?

Solid, or Cubic Measure.

37. How many solid inches in 10 cords of wood?

39. In 40 cords, how many

cord feet?

38. Reduce 2211840 solid inches to cords.

40. In 320 cord feet, how many cords?

41. How many solid inch- 42. In 3732480 solid inches in a pile of timber contain-es of round timber, how maing 54 tons?

ny tons?