Long or Linear Measure.

193. Linear Measure is used in measuring distances, or length, in any direction.

The standard unit for all measures of extension is the yard, which is identical with the Imperial yard of Great Britain.

TABLE.

12 inches, marked in., make 1 foot, marked ft.

REMARKS.-1. The standard

36.

1 = 12.

yard of the United States was

obtained from England in 1856. It is of bronze, and of due length at 59.8° Fahr. A copy of the former standard is deposited at each state capital: this was about ‰ of an inch too long.

2. The rod is sometimes called perch or pole. The furlong, equal to 40 rods, is seldom used.

3. The inch may be divided into halves, fourths, eighths, etc., or into tenths, hundredths, etc.

4. The following measures are sometimes used:

194. Chain Measure is used by surveyors in measuring land, laying out roads, establishing boundaries, etc.

TABLE.

7.92 inches, marked in., make 1 link, marked li.

REMARKS.-1. The surveyors' chain, or Gunter's chain, is 4 rods, or 66 feet in length. Since it consists of 100 links, the chains and links may be written as integers and hundredths; thus, 2 chains 56 links are written 2.56 ch.

2. The engineers' chain is 100 feet long, and consists of 100 links. 3. The engineers' leveling rod is used for measuring vertical distances. It is divided into feet, tenths, and hundredths, and, by means of a vernier, may be read to thousandths.

195. Mariners' Measure is used in measuring the depth of the sea, and also distances on its surface.

REMARKS.-1. A nautical mile is one minute of longitude, measured on the equator at the level of the sea. It is equal to 1.1523 statute miles. 60 nautical miles 1 degree on the equator, or 69.16 statute miles. A league is equal to 3 nautical miles, or 3.458 statute miles.

2. Depths at sea are measured in fathoms; distances are usually measured in nautical miles.

196.

Cloth Measure is used in measuring dry-goods. The standard yard is the same as in Linear Measure, but is divided into halves, quarters, eighths, sixteenths, etc., place of feet and inches.

in

REMARKS.-1. There was formerly a recognized table for Cloth Measure, but it is now obsolete. The denominations were as follows: 2 inches, marked in., make 1 nail, marked na.

2. At the custom-house, the yard is divided decimally.

Superficial or Surface Measure.

197. 1. Superficial Measure is used in estimating the numerical value of surfaces; such as, land, weather-boarding, plastering, paving, etc.

2. A surface has length and breadth, but not thickness. 3. The area of a surface is its numerical value; or the number of times it contains the measuring unit.

4. A superficial unit is an assumed unit of measure for surfaces.

Usually the square, whose side is the linear unit, is the unit of measure; as, the square inch, square foot, square yard.

5. A Rectangle may be defined as a surface bounded by four straight lines forming four square corners; as either of the figures A, B.

6. When the four sides are equal the rectangle is called a square; as the figure C.

A

B

7. The area of a rectangle is equal to its length multiplied by its breadth.

EXPLANATION.-Take a rectangle 4 inches long by 3 inches wide. If upon each of the inches in the length, a square inch be conceived to stand, there will be a row of 4 square inches, extending the whole length of the rectangle, and reaching 1

inch of its width. As the rectangle contains as many such rows as there are inches in its width, its area must be equal to the number of square inches in a row (4) multiplied by the number of rows (3), 12 square inches. This statement (7), as commonly understood, can present no exception to Prin. 2, Art. 60.

TABLE.

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

NOTE. The following, though now seldom used, are often found

in records of calculations:

40 perches (P.), or sq. rds., make 1 rood, marked R.

198. Surveyors' Measure is a kind of superficial measure, which is used chiefly in government surveys.

TABLE.

625 square links (sq. li.) make 1 square rod,

sq. rd.

199. A Solid has length, breadth, and thickness.

Solid Measure is used in estimating the contents or volume of solids.

A Cube is a solid, bounded by six equal squares, called faces. Its length, breadth, and thickness are all equal.

REMARK.-The size or name of any cube, like that of a square, depends upon its side, as cubic inch, cubic foot, cubic yard.

EXPLANATION.-If each side of a cube

is 1 inch long, it is called a cubic inch; if each side is 3 feet (1 yard) long, as represented in the figure, it is a cubic or solid yard.

When the base of a cube is 1 square yard, it contains 3X3=9 square feet; and 1 foot high on this base, contains 9 solid feet; 2

feet high contains 9 X 2 = 18 solid feet; 3 feet high contains 9 X 3

=

- 27 solid feet. Also it may be shown that 1 solid or cubic foot contains 12 X 12 X 12 = 1728 solid or cubic inches.

The unit by which all solids are measured is a cube, whose side is a linear inch, foot, etc., and their size or solidity will be the number of times they contain this unit.

REMARK. The simplest solid is the rectangular solid, which is bounded by six rectangles, called its faces, each opposite pair being equal, and perpendicular to the other four; as, for example, the