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3 miles .
make i league,

marked L. 60 geographical, or 69} statute nuiles,

I degree,

.. deg. or . 360 degrees,

a great circle, or circumference

of the earth. 31. How many barley-corns 32. In 4755801600 barley-corns, will reach round the globe, it how many degrees ? being 360 degrees ?

Note. To multiply by 2, is to Note. The barley-corns being take the multiplicand 2 times; 10 divided by 3, and that quotient multiply by 1, is to take the mul- by 12, we have 132105600 feet, tiplicand i time; to multiply by which are to be reduced to rods. is to take the multiplicand We cannot easily divide by 165 half a time, that is, the half of it. on account of the fraction }; but Therefore, to reduce 360 degrees 165 feet :

= 33 half feet, in i rod; to statute miles, we multiply first and 132105600 feet = 264211200 by the whole number, 69, and to half feet, which, divided by 33, the product add half the multipli- gives 8006400 rods. cand. Thus : 3)360

Hence, when the divisor is en69}

cumbered with a fraction, or ļ,

&c., we may reduce the divisor to 3240

halves, or fourths, &c., and re2160

duce the dividend to the same; 180 half of the multiplicand. then the quotient will be the true 25020 statute miles in 360 de

grees. 33. How many inches from 34. In 30539520 inches, how Boston to the city of Washington, many miles ? st being 482 miles ?

35. How many times will a 36. If a wheel, 16 feet 6 inches wheel, 16 feet and 6 inches in in circumference, turn round circumference, turn round in the 12800 times in going from Boston distance from Boston to Provi- to Providence, what is the disdence, it being 40 miles? tance ?

answer.

LAND OR SQUARE MEASURE. Square measure is used in measuring land, and any other thing, where length and breadth are considered. The denominations are miles, acres, roods, perches, yards, feet and inches.

1 35. 3 feet in length make a yard in long measure ; but it requires 3 feet in length and 3 feet in breadth to make a yard in square measure ; 3 feet in length and one foot wide make 3 square féet; 3 feet in length and 2 feet wide make 2 times 3, that is, 6 sqnare feet; 3 feet in length and 3 feet wide make 3 times 3, that is, 9 square feet. This will clearly appear from the annexed tigure.

3 feet = 1 yard.

3 feet = | yard.

It is plain, also, that a square foot that is, a square 12 inches in length and 12'inches in breadth, must contain 12 X 12 = 144 square inches.

1 square foot.

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TABLE 144 square inches = 12 X 12; that is,

12 inches in length and 12 inches make

in breadth, . 9 square feet 3 X 3; that is, 3 feet in length and 3 feet in breadth,

. I square yard. 30 square yards 55 X 55, or 2724 Si square rod, square feet = 164 X 163,

perch or pole. 40 square rods

i rood. roods, or 160 square rods,

.1 acre.
acres

1
square

mile. Note. Gunter's chain, used in measuring land, is 4 rods in length. It consists of 100 links, each link being 792 inches in length; 25 links make i rod, long measure, and 625 square links make í square rod.

37. In 17 acres 3 roods 12 rods, 38. In 776457 square feet, how how many square feet?

many acres ? Note. In reducing rods to Note. Here we have 776457 feet, the multiplier will be 2721. square feet to be divided by 2724. To multiply by 4, is to take a Reduce the divisor to fourths, fourth part of the multiplicand. that is, to the lowest denominaThe principle is the same astion contained in it; then reduce shown 1 34, ex. 31.

the dividend to fourths, that is, to the same denomination, as

shown | 34, ex. 32. 39. Reduce 64 square miles to 40. In 1,784,217,600 square square feet.

feet, how many square miles ? 41. There is a town 6 miles 42. Reduce 23040 acres- to square ; how many square miles square miles. in that town? how many acres ?

SOLID OR CUBIC MEASURE. Solid or cubic measure is used in measuring things that have length, breadth, and thickness ; such as timber, wood, stone, bales of goods, &c. The denominations are cords, tons, yards, feet, and inches.

I yd. =3 ft. long. 1 yd. =3 ft. wide.

136. It has been shown, that a square yard contains 3 X 3 9 square feet.. A cubic yard is 3 feet long, 3 feet wide, and 3 feet thick. Were it 3 feet long, 3 feet wide, and one foot thick, it would contain 9 cubic feet; if 2 feet thick, it would contain 2 X 9= 18 cubic feet; and, as it is 3 feet thick, it does contain 3 X 9=27 cubic feet. This will clearly appear from the annexed figure

1

[graphic]

It is plain, also, that a cubic foot, that is, a solid, 12 inches in length, 12 inches in breadth, and 12 inches in thickness, will contain 12 X 12 X 12 = 1728 solid or cubic inches.

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TABLE. 1728 solid inches, 12 X 12 X 12,

that is, 12 inches in length, 12 make 1 solid foot.

in breadth, 12 in thickness,
27 solid feet, =3 X 3 X 3

1 solid yard.
40 feet of round timber, or 50 feet
of hewn timber,

1 ton or load.
i28 solid feet, =8 X 4 X 4, that

is, 8 feet in length, 4 feet in . 1 cord of wood.

width, and 4 feet in height, Note. What is called a cord, foot, in measuring wood, is 16 solid feet; that is, 4 feet in length, 4 feet in width, and 1 foot in heignt, and 8 such feet, that is, 8 cord feet, make l cord.

43. Reduce 9 tons of round 44. In 622080 cubic inches how timber to cubic inches.

many tons of round timber? 45. In 37 cord feet of wood, 46. In 592 solid feet of wood, how many solid feet?

how many cord feet? 47. Reduce 64 cord feet of wood 48. In 8 cords of wood, how to cords.

many cord feet? 49. In 16 cords of wood, how 50. 2048 solid feet of wood, many cord feet? how many solid how many cord feet ? how many feet?

cords?

WINE MEASURE. Wine measure is used in measuring all spirituous liquors, ale and beer excepted; also vinegar and oil. The denominations are tuus, pipes, hogsheads, barrels, gallons, quarts, pints, and gills.

qt.

.

.

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TABLE. 4 gills (gi.) make 1 pint,

marked pt. 2 pints

. 1 quart, • 4. quarts . I gallon,

gal. 31¢ gallons . 1 barrel,

bar. 63 gallons . 1 hogshead,

hhd. 2 hogsheads . 1 pipe,

P. 2 pipes, or 4 hogsheads, • 1 tun,

T. Note. A gallon, wine measure, contains 231 cubic inches. 51. Reduce 12 pipes of wine to 52. In 12096 pints of wine, pints.

how many pipes ? 53. In 9 P. i hhd. 22 gals. 3 54. Reduce 39032 gills to qts. how many ills ?

pipes. 55. In a tun of cider, how many 56. Reduce 252 gallons to tuns. gallons ?

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ALE OR BEER MEASURE. Ale or heer measure is used in measuring ale, beer, and milk. The denominations are hogsheads, barrels, gallons, quarts, and pints.

TABLE. 2 pints (pts.) make 1 quart,

marked qt. 4 quarts . 1 gallon,

gal. 36 gallons

1 barrel 54 gallons

i hogshead, Note. A gallon, beer measure, contains 282 cubic inches. 57. Reduce 47 bar. 18 gal. of 58. In 13680 pints of ale, how ale to pints.

59. In 29 hhds. of beer, how 60. Reduce 12528 pints to many pints ?

Thogsheads ?

. bar. . hhd.

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many barrels ?

DRY MEASURE. Dry measure is used in measuring all dry goods, such as grain, fruit, roots, salt, coal, &c. The denominations are chaldrons, bushels, pecks, quarts and pints.

TABLE. 2 pints (pts.) make 1 quart,

marked qt. 8 quarts . 1 peck, ;

pk. 4 pecks

..1 bushel, 36 bushels . I chaldron,

ch. Note. A gallon, dry measure, contains 2684 cubic inches.

A Winchester hushel is 18$ inches in diameter, 8 inches deep, and contains 21502 cubic inches.

bu.

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61. In 75 bushels of wheat, 62. In -4300 pints, how many how many pints?

bushels ? 63. Reduce 42 chaldrons of 64. In 6048 pecks, how many coals to pecks.

chaldrons ?

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Julian year,

.

.. 31

. 30

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TIME. The denominations of time are years, months, weeks, days, hours, minutes, and seconds.

TABLE. 60 seconds (s.) make 1 minute,

marked m. 60 minutes

1 hour,

.h. 24 hours . 1 day,

d. 7 days .

.. . 1 week, 4 weeks

1 month,

. mo. 13 months, 1 day and 6 hours, 1 common, or or 365 days and 6 hours, }

yr. 1 37. The year is also divided into 12 calendar months, which, in the order of their succession, are numbered as follows, viz. January, 1st month, has 31 days. February, 2d,

28 March, 3d, April, 4th,

Note. When any year can May, 5th,

31

be divided by 4 without a June, 6th,

remainder, it is called leap July, . 7th,

31 year, in which February has August, 8th,

31

29 days. September, 9th

. 30
October, 10th,
November, lith,
December, 12th,

. 31 The number of days in each month may be easily fixed in the mind by committing to memory the following lines :

Thirty days hath September,
April, June, and November,
February twenty-eight alone;

All the rest have thirty-one. The first seven letters of the alphabet, A, B, C, D, E, F, G, are used to mark the several days of the week, and they are disposed in such a manner, for every year, that the letter A shall stand for the 1st day of January, B for the 2d, &c. In pursuance of this order, the letter which shall stand for Sunday, in any year, is called the Dominical letter for that year. The Dominical letter being known, the day of the week on which each month comes in may be readily calculated from the following couplet :

At Dover Dwells George Brown, Esquire,
Good Carlos Finch And David Fryer.

• 31 . 30

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