UNITED STATES LAND SURVEYS

230. In 1802 Colonel Mansfield, the surveyor of the Northwest Territory, inaugurated the plan for surveying the public lands which is still in use. The general features of the plan were as follows: The entire public domain was first divided into parts called land districts. In each district a meridian line, called the principal meridian, was run through the entire district from North to South, and from some point on this meridian an East and West line was run which was called a base line. Parallel to the principal meridian, and to the base line, lines were run six miles apart, dividing the land into squares six miles on the side. These squares are called townships. A row of townships extending north and south is called a range.

The ranges are designated as east or west. Thus, in Figure 1 the range of townships marked a, b, c, d, e, is range 3, East. The range containing townships a', b', c', d', e', f', g', is range 5, West. The township marked c is township 3 North, range 3 East. The township marked e' is township 2 South, range 5 West.

Each township is divided into 36 square mile plots, called sections. They are numbered as shown in Figure 2, the section numbered 1 being the north-east corner of the township.

Section 14 in the township marked b' would be described as section 14, township 2 North, range 5 West. Added to this, there would be a designation giving the land district in which the section is located.

The land surveyed in this manner consists of nearly all the land now in the United States which did not belong to the thirteen States at the time of the Revolution, together with the lands which were later ceded to the United States by these original States.

A section of land is divided into smaller parts, as shown in the figure. Thus the piece marked S.E. of S.E. is called the south-east quarter of the south-east quarter.

PROBLEMS

N.E.

N.W.1 (North West! (North East Quarter) Quarter)

N. of S.W.

S.E. of

S.E.

1. Make a figure representing a township, and on it mark the following the S.E. of section 18; the West S.W. of the N.E. of section 9.

NW NW

N NE

y

X

of section 27; the

2. Describe the piece of land marked X in this figure. Also describe the piece marked y.

3. At $75 an acre, what is the value of the South of the N.E. of section 1 ?

4. At 40¢ a rod what is the cost of fencing in a section of land? A quarter section?

5. A piece of land 100 rods wide and 240 rods long is divided into four equal pieces by two fences running through it. At 50¢ a rod how much will it cost to fence the land, including the partition fences and the fences around it?

6. What fractional part of a section is the N.W. of the N.W. 1? If the whole section is worth $20,000, what is this part worth? At 45¢ a rod how much will it cost to fence in this part of the section?

7. If I own the S.W. of section 4, how many acres do I own? Make a diagram representing the section and showing the piece just described. Divide the rest of the section into one half section and eighths of a section.

8. Find the number of acres in each of the pieces shown on the figures in Example 1.

D

DRAWING TO SCALE

c

231. Definition of Scale. - Drawings are frequently made so that a certain unit of length such as one inch in the drawing will represent a definite distance, such as one foot, or 10 feet, or one mile in the object represented by the drawing. If one inch in the drawing represents 10 feet or 120 inches in the object, then the drawing is Isaid to be to the scale 1:120. This is read "scale one to one hundred twenty."

A

Scale 1": 10'

B

This scale is also written 1": 10', which is read "scale: 1 inch to 10 feet."

1

PROBLEMS

1. What are the dimensions of the room represented by this figure? 2. The top of a certain desk is 5 feet long and 3 feet wide. Make a drawing of the top of this desk to the scale 1:12.

3. Make a drawing of the same desk to the scale 1": 2′. Express this scale without using the words "inches " and "feet " in the statement.

4. What is the straight line distance from A to C in the room represented by the figure above?

5. Measure a room in the school building with care, and make a drawing to scale representing it. Enter the scale on the drawing.

6. Measure the dimensions of a room in your home, and make a drawing to scale representing it.

7. Determine the dimensions of a football field by measuring the drawing given on page 163 and then computing them. The points G H and E F mark the goal posts. Determine approximately the distance between each pair of goal posts,

8. Draw a football field to the scale 1": 30'.

9. Express the scale of Example 8 without using the words inches and feet.

Give the lengths of

10. Determine the dimensions of a tennis court by measuring the drawing given here and then computing them. the lines AB, BC, GO, FH, HI.

11. A baseball diamond is a square ninety feet on each side. The pitcher's box is in a straight line between first and third bases and also in a straight line between the home plate and second base. Draw a baseball diamond to the scale 1": 10'.

CHAPTER XVIII

PERCENTAGE

232. Percentage in Business. Next to the four fundamental operations, percentage is the most important subject in the arithmetic of business. Its manifold applications to business occupy nearly one half of this book.

233. Meaning of Per Cent. It has become customary to express a large number of fractions as hundredths, or per cents.

The words per cent are derived from the Latin words per and centum, meaning "in the hundred," or "hundredths."

The symbol for per cent is %.

234. Definition.- Percentage is the name used for calculations in which hundredths, or per cents, are used as the basis of comparison. 235. Base, Rate, Percentage. The principal numbers involved in percentage are the base, the rate, and the percentage.

The base is the number of which a certain number of per cents, or hundredths, are taken.

Thus, in "5% of 200 equals 10," 200 is the base.

The rate is the number of hundredths or per cents taken.

Thus, in "5% of 200 equals 10," 5 per cent is the rate.

The percentage is the result obtained by taking a certain per cent of a number. (Note the two different meanings of "percentage.”) Thus, in "5% of 200 equals 10," 10 is the percentage.

The amount is the base plus the percentage.

The difference is the base less the percentage.

Per cent has come into such general use that 5% means more to the average individual than the equivalent common fraction. We even use fractional per cents. Thus, we say that 3.2% of a certain sample of milk is butter fat, while we would never say that the milk contains butter fat.