202. Long, or Linear Measure, is used in measuring distances, or anything that has length. The Unit of Measure may be 1 mile, 1 rod, 1 yard, &c. A Line has but one dimension-length. Linear measure is so called because it may be taken with a line; it includes Long Measure, Cloth Measure, and Surveyors' Linear Measure. = Since the earth is not a perfect sphere, the degrees of latitude are not of equal length. Their average length, 69.16 miles, is therefore adopted. The geographic mile = 1.15 statute miles, very nearly. The geographic mile is adopted by navigators on account of its convenience, 1 mile corresponding to 1 minute of arc. Cloth Measure has but one denomination, the yard, which is divided into halves, quarters, eighths, sixteenths, &c. The following also come under the head of Long Measure: 4 inches 21.888 inches = 3.45 statute miles. = 1 hand (used in measuring height of horses). A Knot, used in measuring the speed of vessels at sea, is equal to a nautical mile. 203. Surveyors' Linear Measure is used in measuring roads, and boundaries of land. The Unit of Measure is 1 chain = 66 feet. The pole (= 25 links = 161 feet) is rarely used, chains being written as a whole number and links as a decimal. Engineers usually use a chain divided into feet, or a tape measure divided into feet and inches, or into feet and tenths and hundredths of a foot. 204. Square Measure is used in finding areas of surfaces, or of that which has length and breadth without thickness. Its Units of Measure, usually, are square surfaces, each of whose sides is a linear unit of the same name. 205. An Angle is the opening, or divergence, of two lines which meet. Thus, ANGLE B A B and A C meet at the point A, forming an angle A, or B A C. The lines A B and A C are called the sides of the angle. 206. When two lines meet so that the adjacent angles formed by them are equal, the angles are called Right Angles. And the lines are said to be perpendicular to each other. Thus, 207. A figure bounded by four straight anes, and having four right angles is called a Rectangle, and is said to have two dimensions, length and breadth. 208. If the sides are at the same time equal in length then the figure is called a Square. Thus, с The figure ABCD represents a Square. If each of the sides AB, BC, CD, and DA is a linear inch, then the square is a square inch; if each side is a linear foot, the square is a square foot; if each side is a linear yard, the square is a square yard; and in like manner we have a square rod, a square mile, &c.; and also a square link and a square chain. 209. Each square may be used to measure a surface, and the number of these squares that equal any surface is called the Measure of that surface. Thus, will call a square foot; hence there are 4 square feet in Fig. 2. Since Figure 1 contains 5 rows, each of which is in size to Fig. 2, there are 20 square feet in Fig. 1. It will be observed that this is the same result as would be found by multiplying the length and breadth of Fig. 1 together. We, therefore, conclude that 210. The Area of any right-angled four-sided figure will contain as many square units, as there are units in the product of the number of linear units of the same name in its length and breadth. We, therefore, readily see how the table of Square Measure is derived in great part from that of Long Measure. 211. Surveyors' Square Measure is used in obtaining the area or contents of land. The acre is the Unit of Measure. One sq. mi. is called a section, and 36 sections placed so as to form a square are called a township. This applies only to the new States which have been laid out by authority of the General Government. The older States are not regularly laid out, and hence their townships are not uniform in size and shape. A township is a division of a county made for convenience in holding elections. There must be at least one voting place in each township. |