An Obtuse Angle is one that is greater than a right angle, as KIJ.

An Acute Angle is one that is less than a right angle, as KIH.

A Rectangle is a four-sided figure whose angles are right angles, as LMNO.

L

N

J

A Square is a rectangle whose sides are equal, as PQRS.

1 inch..

A Square Inch is a square whose sides
are each an inch long.

A SQUARE INCH.

Its exact size is shown
in the diagram.

P

R

M

A Square Foot is a square whose sides are each a foot long. A Square Yard, a Square Rod, and a Square Mile, may be similarly defined.

TABLE.

144 square inches (sq. in.), 1 square foot, sq. ft.

Construct from the above a Table of equivalents.

Roods and acres have no corresponding denomination in linear measure. A square rod is also called a pole, or perch (P.).—In stead of roods and square rods, hundredths of an acre written decimally are frequently used to express portions of land less than an acre.

A Section of land is a square mile; and a Quarter Section, of a square mile, or 160 acres. In some states, 36 square miles constitute a Township.

Stone-cutters often estimate their work by the square foot; plasterers, paper-hangers, and pavers, by the square yard. Flooring, roofing, brick-laying, etc., are sometimes estimated by the “square," consisting of 100 square feet; but brick-laying is generally estimated by the thousand bricks.

332. Area.―The space contained within the bounding lines of a figure is called its Area, or Superficial Contents.

333. To find the area of a rectangle, multiply the length by the breadth.

The above rule is recommended by its brevity; but, properly speaking, we can not multiply by breadth. We multiply together the numbers representing the length and breadth expressed in the same denomination, and the product is the area in the corresponding denomination of square

measure.

Breadth, 8 ft, or 1 yd.

Length, 3 ft., or 1 yd.

Thus, let the figure in the margin represent a square 3 ft. long and
3 ft. broad; each side is divided into 3 equal
parts, representing 1 ft. each. By drawing
lines perpendicularly across the figure be-
tween the foot-divisions, we form a number
of small squares, each of which represents 1
sq. ft. It will be seen that the whole sur-
face, 3 ft. long by 3 ft. broad, contains 3
times 3 of these squares, or 9 sq. ft.; that a
surface ft. by 2 ft. would contain 3 × 2 of
these squares, or 6 sq. ft.; and a surface 3 ft.
by 1 ft., 3 X 1 of these squares, or 3 sq. ft.
It will now be easy to understand why,
12 in. making 1 ft., 12 × 12 (144) sq. in.
1 sq. ft.
5 yd. 1 rd., 5 × 5 (304) sq. yd. = 1 sq. rd.

Area,
9 sq. ft., or 1 sq. yd.

=

334. Surveyors, taking the dimensions of land in chains, on multiplying the length and breadth together, get the area in square chains (sq. ch.), 10 of which make

an acre.

Show that 10 square chains must make an acre.

335, CUBIC MEASURE

is used in measuring solids, or bodies,-which have length, breadth, and depth or thickness; as stone, timber, earth, boxes, etc.

336. A Cube is a body bounded by six equal squares.

A Cubic Inch is a cube, one inch long, one inch broad, and one inch thick. Each of its six sides, or faces, is a square inch.

A Cubic Foot is a cube, 1 foot long, broad, and thick. A Cubic Yard is a cube, 1 yard long, broad, and thick.

Construct from the above a Table of equivalents.

Cubic Measure is used in estimating the amount of work in solid masonry, excavations, embankments, etc. A perch of masonry is 24 cubic feet.

A cord of wood is a pile, 8 ft. long, 4 ft. wide, and 4 ft. high. One foot in length of such a pile is called a cord foot.

337. The ton of this Table is a measured ton; the avoirdupois ton is a ton of weight. A ton of freight, in the case of some articles, as mahogany, boards, wool, and bale-goods generally, means a measured ton of 40 cubic feet. On the other hand, many kinds of heavy goods, such as iron, copper ore, potashes, rice, and dye-woods, are charged as freight by the avoirdupois ton of 2000 lb.

In the case of other articles of freight, when there is no special agreement, certain quantities are by mercantile usage allowed to the ton: as, 7 barrels of beef and pork; 8 barrels of flour; 1 hogshead of tobacco;

200 gallons of oil, wine, brandy, and other liquors (estimating the full capacity of the cask); 29 bushels of bituminous coal; 36 bushels of European, and 31 of West India, salt; etc.

By the register tonnage of a vessel is meant, according to Act of Congress, her "entire internal cubical capacity, in tons of one hundred cubic feet each".

338. Solid Contents.-The space contained within the bounding sides of a solid is called its Solid Con

tents.

339. To find the solid contents of a cube or other solid whose faces are rectangles, multiply its length, breadth, and thickness together.

That is, multiply together the numbers representing these dimensions expressed in the same denomination, and the product will be the solid contents in the corresponding denomination of cubic measure. Thus, let it be required to find the solid contents of a box, 4 ft. long, 3 ft. wide, and 24 inches deep:

24 in. 2 ft.

4 X 3 X 2 = 24 cu. ft. Ans.

The reason for the above rule will appear from an inspection of the figure, which represents a cubic yard. The length and breadth being each 3 ft., the top surface contains 3 X 3

By the same reasoning, 1 foot containing 12 inches, 1 cubic ft. con

tains 12 X 12 X 12, or 1728, cu. in.

340. LIQUID, OR WINE, MEASURE

is used in measuring liquids generally; as, liquors (beer sometimes excepted), water, oil, milk, etc.

Construct, and memorize as far as 1 gallon inclusive, a Table of equivalents.

42 gallons make 1 tierce (tier.); 2 tierces, 1 puncheon (pun.).

Liquids are put up in casks of different sizes, called barrels, tierces, hogsheads, puncheons, pipes or butts, and tuns; but these casks seldom contain the exact number of gallons assigned them in the Table. The contents are found by gauging, or actual measurement.-When the barrel is used in connection with the capacity of cisterns, vats, etc., 31 gallons are meant; in Massachusetts, 32 gallons.

341. The standard wine gallon of the United States, which is the same as the old Winchester wine gallon of England, is a measure that will just contain 58372.2 grains Troy, or 8.33888+ pounds avoirdupois, of distilled water at its greatest density, weighed in air, at 62 degrees Fahrenheit, the mercury in the barometer standing at 30 inches. The capacity of such a measure is about 231 cubic inches.

This Winchester gallon was superseded in England, in 1826, by the imperial standard gallon,—a measure that will exactly contain 70000 grains Troy, or 10 pounds avoirdupois, of distilled water at its greatest density, weighed as aforesaid. 1 imperial gallon, therefore, equals 1.1992 + U. S. wine gallons, and contains 277.274 cubic inches.

342. The beer gallon of 282 cubic inches, formerly used in measuring beer and milk, has now given place