ALE OR BEER MEASURE,' 26. Is used for measuring malt liquors. 27. For measuring length without regard to breadth or depth. I barley corn ; 3 barley corns 1 inch. 28. Of the foregoing lines the shorter one is exactly 1 barley corn in length; then 3 times the length of this line makes 3 barley corns, or 1 inch, which is the exact length of the longer line. In like manner, 12 times the length of 1 inch makes 1 foot; 3 times the length of 1 foot, 1 yard, &c. 3 barley corns [b. c.] make 1 foot. 8 furlongs, or 1760 yards 3 miles 69 statute miles 60 geographical miles ... • make 1 degree. ... 360 degrees make 1 circle, or the earth's circumference. 4 inches 6 points 12 lines. 5 feet. 29. DISTANCES-DEPTHS-HEIGHTS. ... ... make 1 hand, for measuring the height of horses. make 1 line, used in measuring the length of pen make 1 inch, S dulums for clocks. make 1 geometrical space, used for distances. 6 feet..... make 1 fathom, for measuring depths at sea. 3 miles.... make 1 league, for measuring distances at sea. GUNTER'S CHAIN. 30: For measuring distances, and the length or breadth of land. 1. The dry gallon contains 268 cubic inches; the wine gallon 231 cubic inches and the beer gallon 282 cubic inches. The same standards continued in use in Great Britain, as late as 1826, when the act of Parliament came into operation, by which the Imperiul gallon of 277-274 cubic inches was substituted for the dry, beer and wine gallons 31: The chain for measuring distances varies from 2 to 4 rods in length, reckoning 25 links to a rod. QUESTIONS 32. Repeat the Table of Ale Measure. Its use? 26. Repeat the Table of Long Measure. Its use? 27. For what purpose do we use the league and fathom? the geometrical space, lines and hands? 33. How many barley corns in 20 inches? Inches in 7 feet inches? Feet in 10 yards? Yards in 2 rods? 34. How many leagues in 38 miles? Furlongs in 85 miles! Fathoms in 75 feet? Feet in 100 geometrical spaces? LAND, OR SQUARE MEASURE, 35. For measuring superficies, that is, surfaces or things, whose length and breadth are considered without regard to depth; as, land, paving, flooring, plastering, roofing, slating, tiling, &c. Fig. 1. Fig. 2. Fig. 3. 36. A SQUARE' has four equal sides, and four equal and square corners, commonly called Angles; consequently its length and breadth are equal; as, Fig. 1. 37. A PARALLELOGRAM has only its opposite sides equal, and at least its opposite angles, but may have all its angles equal; consequently it has more length than breadth; as, figures 2 and 3. Fig. 4. Small Squares. 38. Here are several small squares, each of which we will suppose is 1 inch long and 1 inch wide, which make 1 inch square, and therefore is said to contain by measure, 1 square inch. 39. If we count the square inches in the two top rows, they will make 2 times 12 or 24 square inches; 3 rows will make 3 times 12 or 36 square inches; 4 rows, 4 times 12 or 48 square inches; and so on through the 12 rows, which make 12 times 12, or 144 square inches. 40. The same figure taken as a whole, is 1 foot square, for 12 inches are equal to 1 foot; then the whole contains 1 square foot therefore, 1 square foot is equal to 144 square inches. 1 SQUARE, (F. quarre.] A form like Figure 1, above; an area or the open surface with houses on four sides; a rule for measuring; a square body of troops; a squadron; a quarternion; equality; rule; conformity; accord. 2 PARALLELOGRAM is so called from parallelos, G. equally distant, and gramma G a letter; because its opposite sides are parallel; that is equally distant from each other in all their parts; of course parallel lines would not meet if continued ever so far. In common use, his word is applied to any quadrilateral, or four-sided figures of more length than breadth Fig. 5. A Parallelogram. Fig. 6. Squares. 41. This figure we will suppose to be 3 feet long and 1 foot wide; then it will have 3 squares each 1 foot square, and will contain 3 square feet. 42. Three rows of 3 square feet in each row, will contain 3 times 3, or 9 square feet, but the whole figure will be only 3 feet square. Again, as 3 feet are equal to 1 yard; then 9 square feet are equal to 1 square yard. 43. Hence we see that 3 square feet is only one third as much as 3 feet square, making a difference of 6 square feet.. 44. Again; suppose Figure 5 to contain 3 square miles of land, then 3 miles square of land; as, Figure 6, would be 3 times 3, or 9 square miles, making a difference of 6 square miles. 45 Hence a square foot, yard, &c. may be of any shape whatever, provided the foot contains exactly 144 squares, each 1 inch square, and the yard 9 squares, each 1 foot square, &c. 46. From the above we learn that multiplying the length of any square or parallelogram by its breadth, gives its square measure, or, as it is sometimes called, its square contents, as in the following Table: 144 square inches [sq. in.] . make 1 square foot. 9 square feet.. . make 1 square yard. 30 sq. yd. or 2721 sq. ft. . . make 1 square rod or pole. 40 square rods 4 roods. 640 square acres make 1 rood. make 1 acre.. make 1 square mile. sq. ft. sq. yd. sq. r. QUESTIONS. 47. Repeat the Table of Land or Square Measure. Its use? 35. What is a square? 36. Parallelogram? 37. What is meant by 1 square foot? 38. 39. 40. What by 1 square yard? 41. 42. 48. What is the difference between 3 square feet, and 3 feet square, and why? 42. 43--between 3 square miles and 3 miles square? 44. 49. How many square feet in 12 square yards? square rods in 210 roods? acres in 38 roods? 50. What is said of the form of a square foot, square yard, &c. 45. How is the square content ascertained? 46. 51. How many square inches then, are contained in a small slate 4 inches long and 3 inches wide? [3 times 4]. In one 7 inches long and 5 inches wide? What is the form of such slates, and why? 37 52. How many square feet in a board 3 feet long and 1 foot wide? [3]. In one 7 feet long and 2 feet wide? In the floor of a room 10 feet long and 7 feet wide? 53. How many square yards in a piece of carpeting containing 54 uare feet? Roods in a piece of land 10 rods long and 4 rods wide? [1]. In a piece 10 rods square? SOLID OR CUBIC MEASURE, 54. For measuring solids, that is, things that have three dimensions, viz., length, breadth, and depth or thickness; as wood, timber, stones, masonry, &c. 55. A CUBE is a solid, whose length, breadth, and thickness are all equal. [See the Cubical block.] 56. Thus a small block 1 inch long, 1 inch wide, and 1 inch thick, is called a cube, and is said to contain 1 cubic or solid inch. Such a block has of course six equal sides 57. Now suppose a box to be 12 inches square in the inside; we can then place on the bottom 12 rows of 12 cubes, each containing 1 solid inch, making in all 144 cubic blocks. 58. If we lay another tier of 12 times 12, or 144 similar blocks upon the others, we shall have laid 2 times 144, or 288 blocks, and thus we might continue to do, till we had laid 12 tiers, which would make in all 12 times 144, or 1728 cubes; that is, so many solid inches, and all in the form of a perfect cube, for the whole pile would be 12 inches long, 12 inches wide, and 12 inches thick. 59. Then as 12 inches are equal to 1 foot, the above cube would be i foot long, 1 foot wide, and 1 foot thick, which makes 1 solid or cubic foot; hence it takes 1728 solid or cubic inches to make 1 solid or cubic foot. 60. Hence it appears that a solid or cubic inch, foot, &c., arise from multiplying the length of a solid by its breadth, and that result . by its thickness, as in the following Table: 1728 cubic inches [c. in.] 27 cubic feet 50 cubic feet of round timber. 40 cubic feet of hewn timber. 42 cubic feet of shipping 16 cubic feet make 1 cubic foot. make 1 ton. make 1 ton. make 1 cord foot. c. ft. 8 cord feet, or 128 cubic feet make 1 cord of wood. C. QUESTIONS. 61. How many dimensions has a cube? See 54. 55. How many sides has it? See 56. What is meant by one solid or cubic inch? See 56. 62. How many such blocks will exactly cover the space of 12 inches square? See 57. How many such blocks would 2 tiers require? How many would 12 tiers require? See 58. 63. What would be the proper name for the form of such a pile of blocks when taken as a whole, and why? 58. What is meant oy 1 cubic foot, 59. 64. How is the solid content of a cube obtained? 60. How many solid feet in a cubic block 2 feet long, and 2 feet wide, and 2 feet thick? [8] In one 10 feet long, 10 feet thick, and 10 feet wide? 64. How many cord feet in 32 solid feet? in 64 solid feet? How many cubic feet in of a cord of wood? in 1 cord? Repeat the Table of Cubic Measure. Its use? 54. TIME. 65. Which is reckoned by years, months, days, &c. 12 months 100 years make 1 year. 66. The number of days in each month are as follows: April 30 days, August 31 days. September 30 days, December 31 days 67. The days in each month are often expressed thus: Thirty days has September, April, June and November. When we give to February one day more. 68. A natural3 day' is A Lunar month5 A Solar' year' A Civil year' A Julian12 year12 24 hours. 4 weeks or 28 days. 365 days, 5h. 48m. 48 sec. [nearly] 12 calender1o months11 or 365 days. 13 lunar months, 1 d. 6 h. or 365 days 69. When any year can be divided by 4 without a remainder, it is leapyear, except the centurial' years, which are explained below. 1 LEAPYEAR. So called, because the year leaps as it were from 365 to 366 days. 2 CENTURIAL, [L. centuria, a century.] Of, or belonging to a century. 3 A NATURAL DAY is the period in which the earth revolves (13) on its axis, (14) being once in every 24 hours. 4 LUNAR, [L. luna,the moon.] Pertaining to the moon. 5 A LUNAR MONTH, is the period of time required for the revolution (13) of the moon round the earth, being, strictly speaking, 27 days, 7 hours, 43 minutes, 5 seconds. 6 SOLAR, [L. sol,the sun.] Of, or belonging to the sun. 7 A SOLAR YEAR, OF A YEAR, properly speaking, is the period which the earth revolves (13) round the sun, occurring once in every 365 days, 5 hours, 48 minutes and a trifle more than 48 seconds. This period of revolution is therefore called the SOLAR (6) or NATURAL YEAR. 8 CIVIL, [L. civis.] Relating to the community or government; polite. 9 A CIVIL YEAR, is the period of time established by law. 10 CALENDAR, [L. calendarium.] A register in which the months and days are set down in order; un almanac. 11 A CALENDAR MONTH, is a solar month, as it stands in almanacs. 12 A JULIAN YEAR, is so called from Julius Cæsar, Emperor of Rome, who from a desire to make the civil year correspond (15) with the solar, ordered it to consist of 13 months 1 day and 6 hours, or 365 days; and in common reckoning only 365 days Dropping the 6 hours, or of a day for 4 years, makes a loss of one day, which is |