Forming a new table and entering the balanced latitudes and departures with their proper signs, we have,

3

N 89° 05' E 125.50+ 1.96126 +125.49228 +138.03016 270.71303

Having entered the balanced latitudes and departures we seek for the most easterly or westerly station. We see at once that station 2 is the most westerly.

Assuming this for the principal station (see Art. 141), the double meridian distances will all be east, and consequently will be plus.

We then enter the departure of course 2 in the column of double meridian distances, and then calculate the double meridian distance of each course, according to the rule given in Art. 141.

Having done this we multiply each departure by the double meridian distance of its course and place the product in the column of plus or minus areas, according as the signs of the factors are like or unlike. We enter but five decimal places in the columns of areas. This will give the result with sufficient accuracy. We then add up the columns of area, take the difference of the two'sums, divide it by two and reduce the quotient to acres, roods and perches.

Ex, 5. Find the area of a piece of land of which the following are the field notes.

In this example station 2 is the most westerly and station 5 the most easterly point of the land.

6. Find the content of a piece of land from the following field notes.

In this example station 1 is the most easterly and station 4 the most westerly point of the land. If the meridian distances of the courses be calculated from the meridian passing through station 1 they will all be west: if from the meridian passing through 4, they will all be east.

Method of Surveying the Public Lands.

151. Soon after the organization of the present government, several of the states ceded to the United States large tracts of wild land, and these together with the lands since acquired by treaty and purchase, constitute what is called the public lands or public domain. Previous to the year 1802 these lands were parcelled out without reference to any general plan, in consequence of which the titles often conflicted with each other, and in many cases, several grants covered the same premises.

In the year 1802, the following method of surveying the public lands, was adopted by Colonel Jared Mansfield, then surveyor-general of the North-Western Territory.

152. The country to be surveyed is first divided by parallel meridians, six miles distant from each other; and then again, by a system of east and west lines, also six miles from each other. The whole country is thus divided into equal squares, which are called townships. Hence, each township is a square, six miles on a side, and contains 36 square miles.

The townships which lie along the same meridian, are called a range, and are numbered, to distinguish them from each other.

Each township is divided into equal squares, by meridians one mile apart, and by east and west lines at the same distance from each other. Hence, each township is divided into 36 square miles, each one of which is called a section. The sections of a township are numbered from 1 to 36, and each contains 640 acres.

The diagram exhibits the 36 sections of a township.

To describe a section accurately, we say, section number 5, in township number 4, in range 3d, west of a known meridian, the one, for example, drawn through the mouth of the Great Miami river. This description fixes precisely the place of the section. Go to the 3d range of townships, west of the known meridian, find township number 4 in this range, and lastly, section number 5 of that township. The corners of the sections should be marked by permanent corner-posts, or by lines blazed on trees.

The sections are divided into half sections, quarter sections, and even into eighths of sections. The following table shows

the content of a township, and its subdivisions.

1 township 36 sections=23040 acres.

=

1 section=640 acres.

section=320 acres.

section=160 acres.

section= 80 acres.

The principal meridians, and the principal east and west lines, have been established by astronomical observation, and the lines of subdivision run with the compass.

VARIATION OF THE NEEDLE.

153. The line indicated by the magnetic needle, when allowed to move freely about the point of support, and settle to a state of rest, has been called the magnetic meridian. This, in general, is a different line from the true meridian, which always passes through the poles of the earth, when sufficiently produced in both directions.

154. The angle which the magnetic meridian makes with the true meridian, at any place on the surface of the earth, is called the variation of the needle at that place, and is east or west, according as the north end of the needle lies on the east or west side of the true meridian.

155. The variation is different at different places, and even at the same place it does not remain constant for any length of time. The variation is ascertained by comparing the magnetic, with the true meridian.

156. The best practical method of determining the true meridian of a place, is by observing the north star. If this

produced, pierces the heavens, then, the intersection of the vertical plane passing through it and the place, with the surface of the earth, would be the true meridian. But, the star being at a distance from the pole, equal to 1° 34′ nearly, it performs a revolution about the pole in a circle, the polar distance of which is 1° 34': the time of revolution is 23 h. and 56 min.

To the eye of an observer, this star is continually in motion, and is due north but twice in 23 h. 56 min.; and is then said to be on the meridian. Now, when it departs from the meridian, it apparently moves east or west, for 5 h. and 59 min., and then returns to the meridian again. When at its greatest distance from the meridian, east or west, it is said to be at its greatest eastern or western elongation.

The following tables show the times of its greatest eastern and western elongations.

The eastern elongations are put down from the first of April to the first of October; and the western, from the first of October to the first of April; the time is computed from 12 at noon. The western elongations in the first case, and