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In this measure, le. stands for league, m. for mile, f. for furlong, rd. for rod, yd. for yard, ft. for foot, and in. for inches.

Surveyors usually measure distances by means of a chain 4 rods in length, called Gunter's chain, or the Surveyor's chain. This chain contains 100 equal links; 25 links will, therefore, equal 1 rod, and 1 link will equal 73% inches.

I. The following measure is used for measuring cloth, ribbons, &c.

TABLE OF CLOTH MEASURE.

24 inches =l nail.
4 nails 1 quarter.

4 quarters = 1 yard. In this measure, yd. stands for yard, qr. for quarter, and na. for nail.

The yard and inch are the same in length as the yard and inch Long Measure.

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J. Square Measure is used for measuring surfaces. As true ideas of the nature of the right angle, rectangle, and square, are essential to a just appreciation of this measure, we insert the following definitions and illustrations, leaving it with the teacher to give such others as he

may When two lines meet at a point, their difference in direction is called the angle of the two lines. The point where they meet is called the vertex of the angle. Fig I.

In this figure the lines marked B A and B C form an angle whose vertex is at B.

In reading an angle, the letter at the vertex is always made the middle one. The

angle in figure 1 may be read, either as the A

Bangle A B C, or as the angle c B A.
Fig. 2.

In this figure there are two angles, viz. : D B A, and A B C. The first is the difference in direction of the two lines A B and D B, and the second is the difference in direction of the two lines A B and B c. It is evident that

the first is larger than the second. When the two angles formed by one straight line meeting another are equal to each other, they are called right angles, and the two lines are said to be perpendicular to each other.

A

D

B

с

A

B

Fig. 3.

Suppose the straight line D B has met the D

straight line A c, so as to make the adjacent angles A B D and D B C equal to each other;

then A B D and D B C will each of them be

c right angles, and D B and a c will be perpendicular to each other.

An angle greater than a right angle is called an obtuse (blunt) angle, and one less than a right angle is called an acute (sharp) angle. In Fig. 2, D B A is an obtuse angle, and a b c is an acute angle. In Fig. 1, A B C is an acute angle.

A four-sided figure having all its angles right angles is called a rectangle.

A rectangle having all its sides equal is called a square. A square, then, has four equal sides and four equal angles. Figures 4 and 5 represent rectangles. Figure 5 also represents a square. Fig. 4.

Fig. 5.

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If a square measures a foot on each side, it is called a square foot; if it measures a yard on a side, it is called a square yard, &c. &c.

All surfaces are measured by Square Measure, that is, by the number of squares of a given size to which they are equivalent. Thus, a surface contains 5 square feet, when it is equivalent to 5 squares, each measuring 1 foot on a side.

TABLE OF SQUARE MEASURE.
144
square inches

1 square foot.
9 square feet

= 1 square yard.
304 square yards, or
2724 square feet
40 square rods

= 1 rood.
4 roods

1 acre. 640 acres

= 1 mile. In this measure, Sq. M. stands for square mile, A. for acre, R. for rood, sq. rd. for square rod, sq. yd. for square yard, sq. ft. for square foot, and sq. in. for square inch.

}= 1 square rod.

K. A solid is a body which has length, breadth, and thickness.

A cube is a rectangular solid, whose length, breadth, and height are equal. It may also be defined as a solid which is bounded by six equal squares.

A cube 1 foot long, 1 foot wide, and 1 foot high, would be a cubic foot. A cube 1 yard long, 1 yard wide, and 1 yard high, would be a cubic yard.

The solid contents of bodies are measured by cubic measure, i. e., by the number of cubes of a given size which the bodies contain, or to which they are equivalent.

TABLE OF CUBIC MEASURE,

1728 cubic inches = 1 cubic foot.

27 cubic feet = 1 cubic yard.
16 cubic feet

1 cord foot.
8 cord feet, or
128 cubic feet,

= l cord of wood. In this measure, C. stands for cord, Cd. ft. for cord foot, cu. ft. for cubic foot, cu. yd. for cubic yard, and cu. in. for cubic inch.

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L. Circular or Angular Measure is used to measure angles, and the circumferences of circles.

A circle is a surface bounded by a curved line which is every: where equally distant from a point within called the centre. The boundary-line is called the circumference of a circle. Fig. 6 represents a circle of which C is the centre. Fig. 6.

The distance from the centre of a circle to the circumference is called the radius of the circle.

The distance from a point on one side of a circle through the centre to a point on the opposite side is called the diameter of the circle. Any portion of the circumference is called an arc. Every circumference of a

circle, whether the circle be large or small, is supposed to be divided into 360 equal parts called degrees. Each degree is divided into 60 equal parts called minutes, and each minute into 60 equal parts called seconds. A degree is to be regarded simply as the 360th part of the circumference of the circle considered. Hence it is obvious that its length, and that of its subdivisions, must vary with the size of the circle.

If from the vertex of an angle as a centre, we should draw a circumference, some portion of that circumference would be included between the sides of the angle. The larger the angle is, the larger will be the arc included between its sides, and the smaller the angle is, the smaller will be the included arc. Since the angle and the arc thus vary with each other, we take the arc as the measure of the angle. If the arc contains 50 degrees, the angle is one of 50 degrees, &c. Figure 7 may illustrate this. Fig. 7.

In this figure let c be the centre of the circle and the vertex of the several angles, and let Fh and G D be lines perpendicular to each other, and c E and c i be lines drawn at random. Then the arc E D is the measure of the angle E C D; the arc D F, of the angle D CF; the arc D I, of the angle DCI; the arc E F, of the angle E C F, &c.

Since F and G D are perpendicular to each other, the angles F C D, D C H, H C G and G C F are all right angles, and each of them must include 4 of the angular space about the point c. Therefore, the arc included between the sides of a right angle equals of the circumference, and the measure of a right angle is of 360 degrees, which equals 90 degrees. The measure of an acute angle is less than 90 degrees, and that of an obtuse angle more than 90 degrees.

TABLE OF CIRCULAR, OR ANGULAR MEASURE.

60 seconds = 1 minute.
60 minutes = 1 degree.

360 degrees = 1 circumference. . Degrees are marked by the character o, minutes by', seconds by": Thus, 13° 27'49'' = 13 degrees, 27 minutes and 49 seconds.

An arc of 90° is called a Quadrant.
A Sign is an astronomical measure of 30°.

M. Dry Measure is used for measuring all kinds of grain, beans, nuts, salt, &c.

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The Chaldron of 36 bushels is sometimes used in measuring coals. ch. stands for chaldron, bu. for bushel, pk. for peck, qt. for quart, and pt. for pint.

The bushel contains 21502 cubic inches. The quart must, therefore, contain 674 cubic inches.

N. All kinds of liquids are measured by Liquid Measure.

LIQUID MEASURE. 4 gills

= 1 pint. 2 pints 1 quart.

4 quarts = 1 gallon. In this measure gal. stands for gallon, qt. for quart, pt. for pint and gi. for gill.

The hogshead of 63 gallons is used in estimating the contents of reservoirs or other large bodies of water, but in all other cases, the term hogshead is not a definite measure. Casks containing from 50 or 60 to 100 or 200 gallons are called hogsheads.

A barrel of cider is usually reckoned at 314 gallons.

The gallon contains 231 cubic inches. The beer gallon is sometimes used for measuring milk, beer and ale.

The beer gallon contains 282 cubic inches. The beer quart must therefore contain 70 cubic inches.

The following table will be convenient for use in comparing Dry, Liquid, and Beer Measures : 1 qt. Dry Measure

674 cubic inches. 1 qt. Liquid Measure = 57 cubic inches. 1 qt. Beer Measure 704 cubic inches.

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52 weeks and 14 days }=1 year.

The

year is divided into 12 months, which differ somewhat in length. In this measure yr. stands for year, mo. for month, wk. for week, da. for day, h. for hour, m. for minute, and sec. for second.

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